MOORE AND MINER SERIES PRACTICAL BUSINESS ARITHMETIC BY JOHN H. MOORE AND GEORGE W. MINER REVISED BY GEORGE W. MINER GINN AND COMPANY BOSTON • NEW YORK • CHICAGO • LONDON yt <^\5 COPYRIGHT, 1906, BY JOHN H. MOORE and GEORGE W. MINER COPYRIGHT, 1915, BY GEORGE W. MINER ALL RIGHTS RESERVED 515.1 eOUCATION DEPT gfte gtftenaeum Bttea GINN AND COMPANY • PRO- PRIETORS • BOSTON • U.S.A. PREFACE The revised edition of the Practical Business Arithmetic retains those features of the first edition that are so highly commended by teachers ; namely, the development of each topic in such a manner as to make it practical and helpful to the student ; the presentation of each subject in a logical order; the selection of problems that appeal to the needs and the interest of the student, and of the community as well ; the omission of complex and useless problems ; a plan of grading and grouping problems which aids the student in acquiring facility and advancing his educational equipment; the elimination of subjects which have little or no connection with business interests and which have slight practical value ; the inclusion of an amount of work that will contribute to real efficiency ; the development of subjects inductively and the omission of set rules ; the unusual amount of oral work in the different chapters. The revised edition introduces the parcel post, the income tax, the postal savings bank, the computation of loss and gain on the selling price, tests on a time limit, a tariff schedule in accord- ance with the most recent legislative enactments, additional work on graphs, statistical matter based on the latest census, and an appendix on the varied uses of the adding machine. In the first edition the authors acknowledged their indebtedness to Dr. David Eugene Smith, Professor of Mathematics, Teachers College, Columbia University, New York, who read the complete manuscript and much of the proof, and kindly made numerous suggestions for the betterment of the book ; to Mr. George M. Clough of Somerville, Massachusetts, for the larger part of the material in the chapter on life insurance ; to Mr. George Abbot iii 541601 iv PRACTICAL BUSINESS ARITHMETIC of Brown Bros. & Co., Boston, and to Mr. H. T. Smith, Assist- ant Cashier of the Shawmut National Bank, Boston, for valuable assistance on the chapters on interest and banking. In the present edition the author is indebted to Mr. Wm. B. Medlicott, Lecturer on Property Insurance at Harvard University, for his work on the chapter on property insurance ; to Mr. Montgomery Rollins of Boston, author of " Money and Invest- ments," and to Mr. Harold T. Sibley of Chicago, for suggestions on the chapter on stocks and bonds ; to Mr. Alexander H. Sproul of the State Normal School, Salem, Massachusetts, and to Mr. C. D. McGregor of Des Moines, Iowa, for reading the manuscript as a whole, and for their cooperation in revising the text. (^ ^21 CONTENTS FUNDAMENTAL PROCESSES CHAPTER PAGE I. Introduction 1 II. Notation and Numeration 2 III. United States Money 8 IV. Addition • • • .10 V. Subtraction 31 VI. Multiplication 50 VII. Division 66 VIII. Average 85 IX. Checking Results 87 FRACTIONS X. Decimal Fractions 91 XI. Factors, Divisors, and Multiples 113 XII. Common Fractions 119 XIII. Aliquot Parts 158 XIV. Bills and Accounts 170 DENOMINATE NUMBERS XV. Denominate Quantities 191 XVI. Practical Measurements 201 PERCENTAGE AND ITS APPLICATIONS XVIL Percentage .231 XVIII. Commercial Discounts 246 XIX. Gain and Loss 256 XX. Marking Goods 264 XXI. Commission and Brokerage 270 V vi PEACTIOAL BUSINESS ARITHMETIC CHAPTER PAGE XXIL Property Insurance 277 XXIII. State and Local Taxes . . • . . . . 286 XXIV. Customs Duties 291 INTEREST AND BANKING XXV. Interest 300 XXVI. Bank Discount . . . . . . . .326 XXVII. Partial Payments 338 XXVIII. Bankers' Daily Balances 346 XXIX. Savings-bank Accounts . . . . . . 349 XXX. Exchange 354 EQUATIONS AND CASH BALANCE XXXI. Equation of Accounts 384 XXXIL Cash Balance 393 DIVIDENDS AND INVESTMENTS XXXIIL Stocks and Bonds 396 XXXIV. Life Insurance • . 420 PARTITIVE PROPORTION, PARTNERSHIP, AND STORAGE XXXV. Partitive Proportion and Partnership . . . 426 XXXVL Storage 443 APPENDIX A Adding Machines ......... 449 APPENDIX B Tables of Measures and Business Abbreviations . . 451 INDEX 457 PRACTICAL BUSINESS ARITHMETIC PRACTICAL BUSINESS ARITHMETIC FUNDAMENTAL PROCESSES CHAPTER I INTRODUCTION 1. The student who is prepared to study business arithmetic must be famihar with the ordinary symbols used in the state- ment or the sokition of problems; he must have the ability to read and to write numbers with facility; he must know the fundamentals, and he must be able to perform ordinary opera- tions in United States money, and in both common and decimal fractions. 2. In this course in business arithmetic one learns many simple methods for handling numbers and solving problems, and the adaptation of arithmetic to important business operations ; he also acquires skill, rapidity, and accuracy, and he learns how to prove his own work, thus developing self-reliance. Because arithmetic deals with the problems of the home as well as the business office, the study of its practical and everyday features increases one's knowledge of the usages, the phraseology, and the literature of business and commerce. 3. Much attention is given, in the text, to the fundamental processes, for these are at the foundation of all arithmetic. One must acquire a high degree of accuracy and speed in the hand- ling of these fundamentals if he is to achieve any marked degree of success in his subsequent work. The text contains an unusual amount of material for the student's work, and portions of it may be omitted, at the discretion of the instructor, if the advancement of the class warrants it. 1 CHAPTER II NOTATION AND NUMERATION ORAL EXERCISE 1. How many different figures are used to express numbers ? 2. What is the meaning of the syllable teen in the numbers from 13 to 19 inclusive ? 3. What is the meaning of the syllable ty in such numbers as 20, 30, 40, 45, 75, 87, 96 ? 4. What name is given to 10 tens? to 10 hundreds? to 1000 thousands? to 1000 millions? 5. In 7, 70, 700, 7000, and 70,000 how does the 7 change in value ? In 7007 how do the values of the 7's compare? 6. What is the value of the cipher in any number ? Why is it used ? Explain the use of the ciphers in 900,905. 7. Upon what two things does the value of a figure depend ? Illustrate your answer, using the number 121,000,121. 8. Mention five things that are counted in thousands ; three things that are counted in millions ; two things that are counted in billions. Can you think of any use for trillions ? 9. Read aloud the following : a. During a smgle year the coinage department of the United States government received from the superintendent 1,193,100 standard ounces of gold coin, from which was produced standard ounces of coin of the value of S6, 369, 090. During the same period the coiner also received 9,189,533 standard ounces of silver for coinage. h. In the United States Bureau of Engraving and Printing there are printed yearly about 70,000,000 sheets of United States notes, certificates of deposit, bonds, and national cur- rency to the amount of about S500, 000,000. In addition to this there are printed more than 10,000,000,000 postage stamps. 2 NOTATION AND NUMERATION THE ARABIC SYSTEM 4. This is the common system of notation. It is generally called the Arabic system because the numerals which it employs were introduced into Europe by the Arabs. The Arabic numerals 1, 2, 3, and so on to 9 originated in India about 2000 years ago. When only these numerals were used, the system proved to be cum- bersome, and all mathematical operations involved great difficulty. About 1200 years ago the cipher was added, thus making a system sufficiently ample and simple for ordinary purposes of analysis and investigation. The Arabs introduced the system into Europe in the twelfth century, but it was not until about 300 years later that it displaced the clumsy Roman system. 5. The distinctive feature of the Arabic system is the place value of the numerals employed. The value of an Arabic numeral depends as much upon its place in the number as upon its simple or digit value. Thus, in the Roman system, VIl = 5 + 1 + 1. In the Arabic system, 511 = 5 hundreds + 1 ^en + 1. 5 has not only the unit value Jive, but also the place value hundreds; and the 1 following has not only the unit value one, but also the place value ten, 6. The successive places a figure may occupy in a number are called orders of units. 7. Orders of units increase from right to left and decrease from left to right in a tenfold ratio. Therefore, 8. The Arabic system of notation is properly called a decimal system, from the Latin decern,, meaning ten. 9. A comma (separatrix) or a greater space than that between other figures may be used to separate a number into periods. Thus, twenty-five thousand four hundred twenty-one may be written 25,421 or 25 421. ORAL EXERCISE Read aloud the following numbers : 1. 92,482. 3. 375,214. 5. 8 217 000 214. 2. 77,009. 4. 278,900. 6. 7 000 421817. 4 PEACTICAL BUSINESS ARITHMETIC 10. For convenience in reading, the successive orders of units are divided into groups of three figures each, called periods. The first four periods are shown in the following numeration table. The number used for illustration is sixty-seven billion, four hundred twenty-one million, five thousand, two hundred sixteen, and seven hundred fifty-one thousandths. Numeration Table Periods : Billions Millions Tliousands Units Thousandths 2 ' £ 2 ** Orders: ,«!»'^„,!» '^r/>"» -o^w S rt a -s ^S=3 sja 3530 ssa £ WHP WHt:) WHti ffiHt:) Q 6 7, 42 1, 00 5, 216 . 751 11. In reading integers do not use the word and. In deci- mal fractions and has an office to perform, but if it is used in reading integers, misunderstandings may occur. Thus, 400.011 is read four hundred and eleven thousandths ; but .411 is read four hundred eleven thousandths ; and 411. is read four hundred eleven. WRITTEN EXERCISE Write in figures the followiyig : 1. Six million, six thousand, five. 2. Seven hundred fifty-three billion. 3. Four million, one hundred twenty-five. 4. Three hundred twenty-one million, six. 5. Three million four dollars and five cents. 6. Ten billion, one thousand, one hundred three. 7. Twenty-seven and one hundred twenty-five thousandths. 8. Sixty-two thousand and four hundred twenty-five thou- sandths. 9. Three million four hundred twenty thousand one dollars and fifteen cents. NOTATION AND NUMERATION 5 12. Integers should be read in the shortest way possible. Thus, 1946 should be read nineteen hundred forty-six, not one thousand nine hundred forty-six. The space for writing the amount on a check, tJ^irst >^atLonal Mank ^ay to the order o / O^ ^ , >^^^i^^^:-^^-:^^..^>/ /^^(^"^ T^^C^^^^^^yQv^Cd^t^^^^^^^ note, or other business paper is generally limited to one line, and it is im- portant that the amount be expressed in the fewest words possible. ORAL EXERCISE Head aloud the following : 1. Rhode Island has an area of 1250 sq. mi., and contains 800,000 A.; Ohio has an area of 41,060 sq. mi., and contains 26,278,400 A. ; California has an area of 153,360 sq. mi., and contains 101,350,400 A.; Texas has an area of 265,780 sq. mi., and contains 170,099,200 A. 2. Lake Itasca, the source of the Mississippi River, is situated approximately 3160 mi. from the sea; it is 1575 ft. above sea level. The Mississippi River is navigable for a distance of about 2200 mi. ; the area drained by this river and its tributaries is estimated at 1,244,000 sq. mi. 3. The area of the United States is approximately 3,025,600 sq. mi. ; of Alaska, 570,000 sq. mi. ; of Russia in Europe, includ- ing Poland, 2,060,940 sq. mi. ; of Switzerland, 15,792 sq. mi.- 4. The area of Africa is estimated at 11,500,000 sq. mi. ; the coast line approximates 16,000 mi. in length ; the Sahara Desert has an area of 2,000,000 sq. mi. The greatest length of Asia is about 7500 mi., and its greatest breadth Is about 5160 mi. 6 PEACTICAL BUSINESS ARITHMETIC THE ROMAN SYSTEM ORAL EXERCISE 1. Make a list of the Roman numerals used in the headings marking the divisions of this book, and read the list so prepared. 2. What symbol ordinarily appears on a watch face for four? 13. This system of writing numbers is called Roman notation because it was first used by the Romans. It is now rarely used except for numbering books and their parts, for writing inscriptions on buildings, and for marking the hours on the dials of clocks and watches. It employs seven capital letters : I V X L C D M 1 5 10 50 100 500 1000 14. Other numbers are expressed by a combination of these letters on the general principle that A combination of letters arranged from left to right m the order of value is equal to the sum of the constituent letters. 15. But the use of the same letter four or more times is avoided by employing the sub-principle- that When one letter precedes another of greater value the value of the two is that of their difference. Thus, II = 2 ; Vni = 8 ; and CCC = 300. But IV or IIH = 4 ; XL = 40; XC =90; and CD = 400. ORAL EXERCISE 1. Multiply twenty -seven by itself in Roman numerals. 2. Why is the Arabic system better than the Roman system ? 3. Read the following inscription: MDCCCXLVIII — Charlestown High School — MOM VI. Nineteen hundred was formerly written MDCCCC, but it is now often written MCM. 4. Read the following numbers of chapters in a book : XXIX, XXXVIII, LXIX, LII, LXVII, LXXVI, LXXIX, CLIII. 5. Read the following numbers of years : MDCCXCV, MCMVII, MDCCLXXVI, MCMIX, MDCCCXCVIII. NOTATION AND NUMERATION 7 WRITTEN EXfeRCISE 1. Write in the Roman system : 19, 88, 99, 124, 1907, 1910. 2. Write the largest possible number using the six follow- ing numerals : 1, 0, 8, 0, 9, 5. 3. Write in Arabic numerals the following number : five billion, two hundred seventeen million, two hundred ten thou- sand, and fifteen thousandths. 4. Write in the Roman system the following historical years : the discovery of America ; the landing of the Pilgrim Fathers at Plymouth ; the declaration of independence. 5. Write in Arabic numerals the number in problem 3 increased by two hundred seventy-one and four hundred fifteen thousandths ; diminished by two thousand, four hundred sixty, and eleven thousandths. 16. A unit is a standard quantity by which other quantities of the same kind are measured. The simplest form of a unit is a single entire thing by which other simi- lar things can be measured by integral enumeration. Thus, the unit of dis- tance is an inch; a group of 12 in. taken in succession is a foot; 3 ft. is a yard ; and so on. 17. Numbers that have units of the same kind are called like numbers. Thus, ^12 and $15, and 8 hr. and 3 hr., are like numbers. ORAL EXERCISE Name the unit in each of the folloudng : 1. ' A barrel of sugar sold by the pound. 2. A car load of apples bought by the barrel. 3. A car load of lumber sold by the thousand feet. 4. Sixty-four thousand bricks sold by the thousand. 5. Forty and one-half yards of carpet sold by the yard. 6. Twenty-five hundred pounds of beef bought by the hundredweight. 7. When the value in a five-dollar gold piece' is thought of, what is the unit ? CHAPTER III UNITED STATES MONEY ORAL EXERCISE Read the following expressions^ supplying the missing word o words : 1. The denominations of United States money used in busi ness are dollars, , and , 2. mills or cents equal one dollar. 3. The is not a coin, but it is sometimes used in mat ing calculations. 4. The first two figures at the right of dollars denote and the third figure denotes . 5. The two figures denoting cents express of a dollar the figure denoting mills expresses of a dollar. 6. One thousandth of a dollar is mill ; seven mills ar of a dollar. 7. Fifteen hundredths of a dollar are ; nine tenth of a dollar are nine — — or cents. 8. $25 = ^; 3700^ = 1 ; f 1T.85 = ^; 4925 = $ ; 179 = 1 9. State a short method of reducing dollars to cents ; dol lars and cents to cents ; cents to dollars. 18. The following kinds of currency are in daily use in tb United States at the present time : gold coins ; silver dollars subsidiary coins (small change) ; gold certificates ; silver cer tificates ; United States notes ; United States Federal Reservi notes ; National Bank notes. The coins now issued by the United States government are as follows 1. The gold double eagle, eagle, half eagle, and quarter eagle. 2. The silver half dollar, quarter dollar, and dime. 3. The nickel five-cent piece and the bronze one-cent piece. UNITED STATES MONEY 9 19. Gold or silver in bars or ingots is called bullion. The paper money of the United States is at present as follows : 1. Gold certijicates, issued for gold deposited in the U. S. Treasury. 2. Silver certificates^ issued for silver deposited in the U. S. Treasury. 3. United States notes {greenbacks), promises of the government to pay to the holder on demand a definite number of gold or silver dollars. 4. National hank notes, issued by national banks under the supervision of the National Government. 5. Treasury notes, which were issued for silver bullion deposited in the U. S. Treasury. These notes are not now issued. 6. United States Federal Reserve notes. ORAL EXERCISE 1. What is meant by money ^ currency^ legal tender? In such exercises as the above the student should not try to repeat defini- tions, but should explain the terms in his own way. 2. Name the gold coins of the United States; the silver coins ; the paper money ; give the value of each of the gold coins. 3. Read in three ways : $4.8665; $25,871; $178,475. 4. Name the largest gold and silver coins that will exactly express each of the following amounts : $27.90; $28.20; $75.80. 20. When it is desirable to express United States money in written words, the cents should be written in fractional form, as in the following note : $ / ^J 'rP ^^^ New yovkf (l^^^^j^^^/^^ 1 9. x:^^^^^x^^g^.^^<.<:^^ after date ^>^ the order of '^~X/?^^^^t^i^^^^ ArSl^^^:^..^^,^^^ a t ■^r^k^.^^^L^^^J^J-^?-^.^^^^':^^^ Value received No. ^^ Due^ ^^r.V,/^ -r^ /7^. r^^^^^^^rCi^ CHAPTER IV ADDITION ORAL EXERCISE 1. Find the sum of 1, 2, 3, 7, 5, 9, 4, 8, and 6. 2. Read each of the numbers m problem 1 increased by 2 ; by 5 ; by 3; by 7 ; by 8 ; by 9 ; by 17; by 23. 3.. Find the sum of 8, 7, 9, 5, 6, 11, and 12. 4. Read each of the numbers in problem 3 increased by 12; by 15 ; by 18; by 24; by 42; by 19; by 16. 5. Illustrate what is meant by like numbers. 21. Only like numbers can he added. 22. To secure speed and accuracy in addition name results only and express these in the fewest words possible. Thus, in adding 2, 4, 7, 8, 3, 2, and 8 say 6, 13, 21, 4, 6, 34; do not say 2 and 4 are 6 and 7 are 13 and 8 are 21 and 3 are 24 and 2 are 26 and 8 are 34' ORAL EXERCISE Name the sum in ( jacA of the followiyig problems : 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15 3 2 2 8 1 5 8 1 3 5 5 1 3 4 2 2 1 4 2 3 2 2 3 3 14 7 2 5 7 1 6 3 1 6 1 3 6 4 6 4 2 1 2 3 2 8 2 2 4 3 7 4 2 2 3 7 5 8 5 8 4 1 3 4 4 4 9 8 7 2 3 2 6 4 4 8 4 4 3 7 7 5 3 3 1 4 8 4 2 5 6 3 5 2 2 3 8 6 2 5 2 5 1 6 6 2 3 1 4 2 2 5 7 2 6 3 4 3 8 1 7 7 6 1 1 1 1 7 7 1 2 3 3 6 2 2 4 2 2 4 3 4 2 1 1 1 2 2 2 3 5 1 8 3 2 2 3 1 3 8 6 2 4 1 5 1 2 3 2 4 12 4 4 9 8 7 10 ADDITION 11 23. Addition is the basis of all mathematical processes. It constitutes a large part of all the computations of business life and concerns, to some extent, every citizen of to-day. Ability to add rapidly and accurately is therefore a valuable accomplishment. 24. Rapid addition depends mainly upon the ability to group ; that is, to instantly combine two or more figures into a single number. In reading it is never necessary to stop to name the individual letters in the Avords. All the letters of a word are taken in at a glance ; hence the whole word is known at sight. Words are then grouped in rapid succession and a whole line is practically read at a glance. This is just the principle upon which rapid addition depends. PVom two to four figures should be read at sight as a single number, and the group so formed should be rapidly combined with other groups until the result of any given column is determined. This can be done only by intelligent, persistent practice. 25. The following list contains all possible groups of two figures each. ORAL EXERCISE Pronounce at sight the sum of each of the following groups : abcdefghijklmno 1. 112241334 3 14247 1 3 1 2 1 5 2 3 2 6 7 3 5 6 7 2. 8 9 8 5 6 4 5 5 7 1 5 6 6 8 9 9 9 8 5* 1 4 3 4 2 8 6 6 9 6 1 3. 8 7 7 4 9 7 6 7 5 3 2 4 5 7 6 2 3 5 8 3 8 7 9 9 8 9 9 8 4 2 The above exercise may be copied on the board and each student in turn required to name the results from left to right, from right to left, from top to bottom, and from bottom to top. The drill should be continued until the sums can be named at the rate of 150 per minute. This is the first and most important step in grouping. 12 PRACTICAL BUSINESS ARITHMETIC ORAL EXERCISE Name the sum in each of the following problems : 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15 6 7 3 5 6 7 9 9 9 1 2 5 8 2 8 3 1 4 2 4 7 9 8 8 4 7 2 3 7 2 8 7 7 5 8 2 5 9 4 5 8 3 5 4 1 7 9 6 9 3 9 8 4 7 1 1 7 9 5 9 3 8 5 3 8 1 6 4 9 2 6 5 7 3 4 9 4 7 7 2 9 8 5 1 3 5 7 6 5 5 5 6 6 8 2 4 4 3 6 3 6 8 7 4 6 5 6 5 5 7 5 4 2 1 3 6 4 9 4 8 2 3 2 1 1 2 3 1 1 2 5 3 8 1 9 4 3 3 1 4 2- 1 5 6 4 5 9 7 6 6 Name tlie results only and make groups of two figures each. Thus, in problem 1, beginning at the bottom and adding up, say 6, 16, 28, 43, 52. 16-45. Add the numbers in the exercise on page 10 by groups of two figures each. 26. It is practically as easy to add 54 and 9, 59 and 6, etc., as it is 4 and 9, 9 and 6, etc. 4 and 9 are always equal to 1 ten and 3 units, and 9 and 6 to 1 ten and 5 units. Hence in adding 54 and 9 think of the tens as increased by 1, call the units 3, and the result is 63 ; in adding 59 and 6 think of the tens as 6, the units as 5, and the result as QS, ORAL EXERCISE Pronounce at sight the sum of each of the following groups : 1. 27 48 59 77 58 52 59 75 95 84 39 59 84 76 91 7 8 6 8 7 8 8 6 9 7 _6 5 9 8 8 2. 75 59 77 88 74 23 24 44 89 78 67 37 BQ 58 68 8 9 9 5 6 8 9 9 9 9 9 7 7 4 5 3. 37 49 38 37 45 95 98 87 54 72 63 42 73 97 88 5 8 7 6 9 8 7 7 9 9 8 9 8 5 _9 ADDITION 13 27. In combining numbers between 10 and 20 think of them as one ten and a certain number of units and not as a certain number of units and 1 ten. Thus, in combining 17 and 18 think of 28 and 7, or 35; in combining 19 and 15 think of 29 and 5, or 34 ; and so on. ORAL EXERCISE Pronounce at sight the sum of each of the following groups : abode fghi jklmno 1. 12 17 12 16 11 12 18 16 17 11 19 13 18 12 17 l^lll^l^lllll^l^l^ — 1^ — 3^5ti — 2.13 11 15 19 14 19 17 15 13 19 16 14 18 18 12 l^lj6]^U151^1^1^ni^U14111519 3. 11 17 12 17 15 15 12 18 16 14 19 14 19 17 11 nui^i^ni5n]^]^i3i^i^i^iii5 The above exercise contains all combinations possible with the numbers from 11 to 19 inclusive. Drill on the exercise should be continued until re- sults can be named at the rate of 120 per minute. 28. Numbers between 10 and 20 may be combined with num- bers above 20 in practically the same manner as in § 27 Thus, in adding 62 and 12 think of 72 and 2, or 74; in adding 79 and 17 think of 89 and 7, or 96. ORAL EXERCISE Pronounce at sight the sum of each of the following groups: 1. 25 48 59 87 91 75 86 75 48 78 57 89 37 56 75 17 17 16U1^1^1^1216131614171814 2.29 47 83 92 36 54 59 78 67 92 77 86 53 78 85 13 14 19 14 19 13 18 15 13 13 19 19 17 14 14 3. 31 32 45 69 74 95 98 92 96 87 86 34 43 64 38 19 17 19 15 8 18 14 19 15 17 19 18 18 19 17 14 PRACTICAL BUSINESS ARITHMETIC ORAL EXERCISE 1. Count by 7's from 1 to 85. Solution. 8, 15, 22, 9, 36, 43, 50, 7, 64, 71, 8, 85. Count hy : 2. 2's from 39 to 55. 14. 8's from 10 to 138. 3. 5's from 11 to 86. 15. 7's from 19 to 152. 4. 6's from 15 to 63. 16. 6's from 20 to 128. 5. 5's from 2 to 107. 17. 6's from 15 to 111. 6. 7's from 11 to 60. 18. 9's from 12 to 102. 7. 8's from 25 to 89. 19. 8's from 17 to 113. 8. 9's from 31 to 112. 20. 7's from 24 to 108. 9. 8's from 32 to 192. 21. 6's from 27 to 117. 10. 7's from 18 to 102. 22. 4's from 19 to 183. 11. 6's from 72 to 126. 23. ll's from 14 to 102. 12. 9's from 10 to 136. 24. 12's from 17 to 161. 13. 9's from 17 to 152. 25. 13's from 17 to 121. 26. Beginning at 1 count by 4's to 17 ; going on from 17 count by 7's to 52 ; from 52 count by 9's to 133 ; from 133 count by 5's to 158 ; from 158 count by 12's to 206 ; from 206 count by 13's to 271. This exercise furnishes one of the best possible drills in addition, and it should be continued until the successive results can be named at the rate of 150 per minute. 29. If the student is accurate and rapid in making groups of two figures each, he is ready for practice in groups of three figures each. In the following exercise are all the possible groups of three figures each. ORAL EXERCISE Name at sight the sum of each of the following groups: 4, 2, and 3 should be thought of as 9 just as p-e-n is thought of as pen. 1. 419811318145178 131223173314414 332175 6 31941641 ADDITION^ 15 2. 1 6 1 4 1 2 1 1 1 1 7 6 9 8 1 4 1 2 1 2 2 9 1 1 6 6 6 5 5 5 9 2 5 2 3 1 1 8 7 8 1 1 1 1 7 3. 6 5 2 5 2 3 9 2 2 2 2 6 1 1 2 1 1 3 3 3 2 2 8 7 6 5 1 1 1 2 5 5 6 2 4 3 2 2 2 2 2 1 5 4 4 4. 3 2 1 2 2 6 2 6 5 5 7 1 1 1 1 2 2 1 7 6 8 6 2 2 2 2 1 1 6 9 2 2 3 7 9 2 7 6 9 8 5 2 1 9 9 5. 9 8 9 8 7 3 4 5 6 6 5 4 3 3 4 1 1 1 1 1 5 8 7 7 7 5 4 4 4 4 8 8 7 7 7 5 4 9 8 6 7 9 8 6 6. 5 6 6 9 5 7 3 4 9 6 6 8 3 3 3 5 7 6 4 4 3 4 4 4 8 7 4 9 4 4 5 7 9 9 4 4 6 4 8 6 6 8 9 5 4 7. 3 4 6 9 8 5 4 3 3 2 3 3 4 5 8 8 7 6 9 9 9 7 8 3 5 3 7 7 8 8 9 9 6 9 9 9 8 8 9 6 8 9 7 9 8 8. 8 5 4 3 3 5 2 3 3 4 5 7 7 5 4 8 8 9 8 7 2 4 3 7 6 7 9 8 7 6 9 5 6 7 3 5 9 6 7 8 9 9 9 8 7 9. 3 3 2 2 3 3 4 5 7 9 9 9 7 3 6 6 3 4 4 3 6 6 7 8 7 6 5 6 3 4 9 5 8 7 4 8 6 7 8 7 5 4 3 3 2 10. 2 2 3 4 5 7 2 2 3 4 5 7 9 ■6 6 4 9 6 5 6 7 4 8 5 5 6 7 9 6 5 5 9 6 8 8 8 4 9 9 7 7 7 6 5 4 11. 8 8 9 2 2 3 4 5 6 8 8 9 6 8 7 5 8 3 3 7 5 5 5 8 8 5 4 5 7 3 3 2 2 8 9 7 5 9 9 6 5 4 3 2 2 This exercise should be drilled upon until the sums of the groups, in any order, can be named at the rate of 120 per minute. 16 PRACTICAL BUSINESS ARITHMETIC ORAL EXERCISE 1-15. Turn to the exercise on page 10 and find the sum of the numbers given. Name results only, and make groups of three figures each. Thus, in problem 1, say 9, 23, 37, 43. Add from the bottom ujd and check the work by adding from the top down. Find the sum in each of the following problems : 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 131422244 5 12954 113331639574073 1 1 4 1 5 2 2 4 5 2 4 1 2 1 2 1 3 1 3 1 4 1 8 8 9 2 8 1 2 4 1 4 6 4 5 8 3 2 3 6 2 2 3 8 1 1 2 1 7 1 1 5 2 5 8 2 4 2 2 2 2 2 3 8 3 5 7 2 6 1 5 2 1 4 5 3 7 6 2 7 3 7 2 6 6 1 2 9 4 3 2 3 1 8 2 2 1 6 7 5 1 8 3 4 2 1 2 9 9 6 7 2 3 3 3 5 2 3 3 6 9 3 3 1 2 ^ 8 2 6 3 1 3 1 3 3 1 5 6 3 7 4 1 1 3 2 7 2 4 3 2 8 8 4 7 2 5 9 5 4 2 5 2 4 8 5 1 2 3 3 2 3 2 2 4 1 4 4 3 2 2 4 3 5 2 1 1 2 1 2 6 6 4 4 6 6 3 6 2 5 8 8 6 2 3 3 3 5 2 4 4 3 3 2 8 2 1 2 6 5 1 1 1 3 5 6 1 6 2 1 4 4 1 3 7 2 9 3 7 9 1 5 7 5 7 3 5 2 2 2 6 2 2 3 1 7 3 3 7 2 4 2 5 6 1 3 1 3 3 2 2 1 3 1 4 2 1 2 1 2 2 7 7 7 1 1 9 2 2 9 7 2 2 3 8 3 1 2 3 9 1 2 5 2 1 3 4 4 4 1 7 7 1 8 4 8 4 2 1 3 7 3 2 5 7 6 5 5 2 4 4 3 1 6 2 1 5 5 3 2 3 2 8 1 3 6 3 2 3 1 1 2 1 1 2 1 2 1 5 7 1 1 ADDITION 17 30. It is always an advantage to find groups of figures aggre- gating 10 and 20 in the body of a column. These groups should be added immediately to the sum already obtained by simply combining the tens of the two numbers. It is not a good plan, however, to take the digits in irregular order in order to form groups of 10 and 20. ORAL EXERCISE Find the sum in each of the following problems^ taking advan- tage of groups of 10 and 20 wherever possible: 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 525343 7 8 259 554325 54 789 56785 56 321 79874 02 58 1 24312369 7 525 2. 11 21 71 6 9j 8j 3j 4 71 41 51 1 8 3J 6J 5j 9 2 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 3J 8 6 5 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41. 42. 43. 44. 45. 6 6 7 7 7 8 9 7 2 7 6 8 9 7 9 9 4 9 2 9 46. 47. 48. 49. 50. 51. 52. 53. 54. 55. 56. 57. 58. 59. 60. 38 42 25 35 46 14 21 12 18 29 57 17 13 14 15 5 5 4 7 6 8 8 9 8 4 5 5 6 2 7 6 7 2 8 5 8 2 3 6 18 PRACTICAL BUSINESS ARITHMETIC 31. When three figures are in consecutive order the sum may- be found by multiplying the middle figure by 3 ; when five figures are in consecutive order the sum may be found by mul- tiplying the middle figure by 5 ; etc. ; or the sum of any num- ber of consecutive numbers may be found by taking one half the sum of the first and last numbers and multiplying it by the number of terms. ORAL EXERCISE By inspection find the sum of: 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 8 11 14 17 20 23 26 29 32 35 38 41 44 47 50 91215182124273033363942454851 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 11 16 21 26 31 36 41 46 51 56 61 66 71 76 81 12 17 22 27 32 37 42 47 52 57 62 67 72 77 82 13 18 23 28 33 38 43 48 53 58 63 68 73 78 83 1419242934394449 54 59 64697479 84 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41. 42. 43. 44. 45. 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 8 11 14 17 20 23 26 29 32 35 38 41 44 47 50 9 12 15 18 21 24 27 30 33 36 39 42 45 48 51 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 11 14 17 20 23 26 29 32 35 38 41 44 47 50 53 12 15 18 21 24 27 30 33 36 39 42 45 48 51 54 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 14 17 20 23 26 29 32 35 38 41 44 47 50 53 56 15 18 21 24 27 30 33 36 39 42 45 48 51 54 57 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 17 20 23 26 29 32 35 38 41 44 47 50 53 56 59 32. When a figure is repeated several times the sum may be found by multiplication. ADDITION 19 ORAL EXERCISE By inspection find the sum of: 1. 2 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 4 3 4 5 3 7 8 8 15 6 7 8 15 13 9 9 7 4 5 3 7 5 7 15 6 8 7 14 13 8 9 8 4 5 9 7 5 9 15 12 7 8 15 13 8 9 8 9 5 9 8 6 9 8 12 7 7 14 7 9 9 8 9 9 8 8 6 9 8 12 7 8 15 rr 8 16 . 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 3 7 4 2 7 5 12 2 4 6 8 9 8 5 16 3 7 4 2 7 5 5 2 4 6 8 9 8 5 16 3 7 4 2 4 5 5 2 4 6 8 9 8 5 16 2 2 7 8 4 4 5 3 5 4 3 5 8 5 16 2 2 7 -8 2 4 5 3 5 4 3 5 8 5 20 2 2 7 8 2 4 5 3 5 4 3 5 9 8 1 33. In all written work make plain, legible figures of a uniform size, write them equal distances from each other, and be sure that the units of the same order stand in the same vertical column. / Z ^ ^ cr ^ y ^ f ^ 34. Many of the errors that occur in business are in simple addition. Errors in addition result from two main causes : irregularity in the placing of figures ; poor figures. 35. In business it is important that figures be made rapidly ; but rapidity should never be secured at the expense of legibility. WRITTEN EXERCISE Co'py and find the sum of: 1. 2. 3. 4. 5. 6. 1745 1842 1249 4271 6229 1481 1862 1695 1810 8614 4813 1862 7529 4716 6241 9217 7142 4129 8721 8412 1728 8214 6212 2412 20 PKACTICAL BUSINESS ARITHMETIC 7. 8. 9. 10. 11. 12. 4216 2110 4142 1061 4113 4112 8912 8420 4347 1875 8217 1012 4729 1641 1012 6214 8614 1862 8624 1722 1816 1931 1692 1721 4829 1837 4112 1648 1591 1692 6212 4216 4210 1721 1686 1486 4110 4117 1618 1728 2172 4112 4210 1832 4060 1421 1754 1010 36. The simplest way to check addition is to add the columns in reverse order. If the results obtained by both processes agree, the work may be assumed to be correct. 37. In adding long columns of figures it is generally advis- able to record the entire sum of each column separately ; then if interruptions occur, it will not be necessary to re-add any por- tions already completed. After the total of each column has been found the entire total may be determined by combining the separate totals of the columns. 38. The best way to test the accuracy of columns added in this manner is to begin at the left and repeat the addition in reverse order. The entire total of each column should again be written and the complete total of the problem found by adding the sepa- rate totals of the several columns. If the results obtained by the two processes agree, the work may be assumed to be correct. 39. Example. Find the sum of 54,669, 15,218, 36,425, 45,325, and 68,619. Check the result. Solution. Beginning at the bottom of the right-hand column, add each column in regu- lar order and write the entire totals as shown in (a). Beginning at the top of the left- hand column again add each column and write the entire totals as shown ih (6). Next add the totals obtained by the first and second additions and compare the results. Since the total shown by (a) is equal to the total shown by (6), the result, 220,256, is assumed to be correct addition should be carefully checked. (^) 54669 («) 19 15218 36 28 36425 12 21 45325 21 12 68619 28 36 220256 19 220256 220256 med to be correct. All work in ADDITION 21 WRITTEN EXERCISE See how many times the following numbers can be written in one minute. Write each number in form for vertical addition. 1. 426579. 3. i)7983.21. 5. 170812.34. 2. 123987. 4. $4080.91. 6. ^^41182.50. Thus, in repeating the number in problem 1 write it as follows ; ^/ z ^ ^ 7 ^ A^ Z d ^ 7 f A^ Z ^ ^ 7 ^ ^ Z (^ S- 7 f 0^?^. Be sure that the spacing between the lines and between the columns is uniform. Increase the speed gradually until from 150 to 200 figures can be written per minute. 40. Skill in writing figures from dictation should be culti- vated. The dictation should be slow at first, but it should be gradually increased until the requisite speed is acquired. 41. In calling off numbers to another great care should be taken in order that no errors may be made. In reading United States money the word dollars should be called with each amount. The word cents may be omitted in all cases except where there are no dollars. Thus, in calling $400.37 say /owr hundred dollars, thirty-seven; in calling $25.11 say ticentj/- five dollars, eleven; in calling $1573.86 say ffteen hundred seventy-three dollars, eighty-six; in calling $5.31 say Jive dollars, thirty-one. WRITTEN EXERCISE Write from dictation and find the sum of: 1. $75.18, 1123.95, $147.25, $9.50, $181.45, $172.16, $84.98, $314.95, $49.10, $69.90, $312.60, $415.90. 2. $3140.19, $310.92, $3164.96, $3162.19, $18.62, $410.95, $690.18, $10.75, $3100.40, $300.40, $200.50, $100.90, $410.80, $100.85, $310.60, $80.90, $399.80, $412.60. 22 PEACTICAL BUSINESS ARITHMETIC WRITTEN EXERCISE Co'py^ find the sum., and check : 1. 2. 3. .^/ C^Z^ C^.Z/ "^i^ Z^Zf^jTA^.^ Z !^Z /^/ 6 Z /.^// /J^jrCyr.^^ / ZJ- f ^/ ^.^^ / 2 (^ Z/ V/.Cy 3yf^Z(if./y Z/ y ^Z^J.^z^ Z/3 /A^yZ.c^3 ^yZ/z3^.z3 f / 3 / ^z C.6?^ /^(^ z / ^/.izy A^z/ z 1^ / z.^j- / zj-y z/ z.^^ fC^ry (^r.^3 / ZA^f Z / Z.^4^ / 3 Z / C^Z./ y / Z^Zz^y z.A^Z y zrzf /^A^.y (> Z/ z^ / C> z /.^^ yr^r63r.^r z/yyz/6.^zz 3 /^/ z^f.cp ^ z/A^/Z(iz.^f li yZ3 zz ^y/zr Z / / zzZc^ /.^r ry i^yr^Zyi^ / Zzz^ r<^ zy./ ^ 3 / y^Zj-y.(^y / z C Zz/yy/^ Z_y^^£j^A^_Z_£^^Jy.^^ 3^y_^Z^rAf_^ 4. 5 6. // z Cy z^.^ajt ^/ zy^z^z^.A^j^ ^/ Zs- / ^ z^/.^^zz ¥3y.zC y^^/ Zcpzzy.yz yz/z^<^.^A^ Z Z.y / / Z /^ c^j-^^.^z zz/ / z^ ^z.J"^ /. ^f Z/CzZ/zZ'.yy /J-cz^(p^^.yr (^/Zy ^ r^.A^z /C/^y.fz / y C y z/ ^.3zz j~jZ/Cz/,yJ- 7Z/A^6.J~A^ ZzyZc^ / ZC^ /^.ZS y/z.yr / z.ys- / zyf'C3.C^ yz./zz /z^.fZ V zi^A^fz j~6y.rC z/A^C'^/ yj'/Z(^yz.(zy y/.A^ii 3zCzzs:y/ / Cf x/ ^ z.^^zz yzCy.zzz zzrzi^^.^/ /yz/.yc? Cyzzz.y^ 3(Z6^/.yf ^/ li.ys /Zyyr.^y y^.cz/.yy^ ADDITION 23 7. 8. 9. f /^JTJ C.A^/ f Z (^ f^.yJ' Z^/ 1^ Z / A^.Zf (^r/Z.O(P 3 ^y ry.^^ / z (^./ A^Z /^.4^/ Z3 zy / ^./ r / (i y Zf.y^ / c? / f ^ zy.6^ yrz.y^r / r y xy.y^ yf/tsj.A^^ /zj-Cr.3^ 3 yA^z ^ /.A^z yz//C^y^ zz yyv^zyr / cp z (^A^dP ^.^y J r y y ^^j ti z (^ o^A A^Z (^ tJ ^.y^ J~Z./ z cp y.cTA^ li z/ / zys rzy(:^A^-jj~ J y zy z.zo / C / Cy / z.^z 3d-y^rz.zo y z ^ A^^.c? o y^/iT.ys yyCo.^c? yZA^J~.6f / (^ Z / y.y^ r (^J~2 /.A^^ J ^ cp A^y.pzd / A^ / yj-Z /.Ca^ yj'^j y ^.^^ (^ y z^/ / <^.j-z / / z / z/^ oyJ' / (p / (^ r.Z3.z^ y z / z ^37/ / 6y(ry<^.cz ^ z y A^^./ z- ^z/^7^.^/ y Zzz / 3 r.y^" A^r3/^.y^ yz/: / y /j/y/z./r / Z./ Z^ ZX c^ yZ/Z(^y3 Z3~ / y Z C.r(^ / (p / A^ZyX3r z^/ 3 zy./z/ ^/^3~3z.zzj- zz^/^^y.^A^ y3'yyr3.yC zZi^/A^.yz Cyjyr.y^ /C/zC.A^y z/ ^ z zr^z.zo y (p / Z^.yz y z / Z.a^S yy^^z.^/z (^y3~A^.r'y zyyzCy./f 6 r o3~z.^^ / z C y ^ zC.j~A^ / f'y z^zy.ycp /zC/ZJ~.Cs 3z/C/A^.yc> <^yZA^(iy/-r:7^^^-^ ^^ ^zff-70 ^//-7o ^ai'-yo i/i/2--'y/ 4^/(^-1^^ /£> 3 ^ 2A ik*^ 40 PEACTICAL BUSINESS ARITHMETIC Chicago, IIL, July 20, J9 Messrs. A. M. THOMPSON & CO. Rochester, N.Y. Botj§:ht of Nelson, Morris & Co^ Terms 30 da. tubs Lard 72-17 70-14 69-14 71-14 71-15 70-16 *** $0.13 casks Shoulders 421-65 426-70 424-72 422-64 427-72 421-60 #### .14 casks Hams 409-72 412-70 414-71 410-73 412-70 416-71 **#* .18 43 299 368 29 32 28 3. The gross weights and tares of 6 casks of shoulders are as follows : 428 - 68, 419 - 70, 423 - 65, 432 - 72, 436 - 69, 434 — 65 lb. Find the total net weight. 4. The gross weight and tares of 12 tubs of lard are as fol- lows : 71-14, 70-15, 69-14, 71-15, 72-17,, 73-17, 69 - 15, 71 - 16, 72 - 15, 73 - 16, 74 - 17, 75 - 17 lb. Find the total net weight. 5. The gross weights and tares of 10 bbl. of sugar are as follows: 319-18, 331-19, 329-17, 334-20, 338-21, 325 - 18, 326 - 16, 325 - 19, 327 - 19, 321 - 17 lb. Find the total net weight. SUBTEACTION 41 BUSINESS TERMS AND EECOEDS 63. A debit is an expression of value received ; a credit is an expression of value delivered. A buys of B 100 bu. wheat for $100 cash; the vahie received (debit) by A is 100 bu. wheat and the value parted with (credit), §100. A sells C 50 bu. wheat for $75, C agreeing to pay for the same in 10 da. ; the value received by A is C"s express or implied promise to pay for the wheat in 10 da. and the value parted with is 50 bu. wheat. 64. An account is a collection of related debits and credits. 65. Some of the common accounts kept in business are the cash account; personal accounts; the merchandise account; the expense account ; the proprietary account. 66. A resource is any property on hand or any amount owed to a person or concern; a liability is any amount owed by a person or concern. The excess of resources over liabilities is the net capital or present worth ; the excess of liabilities over resources, the net insolvency. 67. A gain is any sum realized in excess of the cost of a business or of business transactions ; a loss is any sum spent or incurred in excess of the returns of a business or of business transactions. The excess of gains over losses is the net gain ; the excess of losses over gains, the net loss. 68. The cash account is kept for the purpose of showing the receipts and payments of cash and the amount of cash on hand. f /2 /JA^-J^ /Z(P0 /A^¥^\J'a The receipts are entered on the left, or debit side, the payments, on the right, or credit side. The excess of debits is the balance or cash on hand. In these exercises the use of red ink is not imperative. 42 PEACTICAL BUSINESS ARITHMETIC 69. Personal accounts are kept for the purpose of showing whether persons owe us or w§ owe them, and how much in either case. On the left (debit) side of these accounts are placed the amounts which the persons owe us or which we j)ay them ; on the right (credit) side, the amounts which we owe them or which they pay us. Wlien the debits of an account are in excess of the credits, the account owes us for the amount of the excess; when the credits are in excess of the debits, we owe the ac- count for the amount of the excess. 70. The merchandise account is kept for the purpose of show- ing the cost of goods purchased, the proceeds of goods sold, and the gain or loss resulting from such dealings. y/^^64.^^izJ^-^:Lff-Ccf firs>-z^ t/3£P 6 a' J ^o /J- JLZA ^ On the left (debit) side is entered the cost of goods purchased and on the right (credit) side the proceeds of goods sold. When the goods are all disposed of the excess of credits is a gain ; the excess of debits, a loss. When it is desired to show the gain or loss on merchandise before the goods are all disposed of, it is necessary to first enter in the credit side of the account the present market value of the unsold goods. SUBTRACTION 43 71. The expense account is kept for the purpose of showing the cost of outlays incurred in carrying on the business. C^. SH^CV^n,^ /^ / 2 JT^ £zk£ ^a Such outlays are entered on the left (debit) side of the account. Ordi- narily there are no credit entries. When the expense items are all used the debit of the account is a loss. When it is desired to show the loss or gain on expense and there are unused expense items on hand, it is first necessary to enter in the credit side of the account the present value of such items. 72. The proprietary account is kept for the purpose of show- ing how much the proprietor invests in the business and how much he withdraws from the business. :^^Jr:^^i:^^ /o '■^u^yy^^r-^^ /Co — ijJs^ ^f f^ On the right (credit) side are entered all sums invested and the net gain, and on the left (debit) side all sums withdrawn and the net loss. The excess of credits is the present worth of the business. ORAL EXERCISE 1. In the cash account on page 41 what are the total receipts? the total payments ? the balance of cash on hand ? 2. At the top of page 42 is your account with J. E. King & Co. On what dates did you sell the firm merchandise ? When and how were payments made on account? What was the balance of the account May 10 ? 44 PRACTICAL BUSINESS ARITHMETIC . 3. In the account with merchandise, page 42, what is the cost of the purchases? the proceeds of the sales? How would the value of the unsold goods be determined in business ? Verify the amount of the gain. Is it correct ? 4. Verify the amount of the loss in the expense account, page 43. Is it correct ? 5. What are the total withdrawals in the account with F. W. Simpson, Proprietor, page 43 ? the total investment ? WRITTEN EXERCISE 1. Copy the cash account on page 41 and continue it with the following items: Jan. 12, receive cash of Jones & Co., 175; Jan. 14, pay cash for groceries, $165.62; Jan. 15, re- ceive cash for groceries, $ 189.75 ; Jan. 18, pay cash to office help, $129.74; Jan. 20, pay cash for stationery, $11.75; Jan. 22, receive cash for groceries, $126.94; Jan. 24, receive cash of H. W. Conant, $200.67. Balance the account as shown in the model. 2. Copy the purchases and sales of the merchandise account, page 42. Assuming that the value of the unsold goods is $327.61, find the gain and close the account. 3. Copy the purchases and sales of the merchandise account, page 42. Assuming that the value of the unsold goods is $50, find the gain or loss and close the account. Assuming that all of the goods are sold, find the gain or loss and close the account. 4. Arrange the following data in the form of your account with Benj. F. Butler. June 1, buy of Benj. F. Butler on account (without making payment) dry goods amounting to $627.96; June 10, pay him for invoice of June 1 less $6.28 discount; June 28, buy of him dry goods amounting to $472.69 and pay cash to apply on the bill, $172.69; July 15, buy of him on account dry goods amounting to $369.71; July 31, pay him cash to apply on bill of July 15, $79.79; Aug. 2, sell him lace amounting to $14.60. Find the balance of the account and tell whether such balance is a resource or a liability. SUBTRACTION 45 5. Using the above data, write Benj. F. Butler's account of his dealings with you. Balance the account. 6. Copy the account with F. W. Simpson, Prop., page 43. Continue the account through June, using the following items : June 6, make an additional investment of flOOO; June 25, withdraw for personal use |160; June 30, the net gain for the month, which is to remain as an additional investment, is $369.75. Find the present worth and close the account. WRITTEN EXERCISE Copy the following statements^ supplying the missing terms : x:^^iz^^^^^<^^^i-^'^z^^/^^^ ^^n^7;^t lows : 2 X 6 = 12 ; write 2 and carry 1. 4 + 6 = 10 ; 2 x 10 + 1 (car- "*" ried) = 21 ; write 1 and carry 2. 2x4 + 2 (carried) = 10 ; write 10. 22 The result is 1012. 1012 2. Find the cost of 122 bu. of potatoes at 66^ per bu. Solution. 6x2 = 12; write 2 and carry 1. 2+2 = 4;6x4 -too + i (carried) = 25 ; write 5 and carry 2. 1 + 2=3; 6x3 + 2 (carried) = 20 ; write Oand carry 2. 6x1+2 (carried) = 8. Write m The result is $ 80.52. 80.52 WRITTEN EXERCISE In the following problems make all the extensions mentally. 1. Find the total cost of : 11 lb. coffee at 42^. 115 bu. rye at 99^. 14 doz. eggs at 21^. 215 bu. peas at 77^. 64 lb. cheese at 22^. 344 bu. oats at 44)^. 33 bu. carrots at b^^, 300 bu. grain at 85^. 11 bu. potatoes at 85^. 115 bu. barley at 88^. 88 bu. wheat at 88/. 400 bbl. apples at ^3.25. 2. Find the total cost of : 77 bu. peaches at 11.85. 820 bu. rye at 88^. 151 bu. corn at m^. 327 bu. oats at 33^. 265 bu. onions at 80)^. 314 bu. peas at m^. 135 bu. apples at 82^. 110 bu. pears at 11.66. 241 bu. turnips at 44< 880 bu. barley at il.l7. 112 bu. tomatoes at 55^. 100 bu. quinces at 11.60. A careful computer checks his work at every step. The student who forms the habit of doing this in all his computations will soon find himself ill no need of printed answers to problems involving only numerical calcula- tion. Checks for multiplication have already been mentioned. To guard against large errors, it is also important to form a rough estimate of an answer before beginning the solution. Thus, in finding the cost of 211 yd, of lining at 32^, at once see that the result will be a little more than I63.0C (210 times 30^); this will do away with such absurd results as ^6752. 1675.20, or $6.75. MULTIPLICATION 3. Copy and find the amount of the following bill: Boston, Mass., July 21, 19 Mrs. GEORGE W. MUNSON 168 Huntington Ave., City Bough, of S. S. PIERCE COMPANY Terms Cash 59 15 cs. Horse-radish $0.66 25 lb. Huyler^s Cocoa .44 31 gal. N. 0. Molasses .63 55 lb. Japan Tea .48 212 ti Raisins .11 Multiplication by 25, 50, and 75 88. Annexing two ciphers to an integer multiplies it by 100. Removing the decimal point two places to the right multiplies the decimal by 100. 89. Example. Multiply 76 by 100. Solution. 76 x 100 = 7600. (Annexing the t\w) ciphers gives the required result without the necessity for a written solution.) 90. Example. Multiply 148 by 25. Solution. 148 x 100 = 14,800. 14,800 -4 = 3700. Hence, to multiply an integer by 25, annex two ciphers to the multiplicand and then divide by 4. 91. Example. Multiply 278 by 50. Solution. 278 x 100 = 27,800. 27,800 -- 2 = 13,900. Hence, to multiply an integer by 50, annex two ciphers to the multiplicand and then divide by 2. 92. Example. Multiply 48 by 75. Solution. 48 x 100 = 4800. 4800 -- 4 = 1200 ; 3 x 1200 = 3600. Hence, to multiply an integer by 75, annex two ciphers to the multiplicand, divide that product by 4, and then multiply by 3. 60 PRACTICAL BUSINESS ARITHMETIC State the product of . 1. 86 X 25. 2. 27 X 50. 3. 28 X 75. 4. 97 X 25. 5. 248 X 25. 6. 126 X 50. 7. 164 X 25. ORAL EXERCISE 8. 48 X 50. 15. 64 X 75. 9. 52 X 75. 16. 63 X 25. 10. 67 X 50. 17. 69 X 25. 11. 89 X 50. 18. 56 X 75. 12. 186 X 50. 19. 240 X 75. 13. 146 X 25. 20. 184 x 75. 14. 204 X 50. 21. 144 X 75. WRITTEN EXERCISE In the following problems make all the extensions mentally. 1. Find the total cost of : 42 lb. cocoa at 40/. 27 bx. salt at 50/. 45 lb. cocoa at 50/. 23 lb. coffee at 25/. 50 lb. coffee at 28/. 21 lb. candy at 75/. 25 lb. raisins at 15/. 83 lb. chocolate at 50/. 28 lb. tea at 40/. 85 lb. Oolong tea at 45/. 2. Find the total cost of : 36 yd. wash silk at 25/. 87 yd. flannel at 50/. 25 doz. whalebones at? 92/. 21 yd. cottonade at 18/. 97 yd. cloth at 75/. 25 yd. denim at 19/. 25 gro. buttons at 35/. 17 yd. dress goods at 50/. 29 yd. gunner's duck at 19/. 23 yd. cheviot at 21/. Multiplication by an Even Number of Hundreds 93. Example. Multiply 468 by 300. Solution. 468 x 100 = 46,800 ; 46,800 x 3 = 140,400. Hence, to multiply an integer by an even number of hundreds, annex twc ciphers to the multiplicand and then multiply by the significant figure in the multiplier. 94. The value of many short methods is that they enable one to write results quickly without performing the mechanical operations. MULTIPLICATION 61 95. Many short methods in niultiphcation are not practical because they require one to remember so many things, or they apply to so few numbers that it is impossible for an ordinary person to remember them. The short methods given in this text are practical. ORAL EXERCISE Find the product of : 1. 234 X 200. 7. 753 x 300. 13. 964 x 200. 2. 175 X 600. 8. 845 x 400. 14. 554 x 300. 3. 335 X 800. 9. 453 x 200. 15. 181 x 700. 4. 216 X 900. 10. 256 x 400. 16. 312 x 800. 5. 648 X 100. 11. 145 X 800. 17. 237 x 600. 6. 452 X 500. 12. 333 x 700. 18. 122 x 900. Multiplication by Numbers from 101 to 109 Inclusive 96. Examples, l. Find the cost of 64 bu. of wheat at $1.02. Solution. 2 x 64 = 128 ; write 28 and carry L 1 x 64 +1 = "^ 65 ; write 65. The result is $ 65.28. 1.02 Some persons may prefer to work this problem as follows ; 64 65.28 bu. at$l =$64; 64 bu. at 2^ = $1.28; $64 + $1.28 = $65.28. 2. Find the cost of 251 bu. of barley at 11.04. Solution. 4 x 51 = 204 ; write 04 in the product and carry 2. 251 4x2 + 2 (carried) -f 1 (the right-hand figure of the nuiltiplicand) -i (\a = 11 ; write 1 and carry 1. 1 x 25 + 1 (carried) = 26 ; write 26. ' The result is $ 261.04. 261. 04 97. Similarly multiply by such numbers as 201, 302, and 405. 98. Example. Find the cost of 124 bu. of beans at $ 2.05. Solution. 5 x 24 = 120. Write 20 and carry 1. 5x1+1 124 (carried) +2x4 (the right-hand figure of the multiplicand) = 14 ; 90^ write 4 and carry 1. 2 x 12 + 1 (carried) = 25 ; write 25. The ' result is $ 254.20. 254. 20 Some persons may prefer the following solution : 124 bu. at $2 = $248; 124 bu. at 5)? = $6.20; $248 + $6.20 = $254.20. The student should try to exercise his own ingenuity in all this work. 62 PRACTICAL BUSINESS ARITHMETIC WRITTEN EXERCISE Find the value of: 1. 215 T. coal at 16.05. 2. 224 bu. rye at $1.02. 3. 215 bu. wheat at $1.02. 4. 318 bu. barley at 1 1.05. 5. 124 bbl. apples at 12.05. 6. 116 bbl. onions at $ 1.08. 7. 232 bbl. potatoes at |2.05. 8. 802 bu. peas at 74 ^. 9. 104 bu. corn at 89 ^. 10. 103 bu. beets at 85 ^. 11. 205 bu. turnips at 54 ^. 12. 215 bu. pears at 11.05. 13. 411 bu. plums at 11.08. 14. 206 bu. parsnips at 98^. Miscellaneous Short Methods 99 . When one part of the multiplier is contained in another part a whole number of times, the multiplication may be short- ened as shown in the following examples. 100. Example. Multiply 412 by 357. Solution. 35 is 5 times 7. 7 x 412 = 2884, which write as the first partial product. 5 x 2884 = 14,420, which write as the second partial product. Check. Interchange the multiplier and multipli- cand and remultiply. 4 x 357 = 1428 ; 3 x 1428 =4284. Add. Since the results by both multiplications agree, the work is probably correct. 412 357 357 412 2884 14420 1428 4284 1470.84 147084 101. Example. Multiply 214 by 756. Solution. 56 is 8 times 7. 7 x 214 = 1498, which we write as the first partial product. 8 x 1498 = 11,984, which we write as the TTog second partial product. The sum (161,784) of these partial products .j .j ^^ . 214 756 is the entire product. Check as in problem 1. (See also pages 89 and 90.) 161784 WRITTEN EXERCISE Find the product of: 1. 319 X 248. 3. 728 x 287. 2. 927 X 279. 4. 848 x 369. 102. The above short methods are practical in a limited num- ber of problems. MULTIPLICATION 63 WRITTEN REVIEW EXERCISE 1. Use 6 as a multiplier for each column. Check. (See page 53.) a. h. c. d. e. 56 U 39 126 215 48 63 58 232 175 73 52 82 311 243 49 65 72 135 223 45 55 85 144 183 ^^ 47 19 225 253 11 88 92 245 127 2. Use 8 as a multiplier for each column. Check. 3. I bought 15 A. of land at $275 per acre and laid it out in 100 city lots. After expending S6750 for grading and taxes, S257 for ornamental trees, and S250 for advertising, I sold 15 lots at $625 each, 35 lots at $415 each, and exchanged the remainder for a farm of 120 A., which I immediately sold at S195 per acre. Did I gain or lose, and how much? 4. Copy and find the amount of the following bill: Rochester, N.Y., July 26, Mr. F. C. GORHAM 120 Spring Street, City Bouglit of C. E. Ferguson G? Son Terms 50 da. 19 37 bu. Oats $0.40 50 u Corn .67 76 n Wheat 1.02 75 u Rye 1,04 95 u Beans 4.00 16 u Clover Seed 3.50 26 M Millet .99 64 PRACTICAL BUSINESS ARITHMETIC WRITTEN REVIEW Copy these examples ; add the checks in the Checks in Detail cohimn and enter the totals in the Total Checks column ; find the new balance, the total old balance, the total checks, the total deposits, and check the work. Checks in Total Name Balance Detail S180.55 Checks Deposits Bala] A S313.25 211.15 165.43 208.19 ? S 278.40 ? B 285.67 100.55 145.97 ? 327.44 9 C 186.53 200.12 45.67 118.95 ? 198.45 ? D 276.65 205.18 ? 210.50 9 E 612.40 64.25 9 918.75 9 xU F 347.85 103.86 6.84 ? 9 ? ? ? ? ? 2. ' Checks in Total Name Balance Detail Checks Deposits Bala A $195.63 S 214.70 71.20 8.50 ? S174.25 ? B 98.40 102.45 74.65 123.52 ? 115.68 9 C 153.30 10.55 75.20 55.34 ? 89.48 ? D 386.54 7.35 ? 275.40 ? 172.38 MULTIPLICATION 65 A WRITTEN REVIEW TEST Write the following i^rohlerm from dictation, and complete the. work. Time, approximately, forty minutes, including the dictation. Mental extensions only. 1. Write in one column, and find the total value : 78 yd. at 11/ 55 yd. at 55/ 69 yd. at 25/ 91 yd. at 50/ 60 yd. at 85/ 89 yd. at 99/ 45 yd. at 98/ 75 yd. at 90/ 37 yd. at 97/ 76 yd. at 70/ 112 yd. at 99/ 125 yd. at 98/ 2. Write in one column, and find the total value : 76 yd. at Sl.lO 82 yd. at S1.05 55 yd. at S1.06 65 yd. at S1.20 108 yd. at $1.11 130 yd. at $1.09 m yd. at $1.25 83 yd. at $1.50 88 yd. at $1.04 97 yd. at $1.03 67 yd. at $1.02 137 yd. at $1.01 3. Write hi one column ; use 11 as the multiplier, and check the results: 49, 16, 34, 78, 57, 73, 85, 94, 59, 64, 56, 81. 4. Write in one column ; use 6 as the multiplier, and check the results : 125, 212, 350, 175, 162, 224, 319, 452, 133, 145, 121, 142. 5. Write in one column ; use 8 as the multiplier, and check .the results : 45, 75, 62, 29, 76, 61, 19, 34, 85, 92, 27, 77. 6. Write in one column ; square each number, and total the products : 25, 55, 15, 45, 75, 35, 85, 65, 95. 7. The text, page 63, problem 3, in the Written Review Exercise. CHAPTER VII DIVISION ORAL EXERCISE 1. What is the product of 12 times 15? How many times is 15 contained in 180 ? What [s.j\ of 180 ? 2. How much is 11 times il7? How many times is il7 contained in $187 ? What is J^ of $187 ? 3. What is the product of 9 times 12 ft.? How many times is 12 ft. contained in 216 ft.? What is J^ of 225 ft.? 4. When one factor and the product are given, how is the other factor found ? 103. The process of finding either factor when the product and the other factor are given is called division. 104. The known product is called the dividend; the known factor, the divisor; the unknown factor, when found, the quotient. 105. The part of the dividend remaining when the division is not exact is called the remainder. While definitions such as the above should not be memorized, the ideas which they express should be thoroughly understood. 106. Since 6 times 7 ft. = 42 ft., 42 ft. -f- 7 ft. = 6, and 42 ft. -^ 6 = 7 ft. It is therefore clear that 1. If the dividend and divisor are concrete numbers^ the quo- tient is an abstract number ; and 2. If the dividend is concrete and the divisor abstract, the quo- tient is a concrete number like the dividend. In §106 it will be seen that there are two kinds of division : 42 ft. h- 7 f t. = 6 is sometimes called measuring, because 42 ft. is measured by 7 ft. ; 42 ft. -^ 6 = 7 ft. is sometimes called partition, because 42 ft. is divided into 6 equal parts. 66 DIVISION 67 ORAL EXERCISE 1. Divide by 2 : 18, 32, 78, 450, 642, 964, 893. 2. Divide by 3 : 27, 57, 72, 423, 642, 963, 845. 3. Divide by 4 : 64, 88, 92, 488, 192, 396, 728. 4. Divide by 5: Qb, 85, 95, 135, 275, 495, 725. 5. Divide by 6 : 84, 96, 54, 246, 546, 672, 846, 636. 6. Divide by 7 : 63, 84, 91, 217, 497, 714, 791, 921. 7. Divide by 8 : 72, 56, 88, 248, 640, 128, 144, 152. 8. Divide by 4 : 56, 96, 77, 241, 168, 128, 920, 848. 9. Divide by 6 : 78, 96, 56, 272, 848, 190, 725, 966. 10. Divide by 9 : 98, 72, 49, 279, 819, 720, 189, 918. ORAL EXERCISE 1. 16 ft. -^ 2 = ? 24 ft. -^ 8 ft. = ? 2. 125 ^ 5 = ? 129.75 - 5 = ? 1129.78 ^ 9 = ? 13.40 h- 4 = ? 3. 126 yd. --3 yd. = ? 1125-25 = ? $6.25 -■ 81.25 = ? 4. If 9 T. of coal cost 149.50, what is the cost per ton? Solution, f; 49.50 -t- 9 = $ 5 ; subtracting 9 times $ 5, the re- $ 5.50 suit is $4.50 undivided J $4.50 -^ 9 = $0.50. Therefore the ^*149 5Q quotient is $5.50. 5. At $1.75 a yard, how many yards can be bonght for 135? Solution. The divisor contains cents and it is therefore 20 better to first change both dividend and divisor to cents. It is -irj cNqcnn found that $35 would buy 20 times as many yards as $1.75 , or ^ 20 yd. 6. If 5 T. of coal cost 131.25, what is the cost per ton? 7. At 1 2.50 per yard how many yards can be bought for $ 550 ? ORAL EXERCISE 1. How many weeks in 98 da. ? 2. What is 2^ of 2250 bbl. of apples? ^i^? J? ^\? 3. The quotient is 8 and the dividend 128. What is the divisor? 4. How many times can 18 be subtracted from 75, and what will remain? 68 PRACTICAL BUSINESS ARITHMETIC 5. At 15^ per pound, Iiow many pounds of beef can be bought for $6.30? 6. The quotient is 5, the divisor 23, and the remainder 2. What is the dividend ? 7. If 5 men earn 117.50 a day, how much can 8 men earn in 2 da. at the same rate? 8. What is the nearest number to 150 that can be divided by 9 without a remainder? 9. If there are 960 sheets in 40 qr. of paper, how many sheets in 5 qr. ? in 11 qr. ? 10. If 6 bbL of apples are worth $ 21, what are 24 bbL worth at the same rate ? 36 bbL ? 11. If 17 bbL of flour cost S85, what will 25 bbL cost at the same rate ? 32 bbl. ? 48 bbl. ? 34 bbl. ? 12. If 8 be added to a certain number, 7 can be subtracted from that number 7 times. What is the number ? 13. If 20 yd. of cloth cost $60, for how much per yard must it be sold to gain 1 25? to gain $15? 14. A grocer sold 250 oranges at 5^ each and gained $5. How much did he pay a dozen for the oranges? 15. A grocer pays $3 for 20 doz. of eggs. At what price per dozen must he sell them in order to gain $1.50? 16. At $2.50 per yard, how many yards of cloth can be bought for $75? for $150? for $2500? for $750? 17. How many days' labor at $3.50 per day will pay for 2 T. of coal at $7 a ton and 5 lb. of tea at 70 J^ per pound? 18. A clothier pays $96 for a dozen overcoats. At how much apiece must he retail them to gain $48 on the lot? 19. A man exchanged 1140 bu. of wheat at $1 per bushel for flour at $6 per barrel. How many barrels did he receive? 20. It was found that after 15 had been subtracted 5 times from a certain number the remainder was 4. What was the number? 21. A man contracts a debt of $175 which he promises to pay in weekly installments of $3.50 each. After paying $35, how many more payments has he to make? DIVISION 69 107. Examples, i. Divide 4285 by 126. Complete Operation Required Work 126)4285 126)4285 378 =3 times 126 378 505 undivided 505 504 =4 times 126 504 1 undivided 1 Check. 34 x 126 + 1 = 4285 The remainder cannot always be written as a part of the quotient. Thus in the problem, "At $7 per head how many sheep can be bought for $37," we cannot say, " 5f sheep," but " 5 sheep and $2 remaining." 2. A farmer received $283.25 in payment for 275 bu. of wheat; How much was received per bushel for the wheat? 11.03 Solution, f 283.75 - 275 = $ 1 and $8.25 undivided. 275)$283.25 $8.25 -f-275 =$0.03. $1.03 per bushel was therefore re- 9fTr ceived for the wheat. — Check. 275 times $ 1.03 = $283.25. ° 25 825 108. Work in division may be abridged by omitting the partial products and writing only the partial dividends. 109. Example. Divide $614.80 by 232. Solution. Omit writing the products; subtract mentally and write the remainder only : 2 x 232 = 464 ; 464 subtracted from 614 equals 150 ; omit the writing of the 464. Proceed as follows : •IS) Z.bO 2 times 2 plus = 4 ; 2 times 3 plus 5 = 11. 2 times 2 + 1 = 5, 232)S614.80 and 5 plus 1 = 6. Bring down 8. 6 times 2 plus 6 = 18 ; 150 8 6 times 3 plus 1 = 19, and 19 +1= 20 ; 6 times 2 plus 2 =14, H (30 and 14 plus 1 = 15. Bring down and proceed as before. Q QQ WRITTEN EXERCISE 1. Find the cost of 8800 lb. of oats at 45/ per bushel of 32 lb. 2. How many automobiles, at S650 each, can be purchased for 84,225,000? 3. By what number must 8656 be multiplied to make the product 8,223,200? 70 PEACTICAL BUSINESS ARITHMETIC 4. If 120 bbl. of flour cost |660, what will 829 bbl. cost at the same rate ? 5. The product of two numbers is 1,928,205. If one of them is 621, what is the other ? 6. If 380 T. of coal can be bought for $3040, how many tons can be bought for f 3600 ? 7. How many cords of 128 cu. ft. in a pile of wood con- taining 235,820 cu. ft. ? What is it worth at 14.50 per cord ? 8. A speculator sold a quantity of apples that cost $2500 for $4750. If his gain per barrel was $1.12^^, how many barrels did he buy ? 9. A man received a legacy of $11,375 which he invested in railroad stock. He paid a broker $ 125 to buy stock at $112.50 per share. How many shares were bought? 10. A dealer bought 250 T. of coal by the long ton of 2240 lb. at S6.50 per ton. He retailed the same at S 8.25 per short ton of 2000 lb. What was the total gain ? 11. In a recent year there were produced in the United States 730,627,000 bu. of wheat on '45,814,000 A. What was the yield per A. ? What was the total yield worth at 90/ per bu. ? 12. Copy and complete the following table of corn statistics. Check the work. (The total yield multiplied by the price per bushel should equal the total valuation.) Principal Corn-growing States in a Recent Year State Yield in Bitshels Farm Price per Bushel Farm Valuation Illinois Iowa Nebraska Missouri Indiana Kansas 426 320 000 ? ? 199 364 000 174 225 000 62j^ 62j* Q2^ 62f 264 318 400 267 853 020 113 221 920 151 220 480 ? ? Total ? 62/ 9 13-15. Make and solve three self -checking problems in division DIVISION 71 SHORT METHODS IN DIVISION Powers and Multiples of 10 oral exercise 1. How many times is 10 contained in 50? 100 in 800? 1000 in 9000? 2. Cutting off a cipher in 30 divides it by what number? 3. Cutting off two ciphers in 800 divides it by what number ? 4. Cutting off three ciphers in 11,000 divides it by what number ? 5. Read aloud, supplying the missing words : a. The number of lO's in any number may be found by cutting off the units' figure ; the number of lOO's by cutting off the and figures ; the number of by cutting off the hundreds' and tens' and units' figures. h. In 4561 there are 456 tens and 1 unit, or 456 Jq tens ; 45 and 61 units, or 45^yQ hundreds ; and thousands and 561 units, or ^^i'i^ tliousands. 6. How many times is $0.10 contained in f 1 ? -$0.01 in II? 10.001 in II? 7. Whatis-Jo of II? ^l^ofll? loVoof^l^ 8. Read aloud, supplying the missing words: 10.60 is of %^ ; 10.06 is of 16 ; 10.006 is of %^, 9. Formulate a short method for dividing United States money by 10 ; by 100 ; by 1000. 10. By inspection find the quotient of : a. 736 -f- 10. e. 1271-^100. L 2140 lb. ^ 100. h. 1531-^100. /. 1519.50-10. j. 3145 1b. ^100. c. 16351-1000. ^. 184.50 -^ 100. A^. 3416 ft. - 1000. d. 311219-10000. h. 12150-^1000. I. 1279 posts -f- 100. 11. Read aloud, supplying the missing amounts : a. 6400-1600 = ; 640^10 = . h. 27000 ^ 9000 = ; 2700 -^ 900 = ; 270 - 90 = ; 27-^9= . c. 18801 - 90 = 9 ; 214200 ^ 700 = 2142 -f- . 72 PRACTICAL BUSINESS AEITHMETIC 12. How is the quotient affected by like changes in both the dividend and divisor ? 13. Divide 1323 by 400. Solution. Cut off the two ciphers in the divisor and two ^11 f digits in the right of the dividend, thus dividing both dividend 4100^13123 and divisor by 100. 4 is contained in 13 three times with a ' ^ remainder 1 hundred. Adding to this remainder the 23 units _ remaining in the dividend after dividing by 100, the true re- 123 mainder is 123, which write in fractional form. 14. Read aloud, supplying the missing amounts : 1611 -4- 400 = ; 2847 -=-700 = ; 1531^300 = ; 16139^ 4000 = . 15. Formulate a rule for dividing a number by any multiple of ten. 16. State the quotient of : a, 1231-^30. /. 96131-400. h, 63571^3000. 5. 9647 -^ 40. g. 84199 -- 700. I. 16657-4000. c. 6551 H- 50. h. 64137 -V- 800. m, 36119-6000. d. 4273^70. . i. 45117 -- 900. n. 18177^-9000. e. 8197 -f- 90. /. 25121-500. o. 42113^7000. ORAL REVIEW EXERCISE The diagram on the opposite page is a portion of the New York Central time-table giving the distances between many of the stations from New York City to Suspension Bridge, and the time taken by two different trains to travel this route. 1. How many miles between New York City and Pough- keepsie? between Poughkeepsie and Utica? between Utica and Syracuse? between Syracuse and Rochester? between Rochester and Buffalo? between Buffalo and Niagara Falls? 2. What is the distance between New York City and Syra- cuse? between Poughkeepsie and Niagara Falls? between Rochester and Suspension Bridge? 3. How many miles between Ludlow and each station below it? between Poughkeepsie and each station below it? between Tarry town and each station below it? DIVISION 73 4. How many miles between below it? between Oscawana and each station below it? 5. At 2j^ per mile, what is the fare from New York to Niagara Falls ? from Poughkeepsie to Syra- cuse ? from Buffalo to Utica ? from Troy to Yonkers? 6. At 2;^ per mile, what is the fare from Rochester to Syracuse? from Rensselaer to Suspension Bridge? from Albany to Niagara Falls? from Syracuse to Buffalo? to Albany ? 7. How long does it take train No. 93 to travel the first 30 mi. toward Poughkeepsie? the first 74 mi. toward Albany? 8. How long is train No. 93 in making the run from Fishkill Landing to Camelot? This is ap- proximately how many miles an hour? 9. How long does it take train No. 73 to make the run from Utica to Syracuse ? How long does it take train No. 73 to make the run from Fishkill Landing to Chelsea ? This is approximately how many miles an hour? 10. Add each number in the col- umn marked " Miles " to the one immediately below it. Montrose and each station 63 NORTH AND WEST BOUND Lv New York Grand Cent. Sta. . 125th St. Sta 138th St. Sta High Bridge Morris Heights Kings Bridge Spuyten Duyvil Riverdale Mt. St. Vincent Ludlow Yonkers Glenwood Hastings-on-Hudson Dobbs' Ferry Ardsley- on -Hudson Irvington Tarrytown Scarborough Ossining = Croton-on-Hudson .. Oscawana Crugers Montrose Peekslcill Highlands Garrison Cold Spring Storm King Dutchess June Fishkill Landing Chelsea New Hamburg Camelot Poughkeepsie Ar Poughkeepsie Lv Hyde Park " Staatsburgh »' Rhineclitf (Rh'b'k).. " Barrytown " Tivoli •' Germantown '• Linlithgo " Greendale *♦ Hudson '* Stockport " Newton Hook " Stuyvesant " Schodack Landing.. " Castleton " Rensselaer " Albany Ar. Troy " Utica Syracuse- Rochester. Buffalo Ar. Niagara Falls Ar. Suspension Bridge " 73 121110 6t01 12*23 6^13 6.15 6.21 625 6.29 6.33 12.46 1.25 1.47 2 24 2.31 2.53 3.05 5.50 6^50 8540 9.55 2513 2£20 6.43 6.46 6.52 6.59 7.01 7.05 7.12 7.19 7.25 7.31 7.34 7.37 7.41 7.49 7.59 8.06 8.12 8.16 8.21 8.27 8.34 8.40 8.46 8*55 Thus, 9, 12, 16, 24, 34, 45, 58, etc. In add- ing 89 and 95 think of 179 and 5, or 184 ; in adding 143 and 149 think first of 243 and 49 and then of 283 and 9, or 292. 74 PEACTICAL BUSINESS AEITHMETIC 11. Multiply each number in the column marked " Miles " by 5; by 8; by 3 ; by 7 ; by 6 ; by 4; by 9. The numbers in the portion of the time-table illustrated may be used for such other exercises as may seem necessary at this point. Students should be impressed with the importance of being able to add, subtract, multiply, and divide numbers in any relative position. « 12. Five parts of 120 are 15, 18, 32, 10, and 20. Find the sixth part, and multiply it by 15. 13. From a flock of 170 sheep I sold at different times 12, 18, 32, and 9. How many sheep remained ? 14. Multiply by 11 each of the following numbers: 21, 32, 43, 54, 65, 76, 87, 98, 61, 28, 37, 14, 21, 62. 15. At 22 / per yard, what will 18 yd. cost ? 21 yd. ? 36 yd. ? 56 yd. ? 29 yd. ? 73 yd. ? 94 yd. ? 72 yd. ? 16. Multiply each number in problem 15 by 33 ; by 44. WRITTEN REVIEW EXERCISE 1. Find the total cost of the articles in problem 3 of the oral exercise, page 56. Find the total of the products in the oral exercise, page 60. 2. A mechanic earns S125 per month and his monthly ex- penses average S72. If he saves the remainder, how long will it take him to save $4352 ? 3. I spent $24,800 for apples at $2.50 per barrel The loss from decay was equal to 74 bbl. What was my gain, if the remainder of the apples sold for $3.75 per barrel, and my expenses for storage were $675.80? 4. During a certain week a contractor employed help as follows: 34 hands, 8 hr. per day, for 5 da., at 15/ per hour; 16 hands, 9 hr. per day, for 6 da., at 25/ per hour; 29 hands, 10 hr. per day, for 6 da., at 18/ per hour. Find the amount due. 5. In a recent year there were produced on 37,917,000 A. in the United States 1,418,337,000 bu. oats, valued on the farm at 31.3/ per bushel. What was the average yield per acre? What was the value of the year's crop ? DIVISION 75 6. Without copying find (a) the total number of raihvay employees in the United States in 1910 and (b) the total num- ber per one hundred miles of line in the same year. Railway Employees in the United States 1910 1911 Total Number Average Total Number Average Class Number PER 100 Mi. Daily Wages Number PER 100 Mi. Daily Wages General officers 5.476 2 $13.27 5,628 2 $12.99 Other officers 9,392 4 6.22 10,196 4 6.27 General office clerks 76,329 32 2.40 76,513 31 2.49 Station agents 37,379 16 2.12 38,277 16 2.17 Other station men 153,104 64 1.84 153,117 62 1.89 Engineers 64,691 27 4.55 63,390 26 4.79 Firemen 68,321 28 2.74 66,376 27 2.94 Conductors 48,682 20 3.91 48,200 20 4.16 Other trainmen 136,938 57 2.69 133,221 54 2.88 Machinists 55,193 23 3.08 55,207 22 3.14 Carpenters 68,085 28 2.51 65,989 27 2.54 Other shopmen 225,196 94 2.18 226,785 92 2.24 Section foremen 44,207 18 1.99 44,466 , 18 2.0f Other trackmen 378,955 157 1.47 363,028 147 1.50 All other employees 229,806 95 2.01 227,779 93 2.08 7. Without copying find (a) the total number of railway employees in the United States in 1911 and (5) the total num- ber per one hundred miles of line in the same year. 8. Find the total salaries paid to railway employees in 1910 ; in 1911. 9. Find the average daily wages paid to railway employees in 1910; in 1911. 10. In a recent year four leading railway systems had out- standing bonds as follows : a, $761,963,000. c. $1,096,773,410. h. $576,300,000. d. $428,649,000. Find the average amount of the bonds outstanding. 76 PRACTICAL BUSINESS ARITHMETIC WRITTEN REVIEW In these problems divide across, and then add the dividend column and the quotient column, Chech : divide the total of the dividend column by the divisor, and this quotient should equal the sum of the individual quotients. Time, approximately, fifteen minutes. 1. 2. 3. 36 -^ 4 = ? -1 45-f-5 = ? ' m-^Q^"^ 48 -^ 4 = ? 75^5 = ? . 72 -J- 6 = ? 56 ^ 4 = ? 1 ^ 95 ^ 5 = ? H 84 ^ 6 = ? 24 ^ 4 = ? b 65^5 = ?/, 78 -^ 6 = ? 84 -V- 4 = ? ^'/ 35^5 = ? 48-^6 = ? ' 44^4 = ? b 55 -f- 5 = ? 36 -^ 6 = ? 64 ^ 4 = ? • 15^5 = ? 54 - 6 = ? 76 ^ 4 = ? ' J 40 ^ 5 = ? 42 -f- 6 = ? 4. ^?- ? -i-5 = ? ? -6 = ? ^ 5. 6. 98-^7-? 88^2 = ? 48^3 = ? 84 ^ 7 = ? ; /i.- '76^2 = ? 54 -^ 3 = ? 63^7 = ? "■'■ 58 ^ 2 = ? 69-^3 = ? 49 H- 7 = ? 64 -^ 2 = ? 72^3 = ? 91-^7 = ? 82-f- 2 = ? 84 ^ 3 = ? 56 -f- 7 = ? 94 H- 2 - ? 93 -f- 3 = ? 77^7-? 52 - 2 = ? 87-f-3 = ? 42^7 = ? 74 ^ 2 = ? 54 -f- 3 = ? ? -^ 7 = ? ? -f-2 = ? ? -V- 3 = ? 7. 8. 9. 126-^2 = ? 144 ^ 4 = ? 129 ^ 3 = ? 152 -f- 2=:? 124-h4 = ? 114 ^ 3 = ? 134 -f- 2 = ? 152-4 = ? 108 ^ 3 = ? 168^2 = ? 148 -^ 4 = ? 147_j.3 = ? 184 -f- 2 = ? 176^4 = ? 189^3 = ? 156 -^ 2 = ? 184 - 4 = ? 165-^3 = ? 172^2 = ? 136^4 = ? 195-^3 = ? 138-^2 = ? 180-4 = ? 138^3 = ? ? -f-2 = ? • ? -v-4 = ? ? -3 = ? 4 DIVISION. U.S. POSTAL SERVICE 77 110. All mailable matter for transmission by the United States mails within the United States or to Cuba, Mexico, Hawaii, Porto Rico, Canada, and the Philippine Islands is divided into four classes : first-, second-, third-, and fourth-class matter. First-class matter includes letters, postal cards, and anything sealed or otherwise closed against inspection. The rate for first- class m'atter is 2/ per ounce or fraction thereof; for a postal card, 1 / ; for a reply postal card, 2 /. Written or typewritten matter is of the first class, whether sealed or unsealed. Second-class matter includes newspapers and periodicals entirely in print. When sent by publishers or news agents, the rate is 1 / per pound or fraction thereof ; when sent by others, 1 / for each 4 oz. or fraction thereof. Third-class matter includes books and catalogues (weighing 8 oz. or less), circulars, pamphlets, proof sheets and manuscript copy accompanying the same, and engravings. The rate is 1/ for each 2 oz. or fraction thereof. The limit of weight is 4 lb. All postal matter of the first, second, or third class may be registered at the rate of 10/ for each package in addition to the regular rates of postage. The rates on special delivery letters are 10 / per letter in addition to the regular postage. Any matter on which a special delivery stamp is affixed is entitled to special delivery within certain limits. Foreign rates of postage are as follows : letters, 5 / per ounce for the first ounce, and 3 / for each additional ounce. (Double rate is charged at delivery office for any deficiency in prepayment.) Postal cards, 2/ each; newspapers and other printed matter, 1/ for 2 oz. Some foreign countries, as Germany and Great Britain, come under the letter rate of 2/ per ounce. All fourth-class matter is now included in the domestic parcel post, by a law which became effective January 1, 1913. The fol- lowing are some of the principal features of this law : The country is divided into zones, the rate of postage being dependent on the zone where the parcel is to be delivered. The zone center is the point of mailing. Regular postage stamps are used on parcel-post packages. 78 PEACTicAL busi:ness aeithmetic Parcels weighing 4 oz. or less are mailable at the rate oi If for each ounce or fraction of an ounce, regardless of distance. Parcels weighing more than 4 oz. are mailable at the pound rates shown in the table, a fraction of a pound being considered as a full pound. Books and catalogues weighing in excess of 8 oz. may be sent by parcel post. The weight limit for zones 1 and 2 is 50 lb. ; for all the other zones, 20 lb. The local rate applies to parcels to be delivered at the office of mailing, or on a rural route starting from that office. A parcel may be insured against loss to the amount of its actual value not exceeding $50. A special delivery of a parcel will be made on the payment of an addi- tional 10)2^, at the mailing office. In the table, the rates are complete up to 11 lb. From this point on only illustrative weights and rates are given ; omissions are indicated by stars. The local post office can furnish a parcel-post map of the United States showing the regions included in the different zones. 50 mi. so- ldo mi. 150- 300 mi. 300- 600 mi. 600- 1000 mi. lOOO- 1400mi. 1400- 1800 mi. All over 1800 mi. First Zone Second Zone Rate Third Zone Rate Fourth Zone RATE Fifth Zone Rate Sixth Zone Rate Seventh Zone Rate Eighth Weight Local Rate Zone Rate Zone Rate lib. $0.05 $0.05 $0.05 $0.06 $0.07 $0.08 $0.09 $0.11 $0.12 21b. .06 .06 .06 -.08 .11 .1.4 .17 .21 .24 31b. .06 .07 .07 .10 .15 .20 .25 .31 .36 41b. .07 .08 .08 .12 .19 .26 .33 .41 .48 51b. .07 .09 .09 .14 .23 .32 .41 .51 .60 61b. .08 .10 .10 .16 .27 .38 .49 .61 .72 71b. .08 .11 .11 .18 .31 .44 .57 .71 .84 81b. .09 .12 .12 .20 .35 .50 .65 .81 .96 91b. .09 .13 .13 .22 .39 .56 .73 .91 1.08 101b. .10 .14 .14 .24 .43 .62 .81 1.01 1.20 111b. .10 .15 .15 .26 .47 .68 .89 1.11 1.32 * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * 151b. .12 .19 .19 .34 .63 .92 1.21 1.51 1.80 * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * 201b. .15 .24 .24 .44 .83 1.22 1.61 2.01 2.40 * * * * * * * * * * * * 301b. .20 .34 .34 * * * * * * * * * * * * 401b. .25 .44 .44 * * * * * * * * * * * * 501b. .30 .54 .54 DIVISION. U. S. POSTAL SEKVICE 79 ORAL EXERCISE 1. What is the postage on a letter weighing 1- oz. ? 4J oz. ? 11 oz.? 3^oz.? 2^oz.? 41 oz.? 2. What will be the cost of postage on the following articles at your post office to points within the United States : an ordinary letter weighing 2| oz. ; a registered letter weighmg 1 J oz. ; a bundle of papers weighing 10 oz. ? 3. Find the total cost of postage on the following to pomts within the United States: a special delivery letter weighing li oz.; some printers' proofs weighing 18 oz. ; some separate matter for the printer weighing 12 oz. ; a pamphlet weighing 6 oz. 4. Use a zone map and find the cost of mailing each of the following articles : Article Weight Destination A pair of opera glasses 21b. 80Z. Kansas City, Mo. A pair of ladies' gloves 60Z. Indianapolis, Ind. A copy of Star-Land lib. 80Z. Macon, Ga. A copy of Whittier's Poems 1 lb. 12 OZ. Pittsburgh, Pa. A copy of Lowell's Poems 1 lb. 10 OZ. Denver, Colo. A box of merchandise 31b. 80Z. Chicago, 111. A box containing a pair of shoes 3 lb. 6 OZ. Austin, Tex. A piece of hardware 6 lb. 9 oz. Detroit, Mich. 5. A publisher sends 20,000 copies of his magazine by mail. If each magazine and wrapper weighs 14i oz. and the total number is weighed at the post office in bulk, what will the publisher have to pay for postage ? 6. A subscriber mailed two copies of the above magazine to a friend. What was the cost for postage ? 7. 25,000 copies of a monthly magazine weighing 14i oz. were sent by mail. What was the cost to the publisher for postage ? 8. Find the total cost for mailing the following: printers' proof weighing 18^ oz. ; manuscript and printers' proof in one package, weighing 28i oz. ; a special delivery letter, weighing | oz. 80 PEACTICAL BUSINESS AEITHMETIC PEICE LISTS AND INVENTOEIES Price Lists These price lists are to he used in making out the inventories which are found on the four pages following : Article 1. 2. 3. 4. Bedsteads $6.25 $8.50 111.75 $5.25 Bookcases 42.00 38.00 25.00 35.00 Bureaus 18.50 27.25 22.50 16.50 Cabinets : China 22.00 20.00 27.50 - 32.50 Medicine 2.25 1.75 2.50 3.25 Music 10.00 11.00 9.00 8.50 Parlor 25.50 • 21.50 25.00 36.50 Chairs : Easy 12.50 10.50 15.00 22.25 Morris 10.50 12.25 12.00 9.75 Piano 5.00 6.50 7.25 9.00 Typewritel- 3.50 4.50 4.00 5.50 Cheval Mirrors 20.00 17.25 18.50 16.50 Chiffoniers 24.00 18.20 31.75 27.50 Davenports 62.50 50.00 60.00 45.50 Desks : Flat-top 21.20 17.60 16.80 22.30 Roll-top 23.50 21.25 25.50 27.25 Typewriter 11.25 12.25 14.25 10.25 Dinner Trays 5.50 6.25 7.25 5.25 Footrests 1.75 1.50 1.60 2.00 Hall Racks 14.25 13.50 17.25 18.50 Lounges 25.00 17.50 21.50 32.00 Mattresses 11.40 12.50 13.25 17.50 Ottomans 5.25 4.50 4.25 5.50 Parlor Suites 63.00 52.50 75.00 67.50 Pillows 2.50 3.00 3.50 2.00 Sideboards 60.00 50.00 45.00 37.50 Tables : Dining 21.50 17.50 22.50 24.50 Dressing 37.50 32.25 21.50 35.25 Serving 13.50 11.00 14.50 10.50 Work 10.00 9.25 9.00 10.25 Wardrobes 20.50 25.25 15.50 21.75 Washstands 6.00 7.50 5.50 8.00 Each inventory may be worked owt jim times, using the above price lists. This work may be done by copying the data and making the extensions, or by making the extensions only and then totaling each inventory. WRITTEN REVIEW 81 Inventories 7 Bureaus 19 Bedsteads 12 Chifeoniers 5 Dressing Tables 21 Washstands 8 Mattresses 23 Pillows 6 Bookcases 3 Davenports 13 Lounges 17 Easy Chairs 7 Morris Chairs 5 Parlor Suites 8 Music Cabinets 12 Piano Chairs 15 Parlor Cabinets 5 Sideboards 13 Dining Tables 8 China Cabmets 4 Serving Tables 9 Work Tables 12 Dinner Trays 4 Medicine Cabinets 8 Wardrobes 11 Cheval Mirrors 15 Ottomans 12 Footrests 5 Hall Racks 6- Roll-top Desks 3 Flat-top Desks 9 Typewriter Desks 8 Typewriter Chairs 8 Bureaus 17 Bedsteads 15 Chiffoniers 3 Dressing Tables 18 Washstands 11 Mattresses 21 Pillows 5 Bookcases 4 Davenports 12 Lounges 20 Easy Chairs 3 Morris Chairs , 6 Parlor Suites 10 Music Cabinets 11 Piano Chairs 21 Parlor Cabinets 2 Sideboards 16 Dining Tables 5 China Cabinets 6 Serving Tables 7 Work Tables 15 Dinner Trays 8 Medicine Cabmets 5 Wardrobes 14 Cheval Mirrors 12 Ottomans 17 Footrests 7 Hall Racks 4 Roll-top Desks 2 Flat-top Desks 10 Typewriter Desks 6 Tjrpewriter Chairs 82 PEACTICAL BUSINESS AEITHMETIC 3. 8 Bureaus 15 Bedsteads 14 Chiffoniers 4 Dressing Tables 19 Washstands 12 Mattresses 18 Pillows 8 Bookcases 5 Davenports 16 Lounges 22 Easy Chairs 6 Morris Chairs 7 Parlor Suites 11 Music Cabinets 14 Piano Chairs 12 Parlor Cabinets 6 Sideboards 10 Dining Tables 7 China Cabinets 6 Serving Tables 8 Work Tables 11 Dinner Trays 7 Medicine Cabinets 9 Wardrobes 13 Cheval Mirrors 19 Ottomans 12 Footrests 6 Hall Racks 8 Roll-top Desks 4 Flat-top Desks 14 Typewriter Desks 10 Typewriter Chairs 4. 9 Bureaus 13 Bedsteads 11 Chiffoniers 7 Dressing Tables 17 Washstands 9 Mattresses 23 Pillows 6 Bookcases 3 Davenports 21 Lounges . 18 Easy Chairs 9 Morris Chairs 4 Parlor Suites 9 Music Cabinets 13 Piano Chairs 18 Parlor Cabinets 4 Sideboards 12 Dining Tables 9 China Cabinets 5 Serving Tables 11 Work Tables 14 Dinner Trays 5 Medicine Cabinets 7 Wardrobes 17 Cheval Mirrors 15 Ottomans 18 Footrests 3 Hall Racks 5 Roll-top Desks 6 Flat-top Desks 11 Typewriter Desks 7 Typewriter Chairs WRITTEN EEVIEW 83 12 Bureaus 23 Bedsteads 13 Chiffoniers 8 Dressing Tables 16 Washstands 14 Mattresses 22 Pillows 4 Bookcases 4 Davenports 17 Lounges 14 Easy Chairs 12 Morris Chairs 10 Parlor Suites 14 Music Cabinets 17 Piano Chairs 22 Parlor Cabinets 7 Sideboards 14 Dining Tables 4 China Cabinets 11 Serving Tables 5 Work Tables 19 Dinner Trays 6 Medicine Cabinets 12 Wardrobes 20 Cheval Mirrors 11 Ottomans 21 Footrests 4 Hall Racks 12 Roll-top Desks 5 Flat-top Desks 13 Typewriter Desks 12 Typewriter Chairs 6. 14 Bureaus 21 Bedsteads ' 16 Chiffoniers 11 Dressing Tables 14 Washstands 15 Mattresses 17 Pillows 7 Bookcases 7 Davenports 19 Lounges 25 Easy Chairs 11 Morris Chairs 9 Parlor Suites 12 Music Cabinets 21 Piano Chairs 16 Parlor Cabinets 9 Sideboards 18 Dining Tables 6 China Cabinets 9 Serving Tables 10 Work Tables 13 Dinner Trays 10 Medicine Cabinets 15 Wardrobes 16 Cheval Mirrors 19 Ottomans 14 Footrests 8 Hall Racks 9 Roll-top Desks 8 Flat-top Desks 7 Typewriter Desks 15 Typewriter Chairs 84 PEACTICAL BUSINESS AEITHMETIC 19 Bureaus 21 Bedsteads 11 Chiffoniers 9 Dressing Tables 15 Washstands 11 Mattresses 24 Pillows 9 Bookcases 6 Davenports 22 Lounges 12 Easy Chairs 8 Morris Chairs 9 Parlor Suites 14 Music Cabinets 9 Piano Chairs 17 Parlor Cabinets 3 Sideboards 13 Dining Tables 4 China Cabinets 11 Serving Tables 13 Work Tables - 24 Dinner Trays 6 Medicine Cabinets 13 Wardrobes 14 Cheval Mirrors 6 Ottomans 8 Footrests 11 Hall Racks 3 Roll-top Desks 7 Flat-top Desks 16 Typewriter Desks 9 Typewriter Chairs 8. 17 Bureaus 20 Bedsteads 16 Chiffoniers 6 Dressing Tables 21 Washstands 15 Mattresses 25 Pillows 10 Bookcases 2 Davenports 16 Lounges 8 Easy Chairs 13 Morris Chairs 3 Parlor Suites 10 Music Cabinets 7 Piano Chairs 22 Parlor Cabinets 5 Sideboards 9 Dining Tables 10 China Cabinets 7 Serving Tables 17 Work Tables 21 Dinner Trays 9 Medicine Cabinets 11 Wardrobes 18 Cheval Mirrors 9 Ottomans 10 Footrests 12 Hall Racks 2 Roll-top Desks 9 Flat-top Desks 10 Typewriter Desks 11 Typewriter Chairs \ CHAPTER VIII AVERAGE ORAL EXERCISE 1. A earns $ 3, B earns $ 4, and C earns $ 5 per day. What do the three earn in 1 da.? If $12 were paid to these men in equal parts, how much would each receive ? 2. What sum is intermediate between 6, 7, and 8 ? between 6, 8, and 10 ? between 6, 12, and 18 ? 111. The process of finding a number that is intermediate between two or more other numbers is called average. 112. Example. What is the average weight of 3 bales of cotton weighing 460, 449, and 475 lb., respectively? Solution. The aggregate of the 3 bales of cotton is 1384 lb. 1384 lb. divided into three equal parts shows the mean or average 449 weight to be 4611 lb. 475 To find the average of consecutive numbers, add the highest 3"\J384 number to the lowest, and divide by 2. r^ ^ o WRITTEN EXERCISE 1. A tapering board is 14 in. wide on one end and 18 in. on the other. What is the average width of the board? 2. A manufacturing pay roll shows that 15 hands are em- ployed at il.25 per day, 12 hands at 81.75 per day, 16 hands at 12.25 per day," 32 hands at 12.50 per day, and 5 hands at 16.50 per day. Find the average daily wages. 3. A merchant's sales for a year were as follows : January, $12,156; February, $14,175; March, 116,152; April, 112,175 ; May, 112,465.95; June, 112,476.05 ; July, 115,145.40 r August, 112,431.46; September, 117,245.90; October, $18,256.45; November, $19,250.65; December, $19,654.20. What were his average sales per month? 86 86 PRACTICAL BUSINESS ARITHMETIC 4. In a certain school of 300 pupils, 85 are 14 yr. of age ; 50, 15 yr. of age ; 25, 16 yr. of age ; 75, 17 yr. of age ; 50, 18 yr. of age; 15, 19 yr. of age. What is the average age of the school? 5. The attendance for a certain school for a week was as fol- lows : Monday, 727 pupils ; Tuesday, 732 pupils ; Wednesday, 756 pupils ; Thursday, 761 pupils ; Friday, 734 pupils. What was the average daily attendance for the week ? 6. What should a ground feed made from 50 bu. of oats worth 38^ per bushel, 30 bu. of barley worth ISj^, and 60 bu. of corn worth 69^ sell for in order to make 10^ per bushel on each ingredient used to make the mixture ? 7. Find the aggregate weight and the average weight per box of 100 bx. of cheese weighing Q.% 64, 62, 60, 61, 65, 62, 64, 61, 62, 61, 60, 60, 61, 62, 60, 68, Q5, 6Q, 64, 62, 61, 6.% 6Q, 62, 64, 67, 58, 62, 59, 59, 60, 62, 64, 66, 67, 58, 60, 65, 58, 62, 69, 62, 65, 68, 69, 61, 65, 62, 61, 65, 68, 59, 62, 64, 58, 62, 65, 71, 70, 58, 67, 58, 62, 64, 58, 62, 64, 65, 69, 65, 65, 62, 64, 60, 60, 65, 60, 65, 65, 62, 60, 62, 64, 60, 72, 64, 70, 61, 62, 60, 60, 59, 65, 60, 70, 58, 62, 61, 64 lb., respectively. 8. Counting 8 hr. to a day, find the total amount and the average daily wages in the following contractor's time sheet : Time Sheet for Week Ending June Name M. T. w. T. F. s. Hours Days Daily Wages A MO TNT C. E. Ames 8 8 8 8 8 8 $1.75 W. 0. Bye 9 10 9 10 10 8 2.00 M. E. Carey 10 9 9 10 8 10 2.00 W. D. Frey 6 8 9 10 7 8 2.25 G. W. Jones 10 10 10 8 10 8 2.25 D. 0. Munn 4 4 4 6 8 6 2.50 E. H. Post 6 6 6 6 4 4 3.00 L. C. Roe 10 10 10 10 4 4 3.25 J. H. Small 6 8 8 10 12 12 3.25 H. M. Young 8 8 8 8 8 8 3.50 Total CHAPTER IX CHECKING RESULTS 113. It has been seen in the preceding exercises on statis- tics, time sheets, etc., that various ruled forms provide for prac- tical and convenient methods of checking results. While- it is possible to give a great variety of these problems it is also necessary to give a great many problems that do not furnish such a check. 114. It is very important that all results be checked. The most common methods of checking addition, subtraction, and division have already been mentioned. Multiplication may be proved by dividing the product by either factor, or as explained on page 52. The properties of 9 and 11 may also be applied to advan- tage in checking results, especially results in multiplication and division. PROPERTIES OF 9 AND 11 Properties of 9 115. Any number of lO's is equal tg the same number of 9's plus the same number of units ; any number of lOO's is equal to the same number of 99's plus the same number of units ; any number of lOOO's is equal to the same number of 999's plus the same number of units ; and so on. Thus, 10 = one 9 + 1 ; 40 = four 9's + 4 ; 100 = one 99 + 1 ; 300 = three 99's + 3 ; 500 = five 99's + 5. 116. Any number may be resolved into one less than as many multiples of 10 as it contains digits. Thus, 946 = 900 + 40 + 6 ; 42175 = 40000 + 2000 + 100 + 70 + 5. 87 88 PRACTICAL BUSINESS ARITHMETIC 117. The excess of 9's in any power of 10 or in any multiple of a power of 10 is the same as the significant figure (unless that figure is 9, then there is no excess) in that number. Hence, The excess of O's in any number is equal to the excess of 9*s in the sum of its digits. Thus, the excess of 9's in 241 =2 + 4 + 1, or 7. The excess of 9's in 946 = 9 + 4 + 6, or 19; but 19 contains 9, and the excess of 9's in 19 = 1 + 9, or 10; hut 10 contains 9, and the excess of 9's in 10 = 1 + 0, or 1; the excess of 9's in 946 is therefore shown to be 1. 118. In finding the excess of 9's in any number, omit all 9's and all combinations of two or three digits which it is seen at a glance will make 9 or some multiple of 9. Thus, in finding the excess of 9's in 9458, begin at the left, reject the first digit 9, the sum of the next two digits, 9, and the single 8 will be the excess of 9's in the entire number. Properties of 11 119. Any number of lO's is equal to the same number of ll's minus the same number of units; any number of lOO's is equal to the same number of 99's plus the same number of units ; any number of lOOO's is equal to the same number of lOOl's minus the same number of units ; and so on. Thus, 40 = four ll's - 4; 500 = five 99's + 5; 7000 = seven lOOl's - 7. 120. It is therefore clear that even powers of 10 are multiples of 11 plus 1 and odd powers of 10 are multiples of 11 minus 1. Thus, 102 or 100 = nine ll's + 1 ; lO^ or 1000 = ninety-one ll's - 1 ; 10* or 10,000 = nine hundred nine ll's + 1. 121. From the foregoing it is evident that : The excess oflfs in any number is equal to the sum of the digits in the odd places (increased by 11 or a multiple of 11 if necessary') minus the sum of the digits in the even places. Thus, the excess of ll's in 45 is 1 (5 — 4) ; the excess of ll's in 125 is 4 (5 - 2 + \^^)) ; the excess of ll's in 2473 is 9 (3 + 4 + 11 - 7+2 = 9); the excess of ll's in 14,206 is 5. D4» = 217 = 8 451 = 688 = 6 CHECKING RESULTS 89 Checking Addition and Subtraction 122. Examples, i. By casting out the 9's, show that the sum of 935, 651, 782, and 465 is 2833. Solution. The sum of the digits in 935 is 17 ; but since 17 935 = 8 contains 9, find the sum of the digits in 17 and the result, 8, is the (?c-i _ o excess of 9's in the entire number. In like manner find the ex- cess of 9's in 651, 782, and 465. Since 935 is a multiple of 9 + 8, ' ^"^ = ^ 651 a multiple of 9 + 3, 782 a multiple of 9 + 8, 465 a multiple of 465 = 6 9 + 6, the sum of these numbers, 2833, should equal a multiple of 2833 = 7 9 4- (8 + 3 + 8 + 6), or 9 + 25. 25 is a multiple of 9 + 7, and 2833 is a multiple of 9 +7 ; hence, the addition is probably correct. 2. By casting out the ll's, show that the sum of 648, 217, 451, and 688 is 2004. Solution. 8-4 + 6-0 = 10, the excess of ll's in 648. 7Tri4.2^ro=8, the excess of ll's in 217. 12 (11+ 1) -5 + 4 — = 11 ; but 11 contains 11, hence, the excess of IPs in 451 is 0. 8 - 8 + 6^^ = 6, the excess of ll's in 688. Since 648 is a multiple of 11 + 10, 217 a multiple of 11 + 8, 451 a multiple of 11, and 688 a multiple of 11 + 6, the sum of these numbers, 2004, 2004 = 2 should be a multiple of 11 + (10 + 8+6), or 11 + 24. 24 is a multiple of 11 + 2 and 2004 is a multiple of 11 + 2; hence, the addition is probably correct. 123. Subtraction may be proved either by casting out the 9's or ll's in practically the same manner as addition. The difference between the excess of 9's or ll's in the minuend and sub- trahend should equal the excess of 9's or ll's in the remainder; or the sum of the excess of 9's or ll's in the subtrahend and remainder should equal the excess of 9's or ll's in the minuend. These methods are but little used for checking addition and subtraction. Addition is generally checked as explained on page 20, and subtraction as explained on page 32. On the other hand, long multiplications and divi- sions are almost always checked by applying the properties of 9 or 11. Checking Multiplication and Division 124. Examples, l. By casting out the 9's show that the product of 64 x 95 is 6080. Solution. The excess of 9's in 95 is 5, and in 64, 1. Since 95 95 = 5 is a multiple of 9 + 5 and 64 a multiple of 9+1, the product of fiA_i 64 X 95 should be a multiple of 9 plus (1x5). 1 x 5 or 5 equals — "" _ . the excess of 9's in 6080 ; hence, the work is probably correct. 6080 = 5 90 PRACTICAL BUSINESS ARITHMETIC 2. By casting out the ll's show that the product of 46 x 95 is 4370. Solution. The excess of ll's in 95 is 7, and in 46, 2. Since 95 = "J 95 is a multiple of 11 + 7 and 46 a multiple of 11 + 2, the prod- Ar — uct of 46 X 95 should be a multiple of 11 plus (2 x 7) or 14; but -^77- ~ - 14 is a multiple of 11 + 3. Since the product 4370 is a multiple of 4370 = 3 11 + 3, the work is probably correct. 125. Division may be proved either by casting out the 9's or ll's in practically the same manner as multiplication. The excess of 9's or ll's in the quotient multiplied by the excess of 9's or ll's in the divisor should equal the excess of 9's or ll's in the dividend, minus the excess of 9's or ll's in the re- mainder, if any. Casting out the 9's will not show an error caused by a transposition of figures; but casting out the ll's will show such an error. The method of casting out the ll's is therefore considered the better proof. WRITTEN EXERCISE 1. Determine without dividing whether 82.64 is the quo- tient of 11375.44-521. 2. Determine without multiplying whether $1807.50 is the product of 482 times $3.75. 3. Determine without adding whether 4231 is the sum of 296, 348, 924, 862, 956, and 845. 4. Multiply 34,125 by 729 in two lines of partial products and verify the work by casting out the 9's. 5. Find the cost of 173,000 shingles at 14.27 per thousand, in two lines of partial products, and verify the work by casting out the ll's. 6. Find the cost of 126,000 ft. of clear pine at 124.60 per thousand, in two lines of partial products, and verify the work by casting out the 9's. 7. Find the cost of 2,191,000 ft. of flooring at $32.08 per thousand, in two lines of partial products, and verify the work by casting out the ll's. FRACTIONS CHAPTER X DECIMAL FRACTIONS ORAL EXERCISE 1. In the number 17.62 what figure stands for the dollars? the tenths of a dollar? the hundredths of a dollar? 2. What name is given to the point which separates the whole number of dollars from the part of a dollar ? 3. Read: 3.5 dollars; 3.5 ft.; 27.5 1b.; .7 of a dollar; .5 of a ton; 16.6; .9; 9.25 dollars; 7.25 ft.; 8.75 rd.; .95 of a dollar; .85 of a pound sterling ; .57. 4. What is the first place at the right of the decimal point called ? the second place ? 5. In the accompanying diagram what part of ^ is ^ ? What part of ^ is (7? What part of C is i>? 6. What part of A is (7? What part of ^ is D? 7. If J. is a cubic inch, what is jB? C? i>? 8. In a pile of 10,000 bricks one brick is what part of the whole pile? 10 bricks is what part of the whole pile? 100 bricks is what part of the whole pile? 1000 bricks is what part of the whole pile ? 9. How may one tenth be written besides ^^q? one hun- dredth besides y^^ ? one thousandth besides i-qq-q ? 126. Units expressed by figures at the right of the decimal point are called decimal units. 127. A number containing one or more decimal units is called a decimal fraction or a decimal. 91 92 PKACTICAL BUSINESS AKITIOIETIC IfOTATIOX AND XUMEKATIOy ORAL KTIBCBgC 1. Read : 0.7 ; 0.03 ; 0.25. How manj jdiftoeB most be used to express completelj any number of hundredths? 2. Read: 0.004; 0.025; 0.725. How many places must be used to express (XMnj^^ely any number of thousandths? 3. Read: .0005; .00007; .000009; .0037; .00045; .000051; .0121; .00876; .000218; .1127; .01525; .0O45S1; .16067. 4. How many places must be used to express oompletely any number of ten>thousandths? any numb^ of hundred-thou- sandths? any number of millionths? 128. In leadmg detwiate pranoiiiiee tiie woid mad at the dedmal pmnt and omit it in all oth^r j^bees. OUSOS or Mo SMY six imtdredjhe say «ur kmmdnd mdJoM The relaticm of integers and decimals with their increas- ii^ and decreasing orders to the left and to the right of the deeimal point is shown in the f (blowing NuMEBATiox Table I 4 £ * 98 7. 654, 321.234 667 130. Hundredths are frequently referred to as per cent, a phrase originally meaning hy tke immdrwd* 131. The symbol % stands for hundredUis and k read jMr«i9il. 49% = .i5; iS%Q{»uanlnr=.4SQfiL DECliMAL FRACTIONS 93 ORAL EXERCISE Read : 1. 0.073. 5. 532.002. 9. 31.08%. 2. 0.00073. 6. 60.0625. 10. 126.75%. 3. 3004.025. 7. 63.3125. ii. 2150.1875. 4. 300.4025. 8. 126.8125. 12! 3165.00625. 13. 131.3125 T. 15. A tax of 1.0625 mills. 14. 240.0125 A. 16. A tax of 9.1875 mills. 17. Read the number in the foregoing numeration table. 18. Read the following, using the words " per cent " : .17; 28; .85; .67; .425; .37 J. 19. Read the following as decimals, not using the words ''percent": 25%; 75%; 87%; 62^ % ; 27.15%. 20. Read aloud the following : a. The value of a pound sterling in United States money is 84.8665. h. A meter (metric system of measures) is equal to 39.37079 in.; a kilometer, to 0.62137 mi. c. 1 metric ton is equal to 1.1023 ordinary tons ; 1.5 metric tons are equal to 1.65345 ordinary tons. d. A flat steel bar 3 in. wide and 0.5 in. thick weighs 5.118 lb. e. The circumference of a circle is 3.14159 times the length of its diameter. WRITTEN EXERCISE Write decimally : 1. Five tenths ; fifty hundredths ; five hundred thousandths. 2. Nine hundred and eleven ten-thousandths ; nine hundred eleven ten-thousandths; five hundred and two thousandths. 3. One hundred seventy-four millionths; one hundred seventy-four million and seven millionths ; seven million and one hundred seventy-four millionths. 4. Seven thousand and seventy-five ten-thousandths; two hundred fifty-seven ten-millionths ; two hundred and forty-six millionths ; two hundred forty-six millionths. 94 PRACTICAL BUSINESS AEITHMETIC 5. Four million ten thousand ninety-seven ten-millionths ; four million ten thousand and ninety-seven ten-millionths; five hundred millionths ; five hundred-millionths. 6. Six hundred six and five thousand one hundred-thou- sandths; six hundred six and fifty-one hundred-thousandths; fifty-six and one hundred twenty-eight ten-billionths. 7. Seventeen thousand and eighteen hundred seventy-six millionths ; seventeen thousand and eighteen hundred seventy- six ten-thousandths ; twenty-one hundred sixteen hundredths. 132. In the number 2.57 there are 2 integral units, 5 tenths of a unit, and 7 hundredths of a unit. In the number 2.5700 there are 2 integral units, 5 tenths of a unit, 7 hundredths of a unit, thousandths of a unit, and ten-thousandths of a unit. 2.5700 is therefore equal to 2.57. That is. Decimal ciphers may he annexed to or omitted from the right of any number without changing its value. ORAL EXERCISE Mead the following (a) as printed and (h~) in their simplest decimal form : 1. 0.700. 3. 16.010. 5. 0.50. 7. 0.7000. 2. 5.2450. 4. 18.210. 6. 0.00950. 8. 12.9010. ADDITION ORAL EXERCISE 1. What is the sum of 0.4, 0.05, 0.0065? 2. What is the sum of 0.3, 0.021, 0.008 ? 3. Find the sum of seven tenths, forty-four hundredths, and two; of four tenths, twenty-one hundredths, and six thou- sandths. 133. Example. Find the sum of 12.021, 256.12, and 27.5. Solution. Write the numbers so that their decimal points 12.021 stand in the same vertical column. Units then come under units, ogg 1 o tenths under tenths, and so on. Add as in integral numbers and 07c place the decimal point in the sum directly under the decimal ' points in the several numbers added. 295.641 DECIMAL FEACTIONS 95 WRITTEN EXERCISE Find the sum of: 1. 7.5, 165.83, 5.12T, 6.0015, and 71.215. 2. 257.15, 27.132, 5163, 8.000125, and 4100.002. 3. 0.175, 5.0031, .00127, 70.2116001, and 21.00725. 4. 51.6275, 19.071, 0.000075, 21.00167, and 40,000.01. 5. 2.02157, 2.1785, 2500.00025, 157.2165, and 7.0021728. 6. Copy, find the totals as indicated, and check : $1241.50 19215.45 $1421.12 $1421.32 ? 1.52 1275.92 1.46.. 1618.40 ? 349.21 3725.41 2.18 1920.41 ? 2975.47 7286.95 7.96 10.20 ? 27.14 8276.92 14.21 41.64 ? 9218.49 7271.44 1240.80 126.18 ? 5.17 8926.95 7216.80 24.17 ? 12627.85 8972.76 4.75 240.20 ? 721.92 7214.25 8.16 960.80 ? 11.41 8142.76 .47 1860.45 ? 1.21 8436.14 .92 9270.54 ? .72 8435.96 9.26 75.86 ? 14178.21 7926.14 1490.75 45.95 ? 2172.14 9214.72 1860.54 75.86 ? 726.95 1241.16 9265.80 72.18 ? 85.21 4214.71 625.50 9260.14 ? 75.92 8726.19 240.75 1.20 ? 72604.25 2140.12 60.50 7.40 ? 124.61 7146.14 120.41 8.32 ? 2114.62 7214.86 4101.08 2860.14 l_ ? ? ? ? ? 7. Find the suni of twenty-one hundred sixty-five and one hundred sixty-five ten-thousandths, thirty-nine and twelve hundred sixty-five millionths, twenty-seven hundred thirty- six and one millionth, four and six tenths, six hundred and six thousandths, and six hundred sixty-five thousandths. 96 PRACTICAL BUSINESS AKITHMETIG SUBTRACTION ORAL EXERCISE 1. From the sum of 0.7 and 0.4 take 0.5. 2. From the sum of 0.07 and 0.21 take 0.006. 3. From seventy-four hundredths take six thousandths. 4. To the difference between .43 and .03 add the sum of .45 and .007. 5. Goods on hand at the beginning of a week, $24.50; goods purchased during the week, $35.50; goods sold during the week, $36 ; goods on hand at the close of the week, $36.50. What was the gain or loss for the week? 134. Example. From 14.27 take 5.123. Solution. Write the numbers so that the decimal points stand 14.27 in the same vertical column. The minuend has not as many places c -i oo as the subtrahend ; hence suppose decimal orders to be annexed ' until the right-hand figure is of the same order, then subtract as t^'.-L^:! in integers and place the decimal point in the remainder directly under the decimal points in the numbers subtracted. WRITTEN EXERCISE Find the difference between: 1. 7.2154 and 2.8576. 5. 9 and 5.2675. 2. 17.2157 and 1.0002. 6. 16 and 5.0000271. 3. 1.0005 and .889755. 7. .0002 and .000004. 4. $1265.45 and $87.99. 8. 24.503 and 17.00021.- 9. The sum of two numbers is 166.214. If one of the numbers is 40.21, what is the difference between the numbers? 10. The minuend is 127.006 and the remainder 15.494. What is the sum of the minuend, subtrahend, and remainder? 11. From the sum of ninety-nine ten-thousandths, one hun- dred lifty-one and five thousandths, two hundred fifty-two and twenty-five millionths, six tenths, and eighteen and one hun- dred seventy-five thousandths take the sum of twelve hundred fifteen millionths, and one hundred eighty-eight thousandths. DECIMAL FRACTIONS 9V 12. From the sum of two hundred fifty-seven thousandths and eight and one hundred twenty-six millionths take the sum of five hundred ten thousandths and two and one hundred twenty-four ten-thousandths. 13. A merchant had, at the beginning of a year, goods amounting to 18165.95. During the year his purchases amounted to $5265.90 and his sales to 19157.65. At the close, of the year he took an account of stock and found that the goods on hand were worth 17216.56. What was his gain or loss for the year ? 14. A provision dealer had on hand Jan. 1, goods worth 14127.60. His purchases for the year amounted to $4165.95 and his sales to $6256.48. Dec. 31 of the same year his in- ventory showed that the goods on hand were worth $3972.50. If the amount paid for freight on the goods bought amounted to $237.50, what was his gain or loss on provisions? 15. I had on hand Jan. 1, lumber amounting to $4210.60. During the year my purchases amounted to $3126.50, and my sales to $4165.85. I lost by fire lumber valued at $506.75, for which I received from an insurance company $500. Dec. 31, my inventory showed the lumber to be worth $5209.08. How much did I gain or lose on lumber during the year? 16. At the beginning of a year my resources were as follows: cash on hand, $1262.50; goods in stock, $1742.85; account against A. M. Eaton, $146.50. At the same time my liabili- ties were as follows: note outstanding, $156.85; account in favor of Robert Wilson, $521.22. During the year I made an additional investment of $1250.65, and withdrew for private use $275. I sold for cash during the year goods amounting to $1250.75, and bought for cash goods amounting to $530.90 ; I also paid Robert Wilson $320 to apply on account. At the close of the year my inventory showed goods in stock valued at $750.48. What was my gain or loss for the year and my pres- ent worth at the close of the year ? Do not fail to check all problems. No phase of arithmetic is more important. 98 PRACTICAL BUSINESS ARITHMETIC MULTIPLICATION ORAL EXERCISE 1. How many times .4 is 4 ? .77 is 7.7 ? .999 is 9.99? 2. 44 is how many times .44? 22 is how many times .022? 1 is how many times .001 ? .01 is how many times .0001 ? 3. Read aloud the following, supplying the missing terms : Removing the decimal point one place to the right multi- plies the value of the decimal by ; two places, the value by ; three places, the value by . 4. Multiply 12.1252 by 1000 ; by 100 ; by 100,000. 5. Multiply 19.375 by 100 ; by 10,000 ; by 100,000. 6. Multiply 5.15 by 10; by 100; by 1000 ; by 10,000. 7. Multiply .000016 by 1000; by 100,000 ; by 1,000,000. 8. Multiply 167.50 by 10 ; by 100 ; by 1000 ; by 10,000. 9. Multiply .0037 by 10; by 100; by 1000; by 10,000,000. 10. What part of 1 is .1 ? of 7 is .7? of 29 is 2.9? 11. What part of 84 is .84? of 129 is 1.29? of 1275 is 12.75? 12. What part of .6 is .006 ? of .64 is .0064? Read aloud the following, supplying the missing terms : a. Each removal of the decimal point one place to the left the value of the decimal by 10. h. To divide a decimal by is to find one tenth (.1) of it, or to it by .1. 13. Give a short method for multiplying a number by .1 ; by .01; by .001; by .0001. 14. Multiply .009 by .1; by .01; by .001. 15. Multiply 217.59 by .1; by .01 ; by .001. 16. Multiply 54.65 by .01; by .00001; by .000001. 17. Multiply 2.375 by .1; by .01; by .001 ; by .0001. 18. Multiply 25.215 by .1; by .01; by .001; by .0001. 19. Multiply 2111 by .01 ; by .001 ; by .0001 ; by .00001. 20. Compare 2400 x $0.06 with 100x24x10.06 or with 24 X $6. 21. Compare 3000 x 612.251 with 1000 x 3 x 612.251, or with 3 x 612251. DECIMAL FRACTIONS 99 22. Multiply 21.25 by 2400. Solution. 2400 is 24 times 100. Multiply by 100 2125 2125 "by removing the decimal point two places to the right. qa oj^ The result is 2125. 24 times 2125 equals 51,000, the - ao^TT required product. ^^^^ ^^^^ In multiplying begin with either the lowest or the 4250 8500 highest digit in the multiplier as shown in the margin. 51000 51000 23. Formulate a brief rule for multiplying a decimal by any number of lO's, lOO's, lOOO's, etc. 24. Find the cost of : a. 500 lb. at 18^. d. 600 lb. at 29^. g, 900 lb. at 34^. b. 150 1b. at 14^. e. 300 1b. at 41^. h. 700 1b. at 51^. c. 200 lb. at 26^. /. 400 lb. at 121^. i. 1400 lb. at 5^. 135. Examples, l. Multiply 41.127 by 4. Solution. 41.127 is equal to 41,127 thousandths. 41,127 thou- 41.127 sandths multiplied by 4 equals 164,508 thousandths, or 164. -508. That 4 is, thousandths multiplied by a whole number must equal thousandths. 164.508 2. Multiply 41.127 by .04. Solution. The multiplier, .04, is equal to 4 times. 01 ; therefore, 41.127 multiply by 4 and by .01. Multiplying by 4, as in problem 1, the qa result is 164.508. Multiplying by .01, by simply moving the decimal -i nAcno point in the product two places to the left, the result is 1.64508. J-.o^OUo It will be seen that the number of deciiyial places in the product is equal to the decimal places in the multiplicand and multiplier. It should not be necessary to memorize the above rule. The student should know at a glance that the product of tenths and tenths is hundredths, of tenths and hundredths is thousandths, and so on. ORAL EXERCISE 1. In multiplying 24.05 by 3.14 can you tell before multiply- ing how many integral places there will be in the product? how many decimal places ? Explain. 2. How many integral places will there be in each of the fol- lowing products ; 2.5x4.015? 27.51x3.1416? 321.1 x 201.51? 1.421x42.267? 126.5 x .01? 1020x5.01? .105x6? 2.41 X 10.05 ? How many decimal places will there be in each of the above products ? 100 PKACTICAL BUSINESS AKITHMETIC 3. What are 400 bbl. of apples worth at |2.12 per barrel? at 11.27^^ per barrel? 4. I bought 60 lb. of sugar at 8 0.04 J and gave in payment a five-dollar bill. How much change should I receive ? 5. A and B are partners in a manufacturing business, A re- ceiving 52 % and B 48 % of the yearly profits. The profits for a certain year are 15000. Of this sum how much should A and B, respectively, receive ? 7. 2.531x31000. 8. .1724x18000. 9. .15539 X 2002. WRITTEN EXERCISES Find the product of : 1. 3.121x152. 4. 12.14x265. 2. 3121 X .152. 5. 9.004 x .021. 3. 31.21x15.2. 6. . 3121 X. 0152. 10. A man owned 75% of a gold mine and sold 50% of his share. What is the remainder worth if the value of the whole mine is $425,000? 11. A man bought a farm of 240 A. at $137.50 per acre. He sold 75% of it at 1 150 per acre, and the remainder at $175 per acre. What was his gain ? 12. Copy and complete the following table of statistics. Check the results. (The total yield multiplied by the price per bushel should equal the total valuation.) Largest Wheat-growing States in a Recent Year State Yield in Bushels Farm Price PER Bushel Farm Valuation North Dakota Kansas Minnesota South Dakota 143,820,000 92,290,000 67,038,000 52,185,000 92.4^ 92.4^ 92.4^ 92.4 j^ ? ? ? ? Total ? 9 ? 13-15. Make and solve three self-checking problems in multi- plication of decimals. DECIMAL FRACTIONS U r7- dy :^ ^--^- -1(2.^^. / l.r^i^ -J^. ':&2^^^1^^^y^^ 2y? ^^^J?^/ c^c^(? '^.^g: ; 3 v^7f?7fi ^ ^ /z- :^/ ^ ^t ^ 7-S'C> ( ? 2^ /^'-L^^7/: fT-CCC^ j^\' ^ /J 108 PRACTICAL BUSINESS ARITHMETIC Buying and Selling by the Ton of 2000 Pounds oral exercise 1. Compare 8000 -;- 2000 x 8 with 8000 -^ 1000 x 4. 2. Compare 7000 -- 2000 x 18 with 7x9. 3. Find the cost of 4250 lb. coal at 1 8 per ton. Solution. 4250 lb. is 4.25 times 1000 lb. If the cost of 2 thou- 4.25 sand pounds is $8, the cost of 1 thousand pounds is $4. Since 1 thousand pounds of coal cost $ 4, 4.25 thousand pounds will cost 4.25 4 times §4,- or 117. 17.00 WRITTEN EXERCISE 1. At $9 per ton, find the cost of the hay in the following weigh ticket. Also find the cost at 88.75 per ton. SCALES OF E. H. ROBINSON & CO. N0..2J22 y9y^^' ^•'^■• From y^K yJA^J^^^T^^A^^ To_ Gross .weight Jj^ J^ / /O lb. Tare / ^ ^ ^ Ih. Net weight Xa^jT^^^ 1h 3^^^=^^ Weigher 2. At 17.50 per ton find the cost of the coal in the fol- lowing weigh ticket. Also find the cost at $6.95 per ton. WELLINGTON ^WILD COAL. CO, 126 Main Street, Rochester, N.Y. j-___ ~^ ^ Tenmaier //Z^r^^i^^-y-?^ Received h,j t..lY\. W rrXH/yx h^* 7. Reduce | and | to fractions having the denominator 24. 122 PEACTICAL BUSINESS ARITHMETIC To Lowest Terms ORAL EXERCISE 1. 2 J equals how many thirds? |^ equals how many halves? 2. Name the largest possible unit frac- tion. Why is this the largest possible unit fraction ? 3. Change -f^ to the largest possible unit fraction ; y^g ; j-^q', 2V0' iWo^* Express ^| in its simplest form. Reduce 2%% to its lowest terms. 161. A fraction is reduced to its lowest terms when the numerator and denominator are changed to numbers that are mutually prime. 162. Example. Reduce -^^^ to its lowest terms. Solution. 6 is a common factor of 96 and 108 ; dividing both terms by 6, the result is {|. 2 is a common factor of _.0= 1^ = 8. 16 and 18 ; dividing both terms by 2, the result is |. ORAL EXERCISE 1. Reduce to fifteenths: J, -|, f, |- 2. Reduce to eighths : 2^^, h h Ih ih h 3. Reduce to fiftieths: 1 |, y2_4_ _.t_^ _8_^ _.u_ 4. Change to twentieths : |, 3^, f , |, i -^%, |. 5. Reduce to lowest terms : ^^g, -^q. -f^^ l|, -^^^ ^. WRITTEN EXERCISE 1. Reduce to sixteenths : llf , l|^, |, |f , |, iff 2. Reduce to lowest terras: -^^^^ cu. ft., ^4_8_ ^^^ _i4_8_ x. 3. Reduce to lowest terms: lj§ mi., Xi-|f, |ff^ lb., |f mi. 4. Reduce to three-hundred-twentieths: -J mi., | mi., ^^ mi. 5. Reduce to their simplest common fractional form : |^||^ T., an T., ^^ A., l|i A., 11^ sq. mi., Ill sq. mi., ||f mi. 83J. 4. 666|. 7. 2655V- 10. 3150|. 166|. 5. 180^. 8. 319j5j. 11. 1625J. 333J. 6. 212J,. 9. 14611. 12. 2150^2 COMMON FRACTIONS 123 Integers and Mixed Numbers to Improper Fractions oral exercise 1. How many quarts in 1 gal.? in 3 gal.? 2. How many sixths in 1? in 3? in 5? in 7? 3. How many fifths in 1? in 1|^? in 1|? in 3J? 4. Express as fourths : 6^, 12|, 13, 87, 64, 281. 5. Express as eighths : 15, 12, lOJ, 1^, 2f, If, ^. 6. Express as halves : 27, 14,301,^1711 1821 249. WRITTEN EXERCISE Reduce to improper fractions : 1. 2. 3. Improper Fractions to Integers or Mixed Numbers ORAL exercise 1. How many pecks in 240 qt.? ^|^ = ? 4" = ? 2. Change to integers: If^, 1|^ -W, %»-, ^^^ ^^K 3. Express 28 J as fourths ; express ^^ as a mixed number. 4. Change to mixed numbers: ^{^, ij^, 1-f^, -IfJ^, ^^. 5. What is the value of : ^-ff- lb.? -\2.8 ib.? i| 1 bu.? ^^ pk.? W ft.? -m'- A.? m mi.? 4<1 lb.? fll sq. ft.? written exercise Reduce to integers or mixed numbers: 1 8 5^ rni 4 iJ_2_8. A 7. ^#^ lb. ■■■• 32 ^"^* 16 -^^ '• 16 ^^' 2. -\^3^ A. 5. IIU T. 8. fill CU. ft. 3. imT. . 6. IflfT. 9. -%Y/sq.mi. 163. When expressing final results reduce all proper frac- tions to their lowest terms and all improper fractions to integers or mixed numbers. 124 PRACTICAL BUSINESS ARITHMETIC To Least Common Denominator ORAL EXERCISE 1. How many pounds in 1 T. 500 lb. ? 5 T. + 1000 lb. = ? lb. 5 T. 1000 lb. = ? T. 2. How must numbers be expressed before they can be added or subtracted? 3. 1 = ? • 1 -L 3 = ? 1 = _?L. 1 TL — _?_ . i — ? . 1 _ 1 _ ? ''•2 ¥'2^8 "4 16'1 16~16'3~~6'3 6"' 4. What kind of fractions can be added or subtracted ? 5. Express | as sixteenths. Add | and -^q ; J and -^^ ; | and |. 6. Express ^ as eighths. Subtract J and | ; i and -^^ ; | and Jg. 164. Two or more fractions whose denominators are the same are said to have a common denominator; if this denominator is the smallest possible, the fractions are said to have a least common denominator. Two or more fractions having the same denominator are sometimes called similar fractions. ORAL EXERCISE Change to similar fractions : 1. 2. 3. 4. ■O' xv o WRITTEN EXERCISE Change to fractions having the least common denominator hi- 6. 4^i- 11. hi- 16. h h i- ii- 7. hi 12. h^- 17. h h h hh 8. hi- 13. h i\- 18. 115 hh 9. hi- 14. h i\- 19. h h 1- I'A- 10. hi- 15. h A- 20. h h l\ 1. 1' A' il 5. 6' 1' t\' 32' 9. iV' h f ' A- 2. *' iV A- 6. h 5' ^6' A- 10. ih A' h a- 3. i' h 1' 4- 7. i'lV'A'H- 11. AV f ' tVV' f • 4. 1' h iV f • 8. A' A' 1^2' h 12. eVo' tV A' A Change the fractions to form for addition or subtraction : 13. 31^5, 7t-V 14. I34J5, 112^. 15. 6126^,178^5. COMMOK FRACTIONS 125 ADDITION 165. It has been seen that only like numbers and parts of like units can he added. ORAL EXERCISE State the sum of: 1. |, |, f. 7. 21, 3|, 12^, 191. 2. i |, i. ■ 8. 51, 12^, 7J, lOJ. 3. I, f, f 9. 7|, 2|, 81, IJ, 21. *• A' fi- A- 10- 2J, 5f, 8J, 12^, 10|. 5- i i *, h i- 11- 11' W|, 15J, 18i, 121 6- iV' A- iV' !%• 12- SiV' 2-/j, IJj, 8^^, S^lg. ^^ horizontal addition find the sum of: 13. 2 pieces of gingham containing 41^ and 43^ yd. In the dry-goods business fourths (quarters) are very common fractions. They are usually written without denominators by placing the numerators a little above the integers. Thus, 51^ equals 51^, 54^ equals 541 (54^), and 528 equals 52f . 14. 4 pc. stripe containing 42^, 38^ 40^, and 49 yd. 15. 3 pc. fancy plaid containing 42^, 40^, and 41 yd. 16. 4 pc. duck containing 48^, 47^, 46^, and 402 j^^ 17. 2 pc. monument cotton containing 54^ and b3^ yd. 18. 4 pc. dress silk containing 32^, 34^, 353, ^nd 322 y^^ 166. Examples, l. Find the sum of ^ and |. Solution. | and | are not similar fractions ; 1. c. m. of 8 and 5 = 40 hence, make them similar by reducing them to 7 __ 3 5. . 2 IQ. equivalent fractions having a least common de- q «5 ^ 16^^ s l^ ~-i 1 1 nominator. | = f^ and f = i§. fs + ^ = s i 10+10=10 = ^17 2. Find the sum of 56^, 34^, 52f . Solution. By inspection determine the least common 561 = 8 denominator of the given fractions ; then make the frac- o j^ i^ _ o tions similar and add them, as shown in the margin. ^ The result is 1 ^V, which added to the sum of the inte- 1 = ir. gers equals 143^\, the required result. -^"^^ A f 1 = -^ A* 126 PRACTICAL BUSINESS ARITHMETIC WRITTEN EXERCISE Find the sum of: 1. ^^,|. 7. 12|,172,V 3. 21, 17^. 9. 52|, 591, 57|, 52Jg. 4. 121 19^V 10. 60f, 18f, 21^5_ i42J^. 5. 1,4^,191. 11. 20^,121,181,921,753. 6. 21, 4f, 25^%. 12. 140f, 2601, 1451, 216|, 3901. 13. A carpet dealer sold at different times 125| yd., 272^ yd., 1691 yd., 186f yd., 241i yd., 265| yd., 296| yd., and 314| yd. of Axminster carpet, at 12.65 per yard. If it cost him $2.45 per yard, what was his gain? 14. A dry-goods merchant bought 50 pc. of dress silk at m per yard. If the pieces contained 42^, 43^, 442, 47^, 44^, 452, 403, 462^ 451^ 42, 471, 482, 40^, 40i, 402, 40a 592^ 493, 472^ 433, 403, 451, 402, 452^ 442^ 473^ 462, 411^ 513^ 423^ 532, 572^ 531, 511, 433, 472^ 401, 452^ 452^ 403^ 401, 453, 472, 481, 511, 522^ 572^ 613, 602, 50i yd., respectively, and he sold the entire purchase at 11.25 per yard, what was his gain ? Short Methods in Addition oral exercise 1. -I" + i = Jf • Observe that the numerator of the sum is equal to the sum of the denominators in the given fractions. 2. -^ + 1^ = ? Give a short method for adding any two sim- ple fractions whose numerators are 1. 3. ^ + I = 1^1^. Observe that the numerator of the sum is equal to the sum of the denominators multiplied by the numera- tor of either of the given fractions. 4. I 4- 1 = ? Give a short method for adding any two frac- tions whose numerators are alike. 5. Find the sum of J, \, and 1* Solution, i 4- i = t\ ; tV + 3 = f ^^ the required result. COMMON FRACTIONS 127 State the sum of: 1. 2. 3. 4. 5. 6. 167, 2' 3 1 1 1[' "5 1 1 5' 6 1 1 y 8 1 1 3' 5 7. 8. 9. 10. 11. 12. ORAL EXERCISE h\- 13. h h 19. i f hi- 14. |,f 20. f ^• if 15. fi 21. h h h f *. 16. |,f. 22. h h h f.f 17. f, |. 23. h h f l-f. 18. f f 24. h i I The most common business fractions are usually small and of such a nature that they may be added with equally as much ease as integers. The following exercise will be found helpful to the student in learning to add these fractions in practically the same manner that he adds integers. 168. Example. Find the sum of y^g, |, |, and ^. Solution. By inspection determine that the least common denominator is 16. Then mentally reduce each fraction to 16ths and add as in whole numbers. Thus, 5, 7, 19, H, m OP AT, EXERCISE Find the «Mm o/".- ^ 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. i 1 i f k 1 i 1 i I f \ i i 1 1 i t i i i 1 1 1 1 3 1 1 1 J 2 6 6 10 3 ^ ^ J 6 3 1 i ^ i i i 1 i ji i 11. 12. 13. 14. 15. 16. 17. 18. . 19. 20. i t f \ \ I J i * 1 2 1 t 1 f 6 i 1 i 1 i i 1 1 f f 1 f i 1 2^ t 1 J i i i f J i I 1 -,v 1 f i 1 i i « % 1 3 1 f 1 5 6 5 1 _7_ ^ 10 TJ 6 ¥ ? 6 ^ 10 i f^ A 1 1 A 1 \ i A i T^ A i f iJ -h I i i Hi 128 PRACTICAL BUSINESS ARITHMETIC Exercises similar to the foregoing should be continued until the student can name the successive results in the addition without hesitation. 169. The ordinary mixed numbers that come to an accountant should be arranged for addition practically the same as in- tegers. In adding, the fractions should be combined first and then the integers. 170. Example. Find the sum of 2^ 5^, and 3|. Solution. By inspection determine that the least common denomi- ni nator of the fractions is 8. Mentally find the sum of the fractions and 5 the result is If. Add this result to the integers and the entire sum is 11|. ^R iif ORAL EXERCISE State the sum of: 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 2J 3J Si 8J iq 5| 4i 2| 31 14i 3J2|^7|-17|13|-7JWfl7i 16f 1/ 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 9| 5| 11 If 8i 4| 5J 41 4^ 41 101 4i 2f 6| 3| 21 2| 5| 2| If 13i IIJ ^^ 51 2J, 4J 41 6f 6t 7| lOi I2J5 8Jj 13| 4J^ 3f 6| 2J 3^3^ 12J 21. 22. 23. 24. 25, 26. 27. 28. 29. 30. H H ^ H 8i 4| 5f n H H 5i ^ 2f ^ 6| 2i IJ H H 6| 3| 5f 2f 2f H H 91 7f H H H 5f 7f 6| 2| H 4* 5* n ^ H 1| 1} H Si H n 2f n 8f H H 2f 2f 5i H H 7^ H 2i H 4i 81V 3|- 2i H 2| 9| Hj> 61 H 2t^ 8^J 13f 5A H 12i 16f 9t^ 12i Exercises similar to the above should be continued until the student can add with great facility. If the principles of grouping have not been well mastered, simple addition should be carefully reviewed. COMMON FRACTIONS 129 WRITTEN EXERCISE Co'py or write from dictation and find the sum of: 1. 16491 43721 8431| 51321 16541 1831| 1831| 14621 1851^ 2. 1672f 1485| 16351 12641 1269f 1748J 1936| 5413J 2114,-V 14361 1390f 24151 18671 16391 41361 16521 31161 1439J^ 4. 21101 16401 36801 4590J 2169| 8432f 40411 6542f 1862| 1114 j72 1116^6 2243yV 3246 1 5. 62141 1745J 3146f 18641 2839| 6241| 4036| 8130^5_. 2148^V 1439^9_ 6. 12141 2167J 31591 92751 7215f 52611 7215f 5144| 6257| 2186,-5^ 7. 8. 9. 10. 11. 12. 91241 72491 16491 75291 73651 28141 27161 25141 29671 29641 68751 8875f 26581 2724f 86921 2476J 86951 62141 72411 86141 27241 8695J 15651 2724^ 86191 2924| 65291 62141 18251 86143 9215f 6719f 8516i • 7528^ 26141 15831 1695^ 17621 1875| 16291 7214| 29101 2817J 27141 2913| 2874| 2619f 14721 8425| 4725J 85921 7216f 25101 2615f 8273J 16491 27251 67291 2625f 18131 1782f 12861 8647| 35141 86141 19621 8695J 24721 6248J 12861 8725f 62191 1686f 17251 2729J 28161 . 18621 17591 62731 9685f 968511 1925^5_ 8537f 69821 3685J 26141 84131 7226| 18251 4725J 2538f 1758f 2752| 21141 28141 2716f 17621 18751 2864| 16241 17291 1805| 4212^5^ 2729^2 87964 1592| 2816f 2519^ 22161 18721 2614| 2075J 1721| 1465f 130 PEACTICAL BUSINESS ARITHMETIC SUBTKACTION ORAL EXERCISE t='.^ 1. 172 A. - 154 A. = ? f 2. Find the difference between ^ 1 bu. - 3 pk. = ? [ind ^ ; J and ^; J and |^; I and |. 171. It is clear that onli/ like numbers and parts of like units can be subtracted, 172. Examples, i. Find the difference between J and ■^^. Solution. The given fractions must be reduced to equivalent fractions having a least common denominator. The least common denominator is 24. t = I? ^^^ h = M- U-H = ih the required result. 2. From 211 take 17^ Solution. Change the given fractions to similar fractions as in example 1. I cannot be subtracted from |, hence 1 is taken from 21 and mentally united to f, making f. | from | leaves |, and 17 from 20 leaves 3. The required result is therefore 3|. Find the value of. 1. 2|-f 2. 2^-\. 3. H-i- 4. 7|-lf. ORAL EXERCISE 5. 6. 7. 8. H 45 - 16|. 11J-6|. If. 9. 30-1 If 6J-4iV 10. 7^-3^5. 11. 12|-6|. 12. 70|-20|. Tlie following is a recent clipping from a daily paper. It shovk^s the prices of wheat on the Chicago market. The first line of prices is for wheat to be delivered in July, and the second line for wheat to be delivered in September. Chicago Wheat Quotations Delivery Previous Closing Opening Highest Lowest Closing July September 87f^ 87J^ 92^ 88J^ 90f^ SI If 92-1^ 87J)^ 13. What was the difference between the highest and the lowest price of July wheat ? of September wheat ? 14. What was the difference between the opening and the closing price of September wheat? of July wheat? COMMON FRACTIONS 131 15. What was the difference between the opening price and the previous closing (yesterday's closing) price of July wheat ? of September wheat ? 16. A bought 1000 bu. July wheat at the lowest price and sold the same at the closing price. What was his gain ? Suggestion. lhf = $0.015 ; 1000 times $0,015 = $ ? 17. B bought 1000 bu. September wheat at the opening price and sold it at the highest price. What was his gain? Had he bought at the lowest price and sold at the closing price, what would have been his gain ? 18. C bought 25,000 bu. July wheat at the opening price and sold it at the highest price. What was his gain ? WRITTEN EXERCISE 5. 1651 -41 3V 6. 245|-17^3,_. 7. 177|-17iV 8. 2150-121i|. 173. When the numerators of any two fractions are alike, the subtraction may be performed as in the following examples. 174. Examples. 1. From | take ^. 2. From | take |. Solutions. 1. 9 — 7 = 2, the new numerator. 9 x 7 = 63, the new denomi- nator. Therefore, the required result is ^. 2. 8 — 5x3 = 9, the new numer- ator. 8 X 5 = 40, the new denominator. Therefore, -^^ is the required result. Find the value of 1. 39- -iii. 2. 85- -21f. 3. 168 -45f. 4. 264- 1^6-131*. 9. i-l-h 10. l-A-i- 11. 2i+lf-l^V 12. 25i - 8f - 151 ORAL EXERCISE State the value of 1- i-h 8. i-i- 15. I - h 22. l-f- 2- l-i- 9. i-i- 16. f-f 23. i-i- 3- 1-^- 10. i-h 17. f-l- 24. f-i- *• i-f 11. l-h 18. l-f 25. i^-^■ 5- i-h 12. l-f 19. t-f 26. ni - 2i. 6- i-i- 13. i-h 20. t-f 27. ^H-'!h '• i-f 14. k-h 21. §-!• 28. 16| - 12| 132 PEACTICAL BUSINESS ARITHMETIC MULTIPLICATION ORAL EXERCISE 1. 12 times 2 A. are how many acres? 12 times 2 fifths (f) are how many fifths ? -^ = ? 2. 32 mi. divided by 4 equals how many miles ? | of 32 mi. equals how many miles? Multiplying by J, ^, ^, and 1, etc., is the same as dividing by what integer ? 3. If 5 men can dig 125 bu. of potatoes in 1 da., how many bushels can 3 men dig in the same time ? | of 125 bu. equals how many bushels ? 175. Example. Multiply f by 248. (a) Solutions, (a) 248 times 3 eighths = 744 eighths | X 248 = ^|^= 93 = i|4 = 93;but, ^ (b) If the multiplication is indicated as in the "^I margin, the work may be shortened by cancellation. f^P times o _ gg 176. Therefore, to find the product of an integer and a fraction, find the product of the integer and the numerator^ and divide it hy the denominator. Before actually multiplying, indicate the multiplication and cancel if possible. ORAL EXERCISE 1. If 1 yd. of cloth costs i0.87| (i|), what will 16 yd. cost? 48 yd.? 128 yd.? 72 yd.? 2. When oats cost $0,331 ^(#1) a bushel, how much must be paid for 29 bu.? for 36 bu.? for 129 bu. ? 3. A boy earns $0.75 (-f |) a day. How much will he earn in 18 da.? in 40 da.? in 84 da.? in 128 da.? in 160 da.? 4. When property rents for $720 a year, what is the rent for ^ yr.? for \ yr.? for \ yr.? for ^V J^'- ^^r 1 yr.? 5. A ship is worth $48,000. What is \ of the ship worth ? -^^ of the ship ? f of the ship ? | of the ship ? {^ of the ship ? COMMON EKACTIONS 133 WRITTEN EXERCISE Find the product of : 1. 98 X |. 7. I of 95. 13. 784 x f . 19. f of 2420. 2. 80 X |. 8. f of 25. 14. 459 x f 20. | of 2500. 3. 50 X 2V 9. I of 88. 15. 400 X ^V- 21. | of 3240. 4. 97 X iV 10- 1^6 of 51. 16. 510 X iV- 22. f of 5117. 5. 92 X ^V 11. -/j of 99. 17. 990 x J^. 23. -/^ of 7254. 6. 188 Xe^. 12. iVof77. 18. 800 x if . 24. -j^ of 1024. 177. Example. Multiply 25 by 4|. 25 Solution. | of 25 = ■?/- or 9f. "Write f as shown in the margin, and carry 9 to the product of the integers. 4 x 25 + 9 = 109. There- fore, 25 multiplied by 4| = 109|. 109| 178. Therefore, to find the product of a mixed number and a whole number, multiply the integer arid the fraction sepa- rately and find the sum of the products, ORAL EXERCISE Find the cost of: 1. 15f lb. of fish at 9^. 6. 6| bu. turnips at 82^. 2. 7f yd. of cloth at 1 3. 7. 12| bu. of oats at 39^. 3. 16 lb. of beef at 12| ^. 8. l^ yd. of calico at 4^. 4. 16J lb. of sugar at 5^. 9. 16J yd. of ribbon at 20^. 5. 12 yd. of cloth at 11^^. 10. 8Jgal. of molasses at 40^. WRITTEN EXERCISE 1. A merchant bought 24 pc. of English serge, containing 52, 472, 501, 483, 49, 513, 47, 482, 453, 491, 522, 592, 513, 50, 52, 531, 523, 473, 481, 512, 513, 482, 49, and 53 yd., at $1,121- per yard, and sold it all at $1.35 per yard. What did he gain ? 2. I bought 25 pc. taffeta silk, containing 42^, 402, 43, 443, 45, 412, 43, 401^ 472, 44, 452, 491, 471, 451, 46, 44, 433, 40, 41^, 46, 47, 402, 451, 42, and 47^ yd., at 871/ per yard, and sold the first 15 pc. at $1.05 and the remainder at $1.10. What did I gain? 134 PRACTICAL BUSINESS ARITHMETIC 3. A merchant bought 25 pc. of striped denim containing 41^, 411, 422^ 432^ 421, 442^ 431^ 402^ 421, 453^ 421, 402, 412, 473, 451, 411, 432^ 472^ 443^ 423^ 432^ 391, 421, 482^ ^nd 47 yd., at 11^ per yard. If he sold the first 11 pc. at 15^ per yard and the remainder at 17^ per yard, what was his gain? 4. Copy and find the amount of the following bill: ^ Little Falls, N.Y., '^^^-/^ J>^ Y , *9 Terms. Bought of ^j^^ Eureka Mills di\ '^^2^^AP-V-f^.-i?-7:z^ ^/' 4^^-^ ^j-' ^^ 4^/ ^/^Vvf J'K^^ r \J2^^ ^:^^^i^^..^^i:'4^'c^^.A^^^^^^. ^2J ^/ .^^-^ 4^/7-^ A^Z. -7^ AO_ .6U 4^/2- y^^. 179. The expressions \^i\ and \ x f have the same meaning ; hence, the sign of multiplication may be read 0/, or multiplied hy^ when it immediately follows a fraction. 180. Examples. 1. Multiply | by |. Solution. To multiply | by | is to find | of |. Let the line AF in the accompanying diagram represent a unit divided into 6 equal parts. Then AD will represent f. Sub- divide each of the five equal parts M M M into 3 equal parts and the line AF will represent a unit divided into 15 equal parts, each of. which is -^^ of the whole. It is then clear that i of \ equals ■^^. Since ^ of ^ is jV» i of f is x\. But f of f is 2 times | of f ; there- fore, I of I equals ^. 2. Find the product of 21 ^, and ^. Solution. Reduce the mixed number 2| to an im- q proper fraction and obtain |. Cancel, and there remains in the which per iraction ana ooiam f . uancei, ana tnere remams 111 « ^ ,j ^ . numerators 2 times 7, and in the denominators 15, from ^ ^ ? ^ TH = 7^ .ch obtain the fraction f|. / ^ 15 15 COMMON FRACTIONS 135 181. Hence, to multiply a fraction by a fraction : Reduce the mixed numbers and integers to improper fractions and cancel all factors common to the numerators and denominators. Find the product of the remaining numerators for the required numerator^ and the product of the remaining denominators for the required denominator, ORAL EXERCISE 1. How many yards in | rd. ? feet in -| rd. ? 2. When barley is worth 25|^ per bushel, what is the value of ibu.? of fbu.? 3. A book, the retail price of which was $5, was sold at wholesale for ^ of the retail price, with Jq off from that for cash. Find the selling price of 10 books. WRITTEN EXERCISE 5. 50x-^Vx'^l- 6. Ifx4ix8|. Reduce to their simplest form : 1. I of f of f 3. 71 X 25 X |. 2. I off of 21 4. 3fx4|x20. 7. A saves 89.75 per week and B | as much. How much more will A have than B at the end of a year ? 8. A merchant bought a piece of cloth containing 43 1^ yd. at $1.50 per yard. He sold | of it at 1 1.62 1 a yard, and the re- mainder at $1.37| a yard. Didhe gain or lose, and how much? The following is a recent clipping from a daily paper. It shows the prices of corn on the New York market. New York Corn (^ ;lTOTATIONS Dklivkkv PKKVIOUS CU)SIN(} Opening Highest ^^OWEST Closing July September 661/ 65|/ 65^/ 641/ 661/ 65|/ 64|/ 64^/ 65|/ 64f/ 9. D bought 25,000 bu. September corn at the opening price and sold it at the highest price. What was his gain ? Had he bought at the lowest price and sold at the highest price, what would he have gained ? 136 PRACTICAL BUSINESS ARITHMETIC 10. E bought 12,500 bu. July corn at the lowest price and sold it at the closing price. What was his gain ? Had he bought at the lowest price and sold at the highest price, what would he have gained ? 11. A gold dollar weighs 25.8 troy grains. For every 90 parts of pure gold there are ten parts of alloy. How many grains of each kind in a gold dollar ? in a 5-dollar gold piece ? 12. A 5-cent piece weighs 77.16 troy grains. For every part of nickel there are three parts of copper. How many grains of each kind in a 5-cent piece ? 13. The second general coinage act (1834) of the United States made one silver dollar weigh approximately as much as sixteen gold dollars, and this ratio of sixteen to one has been maintained up to the present time. What is the approximate weight of a silver dollar ? If silver coins are -^-^ pure, approxi- mately how much pure silver in 10 silver dollars? Short Methods in Multiplication 182. When mixed numbers are large, they may be multiplied as shown in the following example. 183. Example. Multiply 255^ by 24|. 2551 Solution. Multiply the fractions together 242 and obtain ^^, which write as shown in the ^g _ 2 f 1 margin. Multiply the integer in the multi- 15 5 3 plicand by the fraction in the multiplier and 10 J = | 01 ZOO obtain 102. Multiply the fraction in the mul- 8 =24 times J tiplicand by the integer in the multiplier and ^020 obtain 8. Multiply the integers together and >^ ^ add the partial products. The result is ^ , ^ ^ 6230,v 6230^2^ =24f times 2551 WRITTEN EXERCISE Multiply : 1. 975ibyl8l. 3. 720|by21f. 5. 512^7^ by 161 2. 876| by 21 J. 4. 4451 by 46f. 6. 450^9^ by 20|. = 24 times 255 COMMON FRACTIONS 137 SQUARING NUMBERS ENDING IN J OR .5 184. Examples, l. Multiply 9 J by Qi. Solution. | of I = \, which write as shown in the margin. ^ 9-^ of the integer in the multiplicand plus ^ of the integer in the multi- qj^ plier is equal to either the integer in the multiplicand or multiplier. — -| Therefore, add 1 to the integer in the multiplicand and multiply by the ^^ multiplier. 9 x 10 = 90. Then, 9^ x 9| = 90^. 2. Find the cost of 8.5 T. of coal at $8.50 per ton. Solution. The principles embodied in this example are practi- cally the same as those in problem 1. .5 x .5 = .25, 8 x 9 = 72. Therefore, 8.5 tons of coal at $8.50 per ton will cost $72.25. 72.25 3. Find the cost of 75 A. of4a»d at $75 per acre. Solution. This problem is similar to example 2, the only 75 difference being in the matter of the decimal point. Since the nr 8.5 8.5 5625 decimal point has no particular bearing upon the steps in the pro- cess of multiplying, proceed to find the product as in example 2. 5 X 5 = 25, which write as shown in the margin. 7 x 8 = 56, which write to com- plete the product. 75 acres of land at $75 an acre will therefore cost $5625. ORAL EXERCISE Multiply : 1. 11 by 11. 6. 6 J by 61 11. 131 by 13i. 16. 16i by 161 2. 21 by 21 7. 7.5 by 7.5. 12. 141 by 141. 17. 171 by 171. 3. 31 by 31. 8. 8.5 by 8.5. 13. 151 by 151 18. ISJ by 181. 4. 41 by 41. 9. 9.5 by 9.5. 14. 11.5 by 11.5. 19. 195 by 195. 5. 51 by 5f 10. 10.5 by 10.5. 15. 12.5 by 12.5. 20. 205 by 205. WRITTEN EXERCISE In the follotving problems make all the extensioiis mentally. 1. Find the total cost of: 85 lb. of tea at 85 ^. b^ lb. tea at bh ^. 75 gal. sirup at 75^. 75 bbl. flour at 17.50. 45 gal. sirup at 45^. 650 bbl. oatmeal at 16.50. 21 bu. beans at $2.50. 25 doz. cans olives at $2.50. 35 gal. molasses at 35^. 95 cs. salad dressing at 95^. ^b cs. horseradish at 65^. 750 lb. cream codfish at 71^. 4^ cs. baking powder at $4.50. ^ cs. baking powder at $3.50. 138 PRACTICAL BUSINESS ARITHMETIC MULTIPLICATION OF ANY NUMBERS ENDING IN | OK .5 185. Examples, l. Multiply TJ by GJ. Solution, i of the integer in the multiplicand plus | of the integer g i in the multiplier is equal to i of 6 + 7, or 6i, which added to i of ^ rr j equals 6f. Write | as shown in the margin, and carry 6. 6x7 + 6 2 = 48. Therefore, 7^ x 6^ = 48|. 48 1 2. Multiply 71- by OJ. 71, Solution. | of 7 + 9 = 8, with no remainder. 1 of i = }, which ^ write as shown in the margin, and carry 8. 7x9 + 8 = 71. There- _^ • fore, 7^ X .91 = 71f. 71 J Observe that : (1) in finding ^ of any number (dividing a number by 2) there is either nothing remaining or 1 remaining; (2) in finding 1 of an even number there can be no remainder, and in finding ^ of an odd number there is always a remainder 1. Hence, to multiply numbers ending in i or .5 : Mentally determine the sum of the integers in the multiplicand and multiplier. If it is an even number, write \ (.25 or 25) in the product. If it is an odd num- ber, write f (.75 or 75) in the product. Multiply the integers and to the product add \ of their sum. Multiply : ORAL EXERCISE 1. 3^ by 71. 2. 41 by 51. 3. 161 by 41. 4. 171 by 21. 5. 141 by 61. 6. 211 by 91. 7. 3.5 by 8.5. 8. 7.5 by 6.5. 9. 5.5 by 8.5. WRITTEN EXERCISE Make the extensions in each of the following problems mentally. 1. Find the total cost of : 6.5 T. coal at 18.50. 8.5 T. coal at $9.50. 2.5 T. hay at 117.50. 16.5 T. hay at 111.50. 15.5 cd. wood at 13.50. 14.5 cd. wood at f 5.50. 2. Find the total cost of : 45 bu. beans at 12.50. 350 bu. wheat at 11.05. 35 bbl. flour at %6.50. 350 bu. beans at 12.50. 45 bbl. flour at $8.50. 85 bbl. oatmeal at $7.50. COMMON FRACTIONS 139 DIVISION ORAL EXERCISE 1. 8A.-v-4 = ? Snintbs (|)-^4? 2. If 2 lb. of coffee costs |0.66f (ff), what will 1 lb. cost? Divide | by 2. What is the effect of dividing the numerator of a fraction ? 3. 4^2 = ? J-of.| = ? 4. Because |- -^ 2 = ^ of |, therefore, l -f- 5 = i of |, or Ivl ivi— ? 5. What is the quotient of J ^ 5 ? of 1^8? of -1-1-2? 6. Because 1^5 = ^ of J, therefore | -?- 5 = 2 times J of ^. That is, I -^ 5 = 1 of |, or I X 1 f X ^ = ? 7. How much is f ^ 5 ? | -j- 3 ? TJ ( -i/-) -^ 8 ? 31 - 6 ? 8. What is the effect of multiplying the denominator of a fraction ? 186. In the above exercise it is clear that Dividing the numerator of a fraction hy an integer divides the whole fraction ; and, Multiplying the denominator of a fraction hy an integer divides the whole fraction, ORAL EXERCISE Find the quotient of: 1. 1-4. 4. 1-12. 7. ^2^4. 10. f-^9. 13. 1-19. 2. 38.^2. 5. 1^12. 8. 3-V^9. 11. 1^6, 14. ^3_^5. 3. -U_^5. 6. fo^3. 9.-^^7. 12.1^5. 15. ^V- 5. 187. Examples. 1. Divide 28 J by 7. Solution. First divide the integers and the result is 4 ; then 4i divide the fraction by 7 and the result is \. Therefore, 28| ^ 7 = ^. 7)28J 2. Divide 261- by 8. Solution. Divide 26 by 8 and the result is 3 with a remainder 2. 3_5_ Join the remainder, 2, vv^ith the fraction, ^, making 2|. Reduce 2\ to an improper fraction and the result is f . | -j- 8 = ^^. Therefore, Sft- 8)26i 140 PRACTICAL BUSINESS ARITHMETIC Divide : ORAL EXERCISE 1. 2. 3. 4. 161 by 4. 181 by 9. 25| by 2. 171 by 8. 5. 32| by 4. 9. 211 by 8. 6. 271 by 7. 10. 24f by 6. 7. 19| by 9. 11. 45f by 5. 8. 20f by 10. 12. 40f by 10. ORAL EXERCISE 13. 81 by 5. 14. 14| by 7. 15. Ill by 9. 16. 26|byl0. 1. How many eighths m one ? 1 -^- 1 = ? 2. What is the value of : 1 ^ -^^ ? 3^1? 17-^1? 125-^^2? 250-1? 3. Read aloud the following, supplying the missing word : To divide an integer hy a unit fraction^ multiply the integer by the of the fraction. 4. What is the value of 25 ^ 1 ? 2.5 --1? 7.5- |? 25.5^ j^?54^i? 48^i? 29-^1? 21^1? 5. If B^ in the accompanying dia- gram, is 1, what is (7? How many blocks like C in Bl 1^^ = ? 6. If ^ is 1, what is J5 ? A is how many times B ? That is, A-i- B= ? l-f = ? 7. If 1-^1 = 1 (11), then 2-f=? 8. What is the value of 4 - f ? 5 - f ? 9. Read aloud the following, supplying the missing words : If A IB, 1^ B is , and O is . If B is contained in A I (1|) times, it is contained in (7 1 of | times or times. That is, l^-5-f 10. 12-J-2? 15-1? Jx What is the value of \ i? 2? 5 • 1? 3 • 3 .^5? 4 • 6 • 188. The reciprocal of a fraction is 1 divided by that fraction. Thus, the reciprocal of | is 1 -> |, or |. That is, the reciprocal of a fraction is the fraction inverted. 189. Reciprocal numbers, as we use the terms in arithmetic, are numbers whose product is 1. Thus, 4 and \, | and f , | and 6, f and f , are reciprocal numbers, because their product is equal to 1. COMMON FRACTIONS 141 190. It has been seen that the brief method for dividing a fraction or an integer by a fraction is to multiply the dividend hy the reciprocal of the divisor. The principles of cancellation should be used whenever possible. Inte- gers and mixed numbers should be reduced to improper fractions before applying the rule. WRITTEN EXERCISE Divide , 1. 2. 3. 4. 5. 6. |byf. n by h 95 by |. 88 by f . 7. 16 by f . 15| by 1 10. 11. 12. fbyf. ^ by f . fo by |. ^ by 11. 13- |byf 160 by 41 250 by 3f . 191. Examples, l. Divide 2190 by 48|. Solution. Multiplying both dividend and divisor by the same number does not affect the quotient ; hence, multiply the dividend and divisor by 3 and obtain for the new dividend and divisor 0570 and 146, respectively. Divide the same as in simple numbers and obtain the result 45. Or, Reduce both the dividend and divisor to thirds, obtain- ing ^-^'^ and ifs.. Reject the common denominators and divide as in whole numbers. 2. Divide 651 by 12f Solution. Multiply both dividend and divisor by 6, the least common denominator of the fractions, and di- vide as in simple numbers. The result is 5f |. Or, Reduce both the dividend and divisor to sixths, obtain- ing as a result -'/ and ^|^. Reject the common denomi- nator and divide as in simple numbers. 14. 15. 16. 17. 18. I by f. 169 by 4|. 640 by .5f . 625 by 83^. 920f by 73. 48|)2190 _3 3_^ 146) 6570(45 584 730 730 121)651 _6 6_ 74) 393 (5f I 370 23 Divide: 1. 2701 by 121 2. 508iby30f. 3. 14311 by 201. WRITTEN EXERCISE 4. 9621 by 31 J. 5. 650fby26i. 6. 1680Jby45i 7. 7552by78|. 8. 470fbyl7i. 9. 10541 by 168f 142 PRACTICAL BUSINESS ARITHMETIC FRACTIONAL RELATIONS ORAL EXERCISE 1. If / in the accompanying diagram is 1, what is el c?? xf=i. 192. To find what fraction one number is of another, take the number denoting a part for the numerator of the fraction^ and the numher denoting the whole for the denominator. ORAL EXERCISE 1. If a piece of work can be performed in 12 da., what part of it can be performed in 5 da. ? in 7 da. ? 2. If A can do a piece of work in 15 da., what part of it can he do in 1 da. ? in 2 da. ? in 5 da. ? in 1\ da. ? 3. If B can do a piece of work in 7 J da., what part of it can he do in 1 da. ? in 2 da. ? in 5 da. ? in SJ da. ? in ^ da. ? COMMON FRACTIONS 143 4. What part of 100 is 331 ? I2i ? 66f ? 8^ 25 ? 75 ? 125? 16f? 831? 621? 22-| ? 9^^? 56i ? 6f ? What part of SI is 331/? 66|/? 25/? 75/? 16f/? 5. What part ot ^l is 55^/ Y bb|^ Y :iD^ 7 Y£)^ V ibf ^ 81/? 6|/? 31/? 61/? 621/? 871/? 371/? 14|/? 6. What part of 1000 is 125? 166f ? 666f ? 625? 333^ : 7. Whatpartof S10isS3.33i? S1.25? S1.66f? $8.33^ S2.50? S6.25? S6.66f ? WRITTEN EXERCISE 1. A man asked for a horse | more than it cost, but finally reduced the price -^q. He gained $ 26. What was the cost of the horse ? the price asked ? the selling price ? 2. A had 1 of his money invested in bonds, -f^ in bank stock, and the remainder, S1980, on deposit in the First National Bank. How much was invested in bonds ? in bank stock ? 3. A man left his estate to his four sons. To the first son he gave ^ of the estate ; to the second, i of the remainder ; to the third, 1 of the estate ; to the fourth son, $1556. What was the value of the estate ? 4. A merchant reduced the marked price of a machine |, and then sold it so that he gained 1 of the first cost. If he gained S 8, what was the first cost of the machine, and the marked price before any reduction was made ? 5. A man placed a house and lot in the hands of a real estate agent to be sold at such a price that he, the owner, might realize $5985, after paying the agent ^V ^^ ^^® selling price of the property. For how much was the property sold ? 6. A farmer had three bins containing wheat, rye, and oats respectively. The quantity of oats was three times that of the wheat, and the rye was one half of the quantity of the oats. If the value of the oats at 35/ per bushel was $1155, how many bushels of each kind of grain did the farmer have ? If the wheat was worth 95/ per bushel, and the rye 671/ per bushel, what was the value of the entire lot of grain ? 144 PRACTICAL BUSINESS ARITHMETIC WRITTEN EXERCISE 1. The square in the margin represents the total population of the state of New York (state census of 1910), and the shaded area represents the urban (city) population. If the rural (coun- try) population is 1,800,000, what is the entire population of the state ? the urban population ? 2. In a recent year the population of Massachusetts was in round numbers 3,360,000, and there were fourteen persons living in the cities of the state to each person living in the country. Represent this graphically as in problem 1, and find the city population and the country population for the state. 3. Suppose that Q in the diagram represents the population of the United States in 1870, A the population in 1830, and F the population in 1900. If the population in 1870 was 38,400,000 (round numbers), what was the population (round numbers) in 1900? In 1830? 4. Suppose that F in the diagram represents the population of the United States in 1900, and O the proportion of this popula- tion living in cities in 1900. What proportion of the popula- tion lived in cities in 1900? Suppose that F represents the population in 1860 and A the proportion of this population living in cities. Assuming that the city population in 1860 was 5,240,554, find the total population for the same year. 5. The total population of New Jersey (state census of 1910) is 2,537,167, and the rural population, 629,957. Represent this graphically and find the urban population, COMMON FRACTIONS 145 CONVERSION OF FRACTIONS ORAL EXERCISE 1. What is the denominator of the decimal .6? of .75? 2. What is the numerator of .4? of .04? of .004? of .0004? 3. Write as a common fraction .7; .23; .079; .0013; .00123. 193. A decimal may be written as a common fraction. 194. Examples, l. Reduce .0625 to a common fraction. Solution. .0025 means yfff^ ; but yf ?^^ may be _6.2l_ ^ 5_ =, _1 expressed in simpler form. Dividing both terms of lOOOO ¥o iS" the fraction by 625, the result is J^. WRITTEN EXERCISE Reduce to a common fraction or to a mixed number : 1. 0.375. 5. 0.9375. 9. 0.0335. 13. 260.675. 2. 0.0625. 6. 1.66f. 10. 0.0056J. 14. 126.1875. 3. 0.0016. 7. 0.4375. ii. 181.875. 15. 175.0625. 4. 0.5625. 8. 0.125. 12. 171.245. 16. 172.0075. 195.. A common fraction may be written as a decimal. 196. Example. Reduce | to a decimal. Solution, f equals | of 3 units. 3 units equals 3000 thou- sandths. \ of 3000 thousands equals 375 thousandths (.375). 8)3.000 ORAL EXERCISE 1. Reduce to equivalent decimals : J, \, |, J, |, J, |, |, |, |, 13 5 1 JL JL _3_ 1 JL 8' ¥' ¥' 8' 16' 12' 16' 9' 11* 2. Reduce to common fractions : .5, .25, .50, .75, .33^^, .QQ^-, .16f, .121 .6, .4, .60, .40, .2, .83^, .20, .08J, .375, .125, .371 .87f .875, .0625, .111 .09 Jj. WRITTEN EXERCISE Reduce to equivalent decimals : 1. |. 3. Jj. 5. 3f J. 7. 5\V- 9- It'oo- "• 21|. 2. Jj. 4. jfg. 6. if 8. 2V. 10. 5Jj. 12. 1651f 146 PRACTICAL BUSINESS ARITHMETIC THE SOLUTION OF PROBLEMS 197. The steps in the solution of a problem are : (1) reading the problem to find what is given and what is required ; (2) de- termining from what is given how to find what is required; (3) outlining a process of computation and then performing it; (4) checking results. 198. A problem should be thoroughly understood before any attempt is made to solve it ; and when the relation of what is given to what is required has been discovered, the process of computation should be briefly indicated and then performed as briefly and rapidly as possible. 199. To insure accuracy the work should always be checked in some manner. If the answer to the problem is estimated in advance, it will prove an excellent check against absurd results. Thus, 42 doz. boys' hose at $48 a dozen is equal to approximately 40 X 1 50 ; 9f % of 1290 bu. is equal to approximately j\ of 1290 bu. ; etc. 200. Example. A tailor used 30 yd. of flannel in making 18 waistcoats ; at that rate how many yards will he require in making 45 waistcoats ? Solution 1. The quantity needed in making 18 waistcoats is given and tlie quantity needed in making 45 waistcoats is required. 2. One waistcoat requires f ^ yd. ; 45 waistcoats will require 45 times f § yd. 15 5 3. — = 75 ; that is 75 yd. of flannel are required in making 45 waistcoats. 4. If yd. =1 yd. ; Jf yd. = f yd. ; therefore the work is probably correct. 201 . If reasons for conclusions, processes, and results are given, they should be brief and accurate. It is also a mistake to try to use the language of the book or the instructor. Such artificial work stifles thought and conceals the condition of the learner. The subject of analysis should not be unduly emphasized. A correct solution may generally be accepted as evidence that the correct analysis has been made. COMMON FRACTIONS 147 ORAL EXERCISE In the following problems first find each result as required, and then give a brief, accurate explanation of the steps taken in the solution. Do not use pen or pencil. 1. If 2 T. cost 18, what will 5 T. cost? Suggestion. |20; since 2 T. cost |8, 5 T., which are 2^ times 2 T., will cost2| times$8, or $20. 2. 24 is f of what number ? f of what number ? ^^ of what number ? 3. 220 is ^ less than what number ? 450 is I less than what number ? 4. A, having spent -J of his money, finds he has $84 left. How much had he at first ? 5. 1124 is 1 more than what sum of money? fSOO is ^ more than what sum of money? 6. A man sold -f^ of an acre of land for $35. At that rate what is his entire farm of 100 acres worth ? 7. A man bought a stock of goods and sold it at ^ above cost. If he received $275, what was the cost of the goods ? 8. B bought a stock of goods which he sold at ^ below cost. If he received for the sale of the goods $ 240, what was the cost and what was his loss ? 9. yV ^^ ^1^® students in a high school are girls and the re- mainder are boys. If the number of boys is 350, how many scholars in the school ? 10. A bought a quantity of wheat which he sold at ^ above cost. If he received $ 300 for the wheat, what did it cost him and what was his gain ? 11. A bought a quantity of dry goods and sold them so as to realize i more than the cost. If the selling price was $720, what was the cost and what was the gain ? 12. D bought a stock of carpeting which he was obliged to sell at i below cost. If he received $750 for the sale of the car- peting, what was the cost of same, and what was his loss ? 148 PRACTICAL BUSINESS ARITHMETIC WRITTEN EXERCISE In the following problems give both analysis and computation. 1. If J lb. of tea cost 21^, what will 9^ lb. cost ? Computation Analysis 91 = J/- 9i = Y- ; 9| is therefore 19 times |. If | lb. cost 19 X 21 )^ = $3.99 21 ^, 9| lb. will cost 19 times 21)*, or $3.99. 2. If I of a pound of tea cost 42 ^, what will 35| lb. cost ? 3. If a drain can be dug in 17 da. by 45 men, how many men will it take to dig ^ of it in 3 da.? 4. In what time will 3 boys at i0.62| per day earn as much as 4 men at #2.25 each per day will earn in 45| da. ? 5. A spends 172 per week or | of his income ; B saves #48 per week or | of his income. How long will it take A to save as much as B saves in five weeks? 6. If 115 bu. of wheat are required to make 23 bbl. of flour, how many bushels will be required to make 50 bbl. of flour ? 117 bbl. of flour ? 259 bbl. of flour ? ORAL REVIEW EXERCISE 1. .05x6x0x21=? 2. 10.75 is what part of #3? 3. What is the sum of ^, |, ^, and -^^ 7 4. Find the value of .45-f (.25 x 5) -.04. 5. 60 is I of what number ? | ? f ? f ? f ? 6. At 25^ a yard, what will % yd. of cloth cost? 7. y is 1^ of what number? | is f of what number? 8. If I of an acre of land costs $75, what will 50 A. cost ? 9. If I of a number is 84, what is 5 times the same number ? 10. The dividend is 4|- and the quotient is 6|; what is the divisor ? 11. If 6 bu. of apples cost $15, what will 80 bu. cost at the same rate ? 12. At $460 per half mile, what will be the cost of grading 6 mi. of road? COMMON FE ACTIONS 149 13. How much will 4 carpenters earn in 10 da. at the rate of 12.25 each per day? 14. At $4.50 per cord, what will be the cost of 4 J cd. of wood ? of ^ cd. ? of 121 cd. ? of 7^ cd. ? 15. A bought a horse for $96 and sold it for | of its cost. What part of the cost was the loss sustained ? 16. A bought 4J yd. of velvet at f 5.20 per yard and gave in payment a 850 bill. How much change should he receive ? 17. I sold 5 A. of land for $375 and sustained a loss equal to J of the original cost of the land. What did the land cost per acre ? 18. D and E agree to mow a field for $36. If D can do as much in 2 da. as E can do in 3, how should the money be divided ? 19. N sold a watch to O and received ^ more than it cost him. If O paid $64 for the watch, what did it cost N? What per cent did N gain ? 20. A earns $125 per month. Of this sum he spends $75 and saves the remainder. What part of his monthly earn- ings does he save ? What per cent ? WRITTEN REVIEW EXERCISE 1. Find the cost of 1100 eggs at 23| ^ per dozen. 2. Counting 2000 lb. to a ton, find the cost of 5J T. of steel at l^g^ per pound. 3. When flour is sold at $6.02 per barrel of 196 lb., what should be paid for 55^ lb. ? 4. I bought 300 bbl. of flour at $5.75 per barrel. At what price must I sell it per barrel in order to gain $ 150 ? 5. The cost of 200 bu. of wheat was $204.50 and the selling price $212.35. What was the gain per bushel? 6. A can do a piece of work in 5J da. and B in 7J da. If they join in the completion of the work, how long will it take them? 150 .PRACTICAL BUSINESS ARITHMETIC 7. How much will 7 men earn in 6 da., working 10 hr. per day, at 25 i per hour? 8. At |)2.50 per day of 8 hr., how much should a man •receive for W.\ hours' work ? 9. A boy works 4|^ da. at the rate of %bJlb per week of 6 da. How much does he earn ? 10. W, in 1^ of a day, earns il.25, and Y, in |^ of a day, earns f 0.87 J. How much will the two together earn in 40 J da. ? 11. A and B together can do a piece of work in 10 da. If A can complete the work alone in 16 da., how long will it take B to do it ? 12. Nov. 1, in a recent year, was on Tuesday. How much did B earn during November if he was employed every working day at the rate of 83.75 per day? 13. A farm is divided into 6 fields containing, respec- tively, 25f, 26^7^, 32f, ^^, 35^9^, and 52^^ A. How much is the farm worth at 837.50 per acre? 14. Find the total cost of : 630 lb. sugar at 4|^; 375 lb. tea at 38^^; 240 lb. crackers at 5| ^ ; ^b lb. rice at 7y9g ^ ; 521 lb. raisins at 7i-^; and 250 lb. coffee at 24f ^. 15. A retailer bought 5 bbl. of flour at 86.50 per barrel, 12 bu. potatoes at 75 ^ per bushel, and gave in payment a fifty-dollar bill. How much change should he receive ? 16. Five garden lots measuring 2|^, lOJ, 12|, 6y^, and 8j9g A. respectively, were bought at 8212.87|^ per acre and sold at 8250.50 per acre. Find the gain resulting from the transaction. 17. I bought 4120 2 yd. of silk at 81.02 per yard and sold \ of it at 81.50 per yard, and the remainder for 81600. What was the average price received per yard, and how much did I gain? 18. A, B, C, and D hire a pasture for 8419.50. A put in 25 head of cattle for 4 wk.; B, 31 head for 5 wk.; C, 44 head for 6 wk.; and D, 40 head for 8 wk. How much should each be required to pay ? COMMON FRACTIONS 151 19. A grain dealer bought 6750 J bii. of corn at 60 J ^ per bushel, and 2130J bu. of oats at 32| ^ per bushel. He sold the corn at 69| ^ per bushel, and the oats at 39| ^ per bushel. Did he gain or lose, and how much ? 20. A grocer bought 15 bbl. of molasses, each containing 50 gal., at 25^^ per gallon. He retailed 150^ gal. of it at 30^ per gallon, 170i gal. at 28^ per gallon, and the re- mainder at 35^ per gallon. Did he gain or lose, and how much ? 21. Find the cost of 25 bx. of cheese weighing : 67 — 4, 62-4, 61-3, 72-4, 81-5, 64-4, 66-3, 65-5, 61-4, 62-3, 64-4, 66-3, 65-5, 61-4, 62-3, 64-4, 67-3, 65-5, 60-3, 62-4, 67-4, 65-4, 60-4, 68-3, 65-4 lb., respectively, at 11 1 ^ per pound. 22. A dry-goods merchant bought 25 pc. of Scotch cheviot containing 42^, 402, 453^ 411^ 401, 452^ 421, 43^, 38^, 351, 302, 412^ 441^ 452^ 391^ 371^ 422^ 47, 41, 42^, 43^, 40^, 47^, 38, 31 yd., respectively, at 39^^ per yard. If he sold the entire purchase at 43|^ per yard, did he gain or lose, and how much ? 23. C. W. Bender failed in business. He owes A $712.25; B, 11421.25; C, 1625.25; D, $1460.75; his entire resources amount to $2109.75. What fractional part of his indebted- ness can he pay? what per cent? How many cents on f 1 ? If his creditors accept payment on this basis, how much will each receive ? 24. A dry-goods merchant bought 12 pc. of striped denim containing 40^, 45i, 40^, 482, 412, 403^ 452^ 4II, 442, 392, 511, 33 j^^^ respectively, at 14|^ per yard; 15 pieces of cashmere containing 39^, 412, 421, 452^ 39, 52, 40, 45, 46, 51, 472, 421, 411, 471^ 48 yd., respectively, at $1.12 per yard; 10 pc. wash silk containing 35 1, 30, 312, 30^ 30, 30, 32^, 32, 31 1, 32 yd., respectively, at 31^ per yard. He gave in payment, cash, $300, and a 60-da. note for the balance. What was the face of the note ? 152 PRACTICAL BUSINESS ARITHMETIC 25. Find the amount of the following bill : Boston, Mass., Apr. 15, 19 Messrs. Charles H. Palmer & Co. Springfield, Mass. Bought of Edgar W. Townsend & Co. Terms: cash 250 lb. Rio Coffee $0.24| 450 " Mocha Coffee .20i 172 doz. Eggs .241 990 lb. White Sugar .041 900 " Brown Sugar .031 975 " Granulated Sugar .041 172 " Butter .161 3021 " Ham .\^ 280 " Cream Codfish .071 11 pails Mackerel 1.87| 120 lb. Raisins •07f 480 " Starch .03| 225 " Japan Tea .26^ 210 " Young Hyson Tea .241 420 " Oolong Tea .271 157 " Pearl Tapioca •03| 17 pkg. Yeast Cakes .37^ 375 lb. Java Coffee •231 26. C's salary is $17.50 per week of 48 hr. How much should he be paid for 11 da., working 9 hr. per day? 27. A man earning |2.75 per day of 10 hr. lost 7 J hr. during one week of 6 da. How much should he receive for the week's work ? 28. E begins work at 7:30 A.M. and quits work at 6:30 p.m. If he is paid at the rate of $3.75 per day of 8 hr. and he takes the noon hour off for lunch, how much should he receive for his day's labor ? 29. A factory foreman is paid $3.75 per day of 8 hr. and $0.50 an hour for overtime. How much should he be paid for a week in which he begins work at 7 o'clock A.M., quits work at 7:30 o'clock p.m., and takes 1\ hr. off each day for lunch? COMMON FKACTIOISrS 153 GEAPHIC OUTLINE A comparison of the money value of the wheat crop, and the fire losses paid by insurance companies, in the United States, 1890 to 1899 inclusive. value of wheat crop. value of fire losses. 1890 1891 1892 1893 1894 1895 1896 1897 1898 1899 800 million dollars 700 million dollars GOO million dollars 500 million dollars A 400 million dollars /\ A, 300 million dollars / t \ \ \ \ i . / / ^s \ 200 million dollars v \ \ ___^„ 100 million dollars 1 '' 1 WRITTEN EXERCISE 1. The figures below give the value of the wheat crop, and the fire losses paid by fire insurance companies, in the United States, for the years 1890 to 1899 inclusive. (See Graphic Outluie.) Farm Val. of Wheat Fire Losses 1890 8334,773,678 S108,993,792 1891 513,473,711 143,764,967 1892 322,111,881 151,516,098 1893 213,171,381 167,544,370 1894 225,902,025 140,006,484 1895 237,938,998 142,110,233 1896 310,602,593 118,737,420 1897 428,547,121 116,254,575 1898 392,770,320 130,593,505 1899 319,545,259 153,597,830 164 PRACTICAL BUSINESS ARITHMETIC 2. Make a graphic outline comparing the wheat crop, and the fire losses paid by the fire insurance companies, in the United States, for the years 1880 to 1889 inclusive. Farm Val. of Wheat Fire Losses 1880 $474,201,850 $74,643,400 1881 456,880,427 81,280,900 1882 445,602,123 84,505,024 1883 383,649,272 100,149,228 1884 330,862,260 110,008,611 1885 275,320,390 102,813,796 1886 314,226,020 104,924,750 1887 310,612,960 120,283,055 1888 385,248,030 110,885,665 1889 342,491,707 123,046,833 3. Make a graphic outline comparing the wheat crop, the cotton crop, and the fire losses paid by the fire insurance companies, in the United States, for the years 1900 to 1909 inclusive. Farm Val. of Wheat Farm Val. of Cotton Fire Losses 1900 $323,515,177 $515,828,431 $160,929,805 1901 467,350,156 439,166,710 165,817,810 1902 422,224,117 501,897,135 161,087,040 1903 443,024,826 660,549,230 145,302,155 1904 510,489,874 652,031,626 229,198,050 1905 518,372,727 632,298,332 165,221,650 1906 490,332,760 721,647,237 518,611,800 1907 554,437,000 700,956,011 215,084,709 1908 616,826,000 681,230,956 217,885,850 1909 730,046,000 812,089,833 188,705,150 Use a dotted line to represent the cotton crop. The figures representing the fire losses do not include the cost of main- taining fire departments, nor the losses sustained by the interruption of business. The United States exceeds all other countries in losses by fire. A large per cent of these losses are due to carelessness. COMMON FRACTIONS 155 ORAL REVIEW EXERCISE 1. I of 36 is what part of 81 ? 2. Multiply 126 by 101; 92 by 102. 3. Divide 41 by 2| ; 3f by 21. 4. Find the cost of each of the following : a. 35 bn. of seed at 35/ per bushel. h. 65 A. of land at $65 per acre. c. 45 yd.* of cloth at 45/ per yard. 5. Divide! by -I; %^y ^^ t by f 6. Multiply 86 by f ; 49 by f ; 55 by -j^. 7. What is the square of 15 ? of 1.5 ? of IJ ? 8. 64x1 = ? 64^i = ? 1 + 1 + 1=? 9. How many yards of cloth can be bought for S25 at 121/ per yard ? 10. If it costs $7.50 to harvest 61 A. of corn, what will it cost to harvest 65 A. ? 11. An agent received $7.20 for collecting a debt, and the merchant received $232.80. What was the total debt? 12. C and D received $ 21.75 for work done jointly. If C does only half as much work as D, how should the money be divided ? 13. If a lot of articles were bought at the rate of 3 for 2/ and sold at the rate of 2 for 3 /, how many must be sold to gain $ 5 ? 14. A and B received $ 34 for work done jointly. If A can do as much work in 8 da. as B can do in 9 da., how should the money be divided ? 15. Name the results quickly : a. A can do a piece of work in 4 da., and B in 5 da. If they work together, in how many days will they finish the task ? h. F can do a piece of work in 31 da., and G in 5 da. If they work together, in how many days will they finish the task ? c. C can do a piece of work in 2 da., D in 3 da., and E in 4 da. If they work together, in how many days will they finish the task ? d. H and J together can do a piece of work in 20 da. If H alone can do the work in 30 da., in how many days can J alone do the work ? 156 PRACTICAL BUSINESS ARITHMETIC written exercise Problems of the Farm 1. If 15 sheep consume 5785 lb. of dry fodder in a year, what is the cost per sheep if the fodder is worth S8.50 per ton ? 2. If eggs are worth 24^ per dozen, what is the difference in the value of two hens, in a year, if one lays 180 eggs and the other lays 96 eggs ? 3. An apple tree produced 9^ bu. of apples, 6 J bu. of which graded as " firsts " and the remainder as " seconds." What frac- tional part of the yield were firsts, and what fractional part were seconds ? 4. The apple tree referred to in Ex. 3 was sprayed the year following, and that year it produced 10^ bu. of which 9^ bu. were firsts and the remainder seconds. What fractional part of the yield were firsts ? What part were seconds ? 5. If the apples referred to in Exs. 3 and 4 were sold at S1.20 per bushel for firsts and 70 / sl bushel for seconds, what was the value of the spraying ? 6. It is estimated that a quail in one year eats 28/ worth of grain and saves S1.68 worth of grain by destroying insects and weeds. What is the value of a pair of quails to the farmer annually, not counting the value of the brood ? 7. An undrained field produced 24 bu. of grain per acre, and after being drained it produced 33 bu. per acre. What was the fractional increase ? What was the value of the increase if the grain sold for 55^^/ per bushel ? 8. A flock of hens averaged 78 eggs each per year. What would be the value to the farmer of introducing a better breed of hens that would produce 120 eggs each per year, if he kept a flock of 40 hens, and received 24/ per dozen for the eggs ? 9. If 6 A. of unfertilized land produced 275 bu. of corn, and if fertilized, it would have produced 350 bu., what would the farmer have gained by fertilizing the land if the corn was sold for 68 / per bushel, and the fertilizer cost $ 24 per ton, and 400 lb. were used on each acre ? COMMON FRACTIONS 157 WRITTEN REVIEW TEST (Time, approximately, forty minutes) 1. A, B, and C hire a pasture for $81. A puts in 6 cows for 4 mo. ; B, 6 cows for 6 mo. ; and C, 6 cows for 5 mo. What sum should each pay ? 2. A man owned |^ of a tract of land ; he sold | of his share for $14,504.46. At that rate, what was the value of his original share ? What was the whole tract worth ? 3. The owner of a house received a net yearly income from rental of $408.90, after paying the following : insurance, $64.20 ; taxes, $74.50 ; repairs, $28.40. What was the monthly rental? 4. A man drew i of his money from the bank and then paid bills of the following amounts: $12.50, $18.25, and $7.50; he then had left in cash $11.75. What sum had he in the bank before drawing the check ? 5. A man placed a mortgage on his house and lot for $2967. The lot cost $2720 ; the improvements, $260.50; and the dwell- ing, $5920.50. The mortgage was what fractional part of the total value of the property ? 6. At the end of a season a dealer sold a machine for $64, after reducing the marked price ^. If he still gained ^ of the cost, what was the first cost? The marked price was what fraction above the cost price ? 7. From dictation, write results for the following: | of 25J; J of 26i; 1 of 36^; | of 17i; J of 42|; 1 of 281; J_ of 22J ; 1 of 641 ; i of 50 \; ^\ of 35^ ; J^ of 501. 8. A merchant closed his business under the following con- ditions : resources, $22,455.20; liabilities, $33,682.80. What fractional part of his debts can he pay ? If he owes James S. Brown $202.50, how much will Brown receive in settlement? 9. A, B, and C are partners in a mercantile business in which A has invested $9180 ; B, $6120 ; and C, $3060. At the end of 1 yr. they divided a gain of $3060.90. If each partner received of the gain according to his fractional part of the investment, how much did each receive? CHAPTER XIII ALIQUOT PARTS 202. An aliquot part of a number is a part that is con- tained in the number an integral number of times. Thus, 2^, 3|, and 5 are aliquot parts of 10. ORAL EXERCISE 1. How many cents in |i? in |l? in Si? in $1? 2. What aliquot part 6f |1 is 25^? 50^? 6|^? 12^? 3. Read aloud the following, supplying the missing terms : 16 X 50^ = 16 X 1 1 = 1 of 116 ; 16 x 25^ = 16 x I J = ^ of 116 ; 16xl2i^=16xf = of 816; 16x6^^=16x1 = of $16. 4. Give a short method for finding the cost when the quan- tity is given and the price is 50^; 25^; 12-|^; 6J^. 5. What is the cost of 160 yd. of dress goods at |1? at 50^? at 25^? at 121^2^? at 6J^? 6. How many cents in |i? in IJ? in $^j? in | Jg? in |^? in$^?inl3-V? 7. What aliquot part of II is 33i^? 16|^? SJ^? 6|^? 14f^? 20^? lOi^? 8. Read aloud the following, supplying the missing terms : 140xl4f^ = 140 X $i = | of $140; 90 x 6f^ = 90 x $ = of 190; 90x20^ = 90x$ = of $90. 9. Read aloud the following, supplying the missing terms : 240x331^=240x1 =| of $240: 240xl6f = 240x $1 = of $ 240; 240 x 12^^ = 240 x $ = of $ 240. 10. Give a short method for finding the cost when the quan- tity is given and the price is 331^; 16|^; 8J^; 6|^; 14f^. 11. Find thecost of 960 yd. of cloth at 331^; at 16f ^; at Sy. 158 ALIQUOT PARTS 159 ORAL EXERCISE State the cost of: 1. 240 lb. tea at bO^; "at 33J^; at 25^. 2. 3601b. cofPee at 331^; at 25^; at 20^; at 121^. 3. 720 gal. cider at 6^^; at 6|^; at 10^'; at 12 J^. 4. 2400 doz. eggs at 121^; at lOf^; at 20^; at 25^. 5. 2400 yd. prints at 8J^; at 6|^ ; at 6J^; at 12^1^. 6. 960 yd. cotton at 6i^; atSl^; at6f^; at 10^; at 12^^. 7. 2040 yd. plaids at 50^; at 331^; at 25^ ; at 20^; at 16f ^. 8. 480 1b. lard at 81^; at 6^^; atl2i^; at 16|^; at 10^. 9. 36001b. raisins at 121)!^; atl6|^; at20^;at25^; at 331^. 10. 480 yd. lining at 81^; at6|^; at 10^; atl2i^; at6|^. 11. 4200 yd. Silesia at 10^; at 20^; at 12^^; atl6f^; at 142^. 12. 1500 yd. plaids at 81; at 50^; at 33^]^; at 25 ^ ; at 20 ^. 13. 420 yd. stripe at 10^; at 12^^; at 14|^; at 16f ^; at 25^. 14. 120 yd. gingham at 81^; at 6^^; at6f^; at loV; at 121^. 15. 1240 yd. wash silk at 25^; at 50^; at 33^^; at 20^. 16. At the rate of 3 for 50^, what will 27 handkerchiefs cost? 17. At 331^ per half dozen, what will 12 doz. handkerchiefs cost? 17 doz.? 25 doz.? 7 J doz.? 41 doz.? 18. A merchant bought cloth at 33 J ^ per yard and sold it at 50^ per yard. What was his gain on 1680 yd.? ORAL EXERCISE 1. What is the cost of 12^ yd. of silk at 96 ^ per yard? Suggestion. The cost of 12i yd. at 96^ = the cost of 96 yd. at 12^ ^ Interchanging the multiplicand and multiplier considered as abstract numbers does not affect the product. 2. Find the cost of 25 yd. of silk at 11.72 per yard. Suggestion. The cost of 25 yd. at$ 1.72 (172 j>) = the cost of 172 yd. at 25^. 3. Find the cost of : a. 25 yd. at 16^. c. 6| lb. at 32^. e. 25 yd. at 84^. b. 121yd. at 48^. d. 12^ lb. at 80^. /. 12iyd. at |1.75. 160 PEACTICAL BUSINESS AEITHMETIC Table of Aliquot Parts Nos. I's i'« i's tVs fs rs iV's iVs i's rVs 1 .50 .25 .12^ .06^ .33i M6| .08^ .061 .20 .10 10 5. n U .621 ^ If .83^ .66f 2. 1. ICO 50. 25. m 6i m 16f 8^ 6f 20. 10. 1000 500. 250. 125. 62^ 33.3^ 166| 83i 66| 200. 100. WRITTEN EXERCISE In the three problems following make all the extensions mentally/. 1. Without copying, find quickly the total cost of : 84 lb. tea at 50^. 6^ lb. tea at 64:^. 75 lb. tea at 331^. 25 lb. cocoa at 52^. 72 lb. coffee at 25^. 121 lb. cocoa at 48^. 84 lb. coffee at 331^. 360 lb. codfish at 6|^. 25 lb. coffee at 28^. 66 lb. crackers at 8^^. 88 lb. candy at 121^. 25 lb. chocolate at 36^. 24 lb. tapioca at 6|^. 25 cs. horseradish at 64 f^. 2. Without copying, find quickly the total cost of : 25 yd. silk at 84^. 12^ yd. silk at 96^. 750 pc. lace at 6J^. 112 yd. ticking at 6-J^. 210 yd. plaids at 331^. 128 gro. buttons at 12i^. 68 yd. lansdowne at 50^. 77 yd. duck at 142^. 6{ gro. buttons at S2^. 155 yd. cheviot at 20^. 96 yd. gingham at 8J^. 84 yd. shirting at 12|^. 25 doz. spools thread at 25^. 168 yd. striped denim at 8^ ^. 3. Without copying, find quickly the total cost of 25 bu. corn at 64^. 25 bu. corn at $0.72. 121 bu. oats at 10.36. 25 bu. beans at 12.80. 121 bu. wheat at 11.04. 121 bu. millet at 11.24. 25 bu. clover seed at i3.60. 50 bu. clover seed at 13.75. 25 bu. corn at 10.84. 25 bu. corn at 10.44. 25 bu. oats at $0.35. 12Jbu. rye at f 1.04. 6 J bu. wheat at $1.20. 6Jbu. wheat at 11.12. 25 bu. timothy seed at $2.40. 60 bu. timothy seed at $2.75. ALIQUOT PARTS 161 ORAL EXERCISE 1. Multiply by 10: 4; 15;. 07; 8^; 11.12; $24.60; 112.125. 2. Multiply by 100: 3; 17; .09; 12^; 11.64; 121.17. 3. Multiply by 1000: 7; 29; .19; 15^; $1.75; 123.72. 4. What aliquot part of 1 10 is 12.50 ? Find the cost of 16 articles at 110 each; at $2.50 each. 5. Find the cost of 84 bu. of wheat at f 1.25. Solution. $1.25 is \ of $10. 84bu. at $10 = $840; | of $840 = $105. 6. Formulate a short method for finding the cost when the quantity is given and the price is $1.25. Solution. $1.25 is ^ of $10; hence, multiply the quantity by 10 and take \ of the product. 7. Formulate a short method for finding the cost when the quantity is given and the price is $2.50; $3. 33 J; $1.66|. 8. Find the cost of 168 yd. of cloth at $1.25; at $2.50; at $3,331; at $1.66|. 9. What aliquot part of $100 is $25? $12.50? $6.25? 10. Find the cost of 72 chairs at $25 each. Solution. 72 chairs at $100 = $7200; but the price is $25, which is \ of $100 ; therefore, \ of $7200, or $1800, is the required cost. 11. Give a short method for multiplying any number by 25 ; by 121; by 61; by 33^; by 81 12. Find the cost of 25 T. coal at $7.20 ; of 6 J T. ; of 121 T. 13. What aliquot part of 1000 is 250 ? 500 ? 125 ? 621 ? 3331? I66f? 200? 100? 83i ? 66|? 14. Formulate a short method for multiplying a number by 250. Solution. Since 250 = ^^^-^^ multiply by 1000 and take J of the product. 15. Give a short method for finding the cost when the quan- tity is given and the price is $125 ; $166|. 16. Multiply 84 by 50 ; by 25 ; by 121; by 16|; by 331 17. Multiply 160 by 21; bylj; by 121; by 125; by 621 18. Multiply 240 by 3}; by 1|; by 331; by 16f ; by 3331. 162 PRACTICAL BUSINESS ARITHMETIC 19. Find the cost of 250 sofa beds at 132 each. Solution. The cost of 250 beds at $32 = the cost of 32 beds at $ 250, The cost of 32 beds at $1000 = $32,000 ; but the price is $250, which is | of $1000; therefore, ^ of $32,000, or $8000, is the required cost. 20. Find the cost of 720 couches at $12.50 each. 21. Find the cost of 440 lb. sugar at 2^j^. Solution. 2^^ is ^ of 10^. The cost of 440 lb. at 10^ = $44 ; but the price is 2|^, therefore, I of $44, or $11 = the required cost. 22. Formulate a short method for finding the cost when the quantity is given and the price is 1|^. Solution. l\f = ^ oilOf; hence, point off one place in the quantity and take I of the result. 23. Give a short method for finding the cost when the quan- tity is given and the price is 2|-^; 3J^ ; IJ^. 24. Find the cost of 160 lb. at 2|^; at 11^; at SJ^; at 1|^. Also of 240 lb. at each of these prices. 25. Find the cost of 2400 lb. at 2^; at 1^^; at 3|^; at 1|^. Also of 360 lb. at each of these prices. ORAL EXERCISE Bi/ inspection find the cost of : 1. 25 lb. tea at 54^. 16. Hyd. silk at 88^. 2. 25 lb. tea at 33^^. 17. 64 pc. lace at 11.25. 3. 125 lb. tea at 64^. 18. 125 yd. silk at 11.12. 4. 6| A. land at 8112. 19. 1250 bbl. beef at $24. 5. 25 T. coal at 18.40. 20. 78 yd. velvet at $2.50. 6. 25 T. coal at 15.20. 21. 2^ bu. potatoes at 96^, 7. 18 T. coal at 16.25. 22. 640 bu. apples at 871^. 8. 164 A. land at 125. 23. 840 yd. prints at 16|^. 9. 72 T. coal at 16.25. 24. 121 bu. potatoes at 64:^. 10. 250 yd. silk at 88^. 25. 84 bookcases at 112.50. 11. 250 yd. silk at 96^. 26. 810 bbl. pork at 112.50. 12. 25 pc. lace at 16.60. 27. 125 yd. crepon at $3.60. 13. 250 yd. silk at $1.12. 28. 12^ yd. cheviot at $1.04. 14. 192 A. land at $12.50. 29. 24 oak sideboards at $125. 15. 165 gro. buttons at 33lj^. 30. 121 yd. gunner's duck at 48^. ALIQUOT PAETS 163 WRITTEN EXERCISE In the following problems make all the extensions mentally. See how many of the problems can be done in 10 minutes. 1. Without copying, find the total cost of : 425 lb. at 10 ^. 2500 1b. at 64/. 24 1b. atl^/. 310 lb. at 20 ^. 1600 1b. at 25/. 48 1b. at 21/. 100 lb. at 14 ^. 1893 1b. at 31/. 2i'lb..at96/. 1000 lb. at 27 1 2500 1b. at 14/. 125 1b. at 24/. 1000 1b. at 41^. 1400 1b. at 25/. 192 lb. at 31 /. 1250 lb. at 44 ^. 1250 1b. at 88/. 88 1b. at 121/. 2. Without copying, find the total cost of: 88 yd. at 11 A 174 yd. at 10^. 24 yd. at 12 /. 72 yd. at 31^. 123 yd. at 11/. 78 yd. at 31/. 104 yd. at 21 ^. 127 yd. at 11/. 165 yd. at 20 /. 480 yd. at 6| ^. 246 yd. at 25/. 114 yd. at 6f/. 360 yd. at 81 A .1712 yd. at 10/. 1280 yd. at 61/. 121 yd. at 11 ^. 1783 yd. at 10/. 192 yd. at 33 J/. 3. Copy and find the total cost of : 450 1b. ut 11^. 249 1b. at 25/. 6J lb. at 88 /. 820 1b. at 11/. 240 1b. at 31/. 92 1b. at 21/. 1200 1b. at 41/. 200 1b. at 31/. 121 lb. at 24 /. 1400 lb. at 61 /. 450 1b. at6f/. 18 lb. at 41 /. 7961 lb. at 50 /. 791 lb. at 40/. 1251b. at 18/. 1293 lb. at 30 /, 7811b. at 50/. 648 1b. at 61/. 1480 lb. at 40 /. 750 1b. at 331/. 1900 1b. at 4J/. 4. Copy and find the total cost of : 750 gal. at 81 /. 99 gal. at 30 /. 360 gal. at 5 /. 488 gal. at 6| /. 60 gal. at ^ /. 625 gal. at 64/. 640 gal. at 61 /. 50 gal. at 76/. 810 gal. at 11/. 194 gal. at 50/. 25 gal. at 74/. 920gal. at 21/. 176 gal. at 25 /. 121 gal. at 88 /. 165 gal. at 6| /. 280 gal. at 121^. 79 gal. at 331/. 240 gal. at 621 ^ 720 gal. at 331/. 20 gal. at $1.79. 666 gal. at 66f /. 366 gal. at 16f j^. 6^ gal. at $1.96. 1680gal. at 16f/. 164 PEACTICAL BUSINESS ARITHMETIC ORAL EXERCISE 1. How much less than fl is 75^? what fractional part of II less? 2. Find the cost of 144 pc. of lace at 75 P per piece. Solution, At $ 1 per piece the cost would be $ 144 ; but the cost is not $ 1 but I less than $ 1. Deducting ^ of $ 144, the result is $ 108, the required cost. 3. Find the cost of 124 bookcases at $7.50. Solution. $ 7.50 is ^ less than $ 10. $ 1240 less { of itself = $ 930, the required result. 4. Formulate a rule for multiplying a number by .75; by 7J; by 75; by 750. 5. How much more than il is $1.12^7 What fractional part of $ 1 more ? 6. Find the cost of 84 yd. of silk at |1.16| per yard. Solution. At $ 1 per yard, the cost would be $84; but $1.16| is ^ more than $1. Adding ^ of $84 to itself, the result is $98, the required cost. 7. Formulate a short method for finding the cost when the quantity is given and the price is 1 1.12 J; $1.16 J; |1.33i; $11.25; 1112.50. 8. How much less than $1 is 87|^? what fractional part of f 1 less ? Formulate a short method for multiplying a number by 87-^. 9. Formulate a short method for multiplying a number by .831; by 1.25. 10. Compare the cost of Sl^ yd. at 64^ with the cost of 64 yd. at 87^^. ORAL EXERCISE State the cost of: 1. 24 yd. at 75 P. 7. 87^ yd. at $ 2.88. 13. 270 yd. at 111 ^. 2. 75 yd. at 24 ^. a 25 yd. at 4 ^. 14. 144 yd. at 1 1^ ^. 3. 192 yd. at 871^. 9. 28 yd. at 75^. 15. Iliyd.atl8^. 4. 240 yd. at 83| P. 10. 27 yd. at 75^. 16. 1125 yd. at 64^. 5. 871 yd. at $2.48. u. 75yd.at84^. 17. 1125 yd. at 32^. 6. 176 yd. at $1,121 12. 75 yd. atl6f^. 18. 1125 yd. at 48^. ALIQUOT PAETS 165 WRITTEN REVIEW EXERCISE 1. Find the total of the costs called for in problems 1-15 in the oral exercise at the top of page 159. 2. Find the total cost of the items in the oral exercise at the bottom of page 162; of the items in the oral exercise at the bottom of page 164. 3. Find the total cost of : 84 yd. at 7^. 98 yd. at 9^. 1121yd. at 5^. 79 yd. at 11^. 1121yd. at 6^. 17 yd. at 16^. 4. Find the total cost of : 71 yd. at 22^. 85 yd. at 30^. 31 yd. at 44^. 17 yd. at 25^. 82 yd. at 88 jz^. 121 yd. at 39^. 71 yd. at 12 f. 250 yd. at 64^. 5. Find the total cost of : 192 lb. at 31^. 167 lb. at 121^. 3841b. at 6|^. 184 lb. at 371^. 72 yd. at 75^. 871yd. at 88^. 320 yd. at 11^. 30 yd. at 71^. 24 yd. at 81 f^. 56 yd. at 831^. 124 yd. at $1,121 1151f lb. at 10^. 172111b. at 15^. 378 1b. at 61 P. 149 1b. at 6 J f^. 2164 1b. at 2|^. 1369 lb. at 21^. 291111b. at 331^. 2706 lb. at 331^. 6. Copy and find the amount of the following bills, less 3 % a. Rochester, N.Y., Aug. 2, 19 Mr. C. G. Garlic North Rose, N.Y. To Smith, Perkins & Co., Dr. Terms : cash, less 3 %. 330 lb. Granulated Sugar 6^^ 32 « Butter 22^ 64 " Cheese 161^ 75 " Young Hyson Tea 24^ 155 " Dried Apples ^^ 300 " Brown Sugar H^ 60 " Oolong Tea 51^ 125 « Rio Coffee 28^ 250 " Mocha Coffee 24 j* 166 PRACTICAL BUSINESS ARITHMETIC h. Buffalo, N.Y., Aug. 5, 19 Mr. George A. Collier Savannah, N.Y. Bought of George H. Buell & Co. Terms : cash, less 3 %. 72 pr. Boys' Hose 12^^ 18 doz. Linen Handkerchiefs 2.50 18 " Lace Handkerchiefs 3.33^ 78 yd. Silk Velvet 3.33^ 75 pc. Black Ribbon 28^ 347 yd. Pontiac Seersucker Q\^ 186 " Washington Cambric 12^^ ORAL EXERCISE 1. At 33^ ^ per pound, how many pounds of coffee can be bought for $12? Solution. .33^ = $ i ; 3 pounds can be bought for $ 1 ; then, 12 x 3 lb. = 36 lb., the required result. 2. When the cost is given and the price is 25^, how may the quantity be found? Solution. When the price is 25 ^, the quantity is 4 times the cost ; hence, multiply the cost by 4- 3. Give a short method for finding the quantity when the cost is given and the price is 20^; 33^^; 12^^; 6^^; 6|^; 16|^. 4. Formulate a short method for dividing any number by 125. Solution. 125 is \ of 1000 ; then the quotient by 125 will be 8 times the quotient by 1000. Therefore, divide by 1000 and multiply the result by S. Or, tI? = ttjW- Therefore, multiply by 8 and move the decimal point three places to the left. 5. Give a short method for dividing by 6J. Solution. 6^ = -^ of 100 ; then the quotient by Q\ -will be 16 times the quotient by 100. Therefore, move the decimal point two places to the left and multiply the result by 16. Or, i = ^^^. Therefore, multiply by 16 and move the decimal point two places to the left. ALIQUOT PARTS 16^ 16|; 6. Give a short method for dividing a number by 12| ; by by 33J ; by 6^ ; by 66| ; by 333|.; by 166|. 7. Formulate a short method for dividing a number by .75. Solution. .75 increased by | of itself = 1. When the divisor is 1 the quo- tient is the same as the dividend. Hence, to divide a number by .75 increase the number by ^ of itself. 8. At 75 ^ per bushel, how many bushels of wheat can be bought for .t?144? for 1192? for $240? for 1780? for |1260? for 1 360? for $1350? for $810? 9. At $7.50 per dozen, how many dozen men's gloves can be bought for $1440? Solution, f 7.50 + ^ of itself = $10. To divide by 10 is to point off one place to the left. $ 1440 + | of itself = $1920 ; $ 1920 ~ $ 10 = 192, the number of pairs of gloves. 10. State a short method for dividing a number by 7^ ; by 75 ; by 750. ORAL EXERCISE Find the quantity: Price per Price per Cost Yard Cost Pound 1. $65 331^ 7. $75 6|^ 2. $250 25^ • 8. $12 1|^ 3. $120 H^ 9. $25 n^ 4. $215 2|^ 10. $38 H^ 5. $126 12|^ 11. $125 $1.25 6. $125 20^ 12. $420 12^^ WRITTEN EXERCISE Find the quantity : Price per Price per Cost Yard Cost Bushel 1. $570.00 75^ 6. $1721.00 88i** 2. $612.00 75>^ 7. $1842.50 25^ 3. $274.50 n^ 8. $1785.00 8Yi^ 4. $281.50 v^\i 9. $2142.00 zz\t 5. $864.50 121^ 10. $2720.50 16|^ 168 PRACTICAL BUSINESS ARITHMETIC REVIEW EXERCISE This exercise may be used in a number of different ways, some of which are suggested below. 1. One student may make the oral extension, using the first quantity, 60 yd., by each price in column 1 ; a second student may use the same quantity and make the extension by each price in column 2, and so on for the ten lists. 2. Each student in the class may take the same quantity and make the extension by each price in column 1, and foot the extensions. Compare results. Such an exercise should occupy one minute. This work may be continued for ten or fifteen minutes daily, as the instructor desires, a different quantity being used for each minute. 1 8 3 4 5 6 7 8 9 10 50/ 25/ 66f/ 60/ 25/ 6i/ 50/ 75/ $1.50 $1,331 20/ 62^/ 6|-/ 87^/ 20/ 16f/ 90/ 81/ $1.25 $1.66§ 12i/ 331/ 75/ 37^/ 60/ 30/ 10/ 371/ $1,121 $1.20 16f/ 30/ H^ 6i/ 12^/ 66f/ 62^/ 80/ $1.10 $1.16§ 90/ 10/ 40/ 80/ 331/ 6f/ 40/ 87^/ $1.75 $1.30 1. Find the cost of : a. 60 yd. 80 yd. 40 yd. b. 72 yd. 50 yd. 44 yd. 90 yd. 20 yd. 25 yd. d. 75 yd. 84 yd. 54 yd. 48 yd. 96 yd. 64 yd. 2. Find the cost of a. 24 yd. 16 yd. 32 yd. h. 78 yd. 69 yd. 81yd. 12 yd. 36 yd. 42 yd. d, 92 yd. 21yd. 46 yd. 15 yd. 18 yd. 10 yd. 3. Find the cost of a. 100 yd. 120 yd. 150 yd. h, 108 yd. 135 yd. 144 yd. e. 160 yd. 180 yd. 128 yd. d. 200 yd. 240 yd. 300 yd. 320 yd. 400 yd. 360 yd. ALIQUOT PAliTS WRITTEN REVIEW EXERCISE 169 Name Quan- tity Prices 1 2 3 4 6 6 Boucle Stripe yd. 10.104 $0.11 $0.10 $0,114 $0.12 $0,124 Dress Silks yd- 1.20 1.25 1.33^ 1.374 1.40 1.50 English Serge yd. 1.33^ 1.30 1.35 1.25 1.374 1.45 Fancy Gingham yd. .061 .06 .064 .07 .074 .071 Fancy Plaids yd. .3H .32 .331 .35 .34 .374 Gunner's Duck yd. .14 .15 •144 .16 .17 .174 Percale Shirting yd. .07 .071 .08 .084 .09 .094 Scotch Cheviot yd. .39 .40 .371 .45 .44 .48 Taffeta Silk yd. .874 .85 .90 .88 .921 .95 Wash Silk yd. .30 .374 .40 .35 .42 .414 Prepare each of the following invoices in correct form^ omit the headiiig^ and find the value hy each price list. 3. 22 3^d. Boucle Stripe 2. 72 yd. Dress Silk 27 yd. English Serge . 104 yd. Scotch Cheviot 56 yd. Percale Shirting 64 yd. Taffeta Silk 48 yd. Wash Silk 60 yd. Gunner's Duck 36 yd. Fancy Gingham 4. 96 yd. Fancy Plaids 88 yd. Scotch Cheviot 36 yd. English Serge 92 yd. Wash Silk 100 yd. Taffeta Silk 120 yd. Boucle Stripe 70 yd. Percale Shirtuig 80 yd. Gunner's Duck 90 yd. Wash Silk 72 yd. Boucle Stripe 6. 84 yd. Taffeta Silk 56 yd. Wash Silk « QQ yd. Fancy Gingham 50 yd. Fancy Plaids 84 yd. Scotch Cheviot 80 yd. Dress Silk Q^ yd. English Serge 70 yd. Gunner's Duck 45 yd. Percale Shkting CHAPTER XIV BILLS AND ACCOUNTS BILLS 203. A detailed statement of goods sold, or of goods bought to be sold, is called either a bill or an invoice. A detailed state- ment of goods bought to be used or consumed, such as office furniture, stationery, and fuel, or a statement of services ren- dered, or of a work performed, is called a bill. Thus, a physician's statement of services rendered, or a transportation company's bill for work performed, and the charges for the same, is called a hill; but a statement of a quantity of silk bought or sold by a dry-goods merchant in the course of trade is called either a hill or an invoice, 204. The models following show a variety of current prac- tices in billing. They will therefore be found helpful as studies. 1. Groceries Boston, Mass., Oct. 15, 19 Messrs. SMITH, PERKINS & CO. Rochester, N.Y. Bought of E. E. GRAY COMPANY Terms 30 da. Telephone, Main 167 bbl. Rolled Oats " Gold Medal Flour bx. Wool Soap $6 . 25 6.50 3.10 18 65 15 75 00 50 99 25 This is one of the simplest bill forms; it is the form that is common in a great many lines of business. 170 BILLS AND ACCOUNTS 171 2. Groceries on. Mass., Nov. 12, 19 Messrs. E. 0. Sherman & Co. Charlestown, Mass. Bought of S. S. PIERCE COMPANY Terms 30 da.; 3fo 10 da. 10 Red Label Hams 146 lb. 20 mats Java Coffee 1500 " 12 6-lb. tins Mustard 72 « 15 6-lb. tins Cocoa 90 " $0.23 $33.58 .25 375.00 .36 25.92 .34 30.60 $465.10 Goods bought by the mat, chest, case, etc., are frequently billed by the pomid. The above bill shows the form in such cases. 3. Hardware The following bill is sometimes used in the hardware business. The first number after the name of the article is the quantity ; the number above the horizontal line following, the price ; and the number below the line, the grade. Thus, the first item in the bill shows that 12 doz. porcelain knobs in all were sold, of which 6 doz. were No. 8 at ^1.25 and 6 doz. No. 16 at $1.33J. JTeu, York.- (W^Jz-^. C , 19 ^.^LA^^^LA. bought of Cf/ie Eureka hardware Qompani^ A^. Q ^^^^^^.^ ^.^ /^^ / C / z^ Iz^ zj: 172 PEACTICAL BUSINESS ARITHMETIC 4. Wholesale Dry Goods M ^^^^^ CHICAGO. /V^^^^^- /.^ 10 -i<2../j^y^ T^^a^ TERMS-^22^^^^^ Bought of MARSHALL FIELD & CO. Franklin Street and Fifth Avenue / 2.^ Z^ ^^'1^^^^^^ jiLL ^J ^/' ¥^^ ^O' ^Z ^atp J3'A ' /^.C ^ JLZJL J^ J (7 3 2.^ 14^' ¥/^ 3 ^2^ ^^ -?^'y:iC- J^ ¥/' ^^-^ ¥C W ¥3 a!C^7^:7y/^..^^^^^-r^-y7 ^ ^ J^Ll—^^ 2.ro Z2. /«<7 i:^f?^,^^>-ir(^'/-Air^n^i^i^r?'i^^ ^/^ 2^\ m ££0. ;Z£ In the wholesale dry-goods business the price is generally for a yard, and the number of yards to the piece varies in some kinds of cloth. The first item in the above bill is followed by a series of numbers, 41, 42, etc. ; these represent the number of yards in each of the 12 pc. Immediately following these numbers is recorded the total number of yards in the 12 pc. The total number of yards should be found by horizontal addition. 5. Manufacturer's The following is a bill for neckwear. The different styles are distin- guished by the marks at the left of the quantity. This form is common among manufacturers, jobbers, and wholesalers. Bills on which trade discounts (sefe page 246) are allowed are arranged as shown in this bill. BILLS AKD ACCOUNTS 173 BetoP0rlt, Oct. 10, 19 ,essrs. J. E. Whiting & Co. Boston, Mass. ^ongfyt of 2Pol)u^on ^ttx^.y M>on^ S. €o* Cermfli Net 30 da. 721 n 1026 1 2 1025 1^ 1020 3 4 923 2J 1015 li doz. Neckwear Less 25s $4.50 6 75 27.00 13 50 27.50 41 25 9.00 6 75 18.00 45 00 24.00 42 00 155 25 3 11 152 14 6. Furniture In the following bill the goods were sold delivered on the cars (f. o. b.) Boston, but the shippers prepaid the freight to Bangor. The freight is a part of the selling price and is added to the amount of the bill, as shown in the model. yi..£.<£dLLJL ^j^;;^ . BOSTON,. K^^w^ 2=^ .9 — ^^^'■f^TL.-r^t'^r?-'^^ .^ Bought of E. M. PRAY, SONS & CO. ^o Manufacturers of Fine Furniture TERMS // C^J^^-1^^ AJl. ./T ^^yfJi^^-<^^A ^ 1^ ? r^ ^^^ Ll^ 7^- ^ ^^^22^^;2^:^2l^^,i^^^^^-2Z-^^L^^l;^^ r/0 174 PRACTICAL BUSINESS ARITHMETIC 7. Wholesale Coal F. H. OSBORN & CO. SHIPPERS OF Anthracite, Bituminous, and Qas Coal Sold to Y^ . Jfp^^T^J-^^^^ r^f^, c^ r ?- ? ^. Aff .I9_ Terms '-yy^A^^ /^ Z ^/^^^^^^^y-C7^^^i,^d^^. ^^^ r 27 tr? ^ ^-^^^yj>. oT-i ^5-0 ^(^ ^g :^ ^^'?€^ y .^^ AJ7 X^ l0Ai2J2J^t^H^ ^222^2^ M~££ -/^ Xf y o r?^ ,^^^^^^^^ 2=£L S3_ ^^^^^.^C^/-^^-- ^^i^a ^ y^-?^ ^.^y r ^^ ^^^^n^^^.^^ ^^^^O^ The above is a form of bill that is generally used for wholesale transactions in coal. It is called a receipted bill, and shows that the coal has been paid for. \^yLL 8. Retail Coal ^ottton,- ^ 19 2-/ 2- ^^yf.^J^'^^^^^^iCfP-^^ f yf^A-^^y^^J>?. Crcrm0- Trnm of jf. ia. C\)mtt &. Co. T 2. -t^r777^^c7^^i<^W7^, V?yr^^z7. ^J^£?-Z/^0 ^JS>0- 2./F0 /V/^/?#- C'- J^ 2^ Z^ 2. -i^^^T-g?.^^ --^^<^- ^^,y9..^:^-r7^^ /".JPO-Z/^e? /'.^^00-2,/^/:^ ^-^OOr^ ^- ^^ i£^ _.i:^ ^ /^Y^ ^m^^^^^^ ^^-/J/^. - BILLS AND ACCOUNTS 175 The foregoing bill shows a form sometimes used by retailers. The numbers at the left of the hyphen are the gross weights, and the numbers at the right the tares of the different loads. 9. China and Glassware ^/joston, Nov. 6, ^£ THE WENTWORTH = STRATTON CO. Rochester, N.Y. 79 bought of Osgood, Kyraoer &- ^ort *Jerm^ 60 da. not; 2$ 10 da. Dinner Set, 130 pieces; viz. 1 doz. Plates. 8 in. 188 /5^ .SJ>' 1. 13 .^¥ ^9 • 1^ SS 1(0 ,3H ■ 17 .JO J..«-i' 25 more Dinner Seta as above 19.07 476 75 7. 'tTL^ - 505 42 The above form is common in the china and glassware business. In^thfs. y^" case a charge is made for the crates used in packing and the prices do"*nbt' include delivery. The cost of the crate and the cost for carting are there- fore made a part of the bill. 1 " 7 •' 1 " 6 •' 1 •' 7 *• (deep) 1 ** Fruit Saucers. 4 in. 1 " Individual Butters 1/12 doz. Covered Dishes. 8 i 1/12 * * Casseroles. 8 in. 1/4 * Dishes, 8 in. 1/12 • 10 " 1/12 * 12 •• 1/12 • 14 *• 1/6 Bakers, 8 in. 1/12 * * Sauce Boats 1/12 ' * Pickles 1/12 * * Bowls 1/12 * * Sugars 1/12 ' Creams 1 Handled Teas 1/2 ' Coffees 1/12 ' ' Pitchers 1/12 • Covered Butters and Drainers more Di nner Seta as above Crates Carting 1 88 1 63 1 38 1 63 75 50 ♦12.00 1 00 13.50 1 13 2.50 63 4.50 38 7.50 63 10.50 88 4.50 75 4.00 33 3.00 25 2.00 17 6.00 50 2.79 2 23 00 2.33 1 17 6.00 50 9.00 75 19 07 19.07 476 495 '7 2 75 82 50 10 176 PRACTICAL BUSINESS AEITHMETIC 10. Lumber Jhe 7{. ^. SSickford Co. 68oston, ^Kass., Oct. 8, 79 Sold to L. A. Hammond & Co. Paterson, N.J. J^enms Pgt . net cash; bal. in 5 da. less iJ^S 23,289 ft. \ X 2\ #1 N. C. Ceili ng $18.50 $430.85 3,520 " " 2 " '» " 17.00 59.84 10,307 " i X 2l 1 " " " 13.50 139.14 1,690 " " 2 " »» " 12.50 21.13 $650.96 Less freight (45,200 lb. at 24F^) 108.48 $542.48 Lumber is generally sold by the thousand feet. In the above bill the goods were sold free on board cars (f. o. b.) Paterson, N.J., but the shippers have, not prepaid the freight. They find that these charges are % 108.48 and deduct this amount from the total of the bill. In the wholesale lumber business the prices quoted usually include the cost of delivery, and when the freight charges are not known at the time of making the shipment, they are paid by the consignees and deducted from the amount of the bill on the arrival of the goods. The freight bill is then sent to the shippers for credit. WRITTEN EXERCISE 1. Study the model bill, page 170. Increase the price of each article 25^ and then copy and find the amount of the bill. 2. Study the first model bill, page 171, and then copy and find the amount of it at the following prices: hams, 27 J^; coffee, 23^; mustard, Z\^\ cocoa, 39^. 3. Study the second model bill, page 171, and then copy and find the amount of it at the following prices : porcelain knobs #8,11.121; #16,11.25; steelyards #64, $11 ; #17,18.331; jack-planes #14, |6; #21, 16.25; #48, $6.75. BILLS AND ACCOUNTS 177 4. Apr. 15, you bought of S. S. Pierce Co., Boston, Mass., for cash: 25 gal. finest New Orleans molasses at 48^; 15 gal. fancy sugar-house sirup at 49^; 75 lb. raw mixed coffee at 29^; 25 lb. raw Pan-American coffee at 19^; 5 cartons Fowle's entire-wheat flour at 39 J ^; Jbbl. Franklin Mills flour at 16.75; I bbl. pastry flour at 15.25. Write the bill. 5. Mar. 19, Frank M. Richmond & Co., New York City, sold to Charles M. Thompson, Poughkeepsie, N.Y., 12 doz. por- celain knobs: 3 doz. #71 at 16.35, 9 doz. #74 at $6.75; 12 doz. shingle hatchets: 6 doz. #16 at 19.75, 6 doz. #34 at 112.50; 7 doz. steel squares: 3 doz. #91 at $35, 4 doz. #73 at 133. Terms: 30 da. Write the bill. 6. Study the model bill on page 172. Increase the prices of the articles marked 124 and 132 five cents each and the re- mainder of the articles one cent each; then copy and find the amount of the bill. 7. Nov. 15, J. B. Ford & Co., Albany, N.Y., bought of the Clinton Mills, Little Falls, N.Y., 10 pc. percale shirting con- taining 42, 48, 521, 58^ ^2, 38, 49, 51, 54, and 46^ yd. , at 7| ^ ; .10 pc. fine wool cheviot containing 58^, 42, 49, 51, 442, 43^ 43^ 412^ 39^ and 42 yd., at 1 1.12 J ; 5 pc. cashmere containing 49^ 40^, 48^ 491, and 49 yd. at $1.37 J. Terms: 60 da., or 3% discount for cash within 10 da. Write the bill. 8. Study the first model bill on page 173. Increase the prices of styles 1026, 1025, 1020, and 923, 25^ each and diminish the prices of the other styles 25^ each; then copy and find the amount of the bill. Omit the discount. 9. Sept. 24, Geo. W. Fairchild, Buffalo, N.Y., bought of E. M. Lawrence & Co., New York City, silk ribbon as follows : 12 pc. #1142 at $2.25; 5 pc. #1321 at $1.25; 25 pc. #171 at $4,371; 8 pc. # 1927 at $1.75 ; 36 pc. #2114 at $1.66f ; 15 pc. #1371 at $1.33J; 15 pc. #624 at $4.371 ; 12 pc. #909 at $1,871; 25 pc. #1008 at $3,331; 25 pc. #1246 at $4.75; 18 pc. #2119 at $1,121 Terms: 30 da., or 2% discount for cash in 10 da. Write the bill. 178 PRACTICAL BUSINESS ARITHMETIC 10. Study the second model bill on page 173. Increase the price of the articles marked Q5 and 396, 25^ each, and diminish the price of the other articles 12|^ each; then copy and find the amount of the bill. Freight added, $14.70. 11. July 20, The Hayden Furniture Co., Rochester, N.Y., bought of John H. Pray & Son, Boston, Mass., 25 #31 card tables at 111 ; 24 #94 china closets at $27.50 ; 15 #16 dining sets at $85; 25 #3060 fancy rockers at $9.25; 15 #35 music cabinets at $2.75; 25 #26 mahogany office chairs at $12.50; 12 #89 oak sideboards at $125. Terms: 30 da. The prices are free on board Boston, and the shipper prepaid the freight, $34.50. Write the bill. 12. Study the first model bill on page 174. Increase the price of the stove coal 25^ per ton and the price of each of the other kinds 12^^ per ton; then copy and find the amount of the bill. Receipt the bill for F. H. Osborn & Co. 13. May 19, C. E. Williams & Co., Cleveland, O., bought of Fairbanks & Co., Scranton, Pa. : 3 car loads of stove coal weigh- ing 20,500, 26,400, and 25,600 lb., respectively, at $4.75 per ton (2000 lb.); 1 car load grate coal weighing 21,900 lb. at $4.25 per ton; 1 car load cannel coal weighing 22,500 lb. at $7.75 per ton. Terms: 30 da., or 3% discount for cash in 10 da. Write the bill. 14. Study the second model bill, page 174, then copy and find the amount of it at $6.25 per ton for each sale. 15. Copy the bill in problem 14 in accordance with the model shown on page 174. Make the price of the coal $6.66|. 16. Study the model bill on page 175. Increase each price given five cents and then copy and find the amount of the bill. Cost of crates used in packing, $6.40; carting, $2.80. 17. July 15, Henry Nelson & Co., Portland, Me., bought of Jones, Stratton & Co., New York City, 5 doz. plates, 8 in., at $1.50; 35 doz. plates, 7 in., at $1.35; 15 doz. plates, 6 in., at $1.10; 10 doz. plates, 5 in., at 90^; 65 doz. handled teas at $1.85. Terms: 30 da. Cost of crate used in packing, $2; cartage, 75^. Write the bill. BILLS AND ACCOUNTS STATEMENTS 179 FOLIO 7^^ Jn account with ^Y^^H^^^.^7^ \ -1^^/-^^ £:_^-:/^r.^7^^yi-e-. ^ ^r?(? /^ ZA 2.J1 ^^ff ^2 'J2. np W^ /ji. z^ :^ w^^C^ i^ . JC ^i^-^ ^ J ( ? C? Zi^ i^ ,; // i:^ ^(^ 7/ 4A^ 205. A statement is an abstract of a customer's account, show- ing under proper dates the details and totals of debits and credits and the balance remaining unpaid. Sn account with /CpW^^^ -;^ .^^W^^P^-7^/^^-^^ Z^ z^ -/t- ^^^^^ ^ ^.^^?^ '^^^^ .'<^-^^^-^^<±y^ -tM 9^ .^.^^. -^ ^9- '.^^ 3J2J2. 2=JL il/l fe^ /otC l2^ ±a, -^/^ nL 1=11. 180 PEACTICAL BUSINESS ARITHMETIC The first model on the preceding page is a statement of C. B. McMeni- men's account for January. It shows that the charges aggregate $997.10, the credits $671.40, and that the balance remaining unpaid is 1325.70. The second model on the preceding page is a statement of C.B. McMeni- men's account for January and February. The items on the January state- ment are summarized in the record "To account rendered, $325.70." The first item on the March statement will be " To account rendered, $412.20." WRITTEN EXERCISE 1. During March, F. E. Smith, Buffalo, N.Y., bought mer- chandise of The Hayden Furniture Co., Rochester, N. Y., as per bills rendered: namely. Mar. 3, $400.80; Mar. 15, $360.90; Mar. 20, $200.70; Mar. 26, $260.90; Mar. 28, $130.50. During the same time he made cash payments on account as fol- lows : Mar. 15, $400.80; Mar. 23, $360.90. On Mar. 2T he also returned goods for credit amounting to $18.60. Render a statement of F. E. Smith's account. 2. During April the above account was charged for merchan- dise as follows: Apr. 15, $720.50; Apr. 27, $260.90. The account was also credited for cash as follows : Apr. 16, $200.70 ; Apr. 28, $100.00. Render the April statement. . 3. Copy and find the balance of the following statement: Boston, Mass., Feb. 1, 19 Mks. C. M. Shermak 931 Beacon St., City In account with Spencer, Mead & Co. Jan. 1 Account rendered 3 2 pr. Gloves 2.50 3 yd. Velvet 3.75 12 " Black Silk 2.10 12 6 pr. Hose 35^ 2 Hats 9.00 30^ yd. Muslin 121;^ Cr. 5 2 pr. Gloves 2.50 15 IHat 9.00 13 64 BILLS AND ACCOUNTS 181 PAY ROLLS PAY ROLL For the week end ing .^-^^4^' ^ 19 Mo. NAME Number oi Houri' Work Euh Day Toul No. ofHotin w«« poHour .t^ REMARKS M T w T F s / \(Z^^y//rr2/^^^^ <^ ^ ^ f7 r^f' (7 ^4^ 2,r-^ /,? jji c '~(/7. Co A^^^y-rp—r^y'-T^ r/. ^^ ^'A rA ^ ^ .jT/ ^r/ /^ y3- 1 ^^w^Yy/^A^.^^^ a'A ^0 a'A /p /l^ ^n .r^ ^^j^ 2^ A.A- //■ r^^/^TZA-r^-r^ 7^ a'A U a'A / A column. Adding the first column at the right, the result is ^^ /: 27 oz. = 1 lb. 11 oz. ; write 11 oz. and carry 1 lb. Adding "^"^ ^^ the pounds, the sum is 147. . 147 lb. 11 OZ. 2. From a barrel containing 379 gal. 1 qt. of molasses, 17 gal. 3 qt. were sold. How much remained unsold ? Solution. Arrange the numbers as in simple subtraction, 07 ^.^ lot so that units of the same order stand in the same vertical 17 * ^ column. 3 qt. cannot be subtracted from 1 qt.; therefore mentally take 1 gal. (4 qt.) from 37 gal. and add it to 1 qt., ^^ ^^^' ^ ^^' making 5 qt. 5 qt. — 3 qt. = 2 qt. Inasmuch as 1 gal. was added to 1 qt., there are but 36 gal. remaining in the minuend ; 36 gal. — 17 gal. = 19 gal. DENOMIISrATE QUANTITIES 195 WRITTEN EXERCISE Find the sum of : 1. 2. 3. 4 L £140 68. £139 5s. 84 T . 75 lb. 279 T . 840 lb. 159 3 214 5 96 14 364 210 162 4 921 3 78 79 872 220 139 2 141 7 37 41 146 140 167 4 10 9 19 63 214 180 129 3 171 8 84 79 926 230 136 4 215 7 97 13 210 420 147 2 321 5 87 125 75 750 Find the diffi 3rence between : 5. 6. 7. 8. 11 mo. 17 da. 11 mo. 1 da. 8 mo. 14 da. 9 mo. 17 da. 8 31 9 31 2 29 2 31 9. From a pile of wood containing 74| cd., 28^ cd. and 15^ cd. were sold. How much remained unsold? 10. I owned a farm of 340 A. when I bought an adjoining field of 741 A. I then sold 140f A. What is the remainder of the farm worth at 175 per acre ? 11. An English merchant had on hand Jan. 1 goods valued at X5927 10s.; during the following six months he bought goods at a cost of <£ 4920 10s. and sold goods to the amount of £ 7926 4s. If the value of the goods on hand July 1 of the same year Avas £4120 10s., what has been the gain or loss in English money ? in United States money ? Finding the Difference between Dates 209. In the foregoing problems in addition and subtraction only compound numbers of two denominations were used. These are practically the only compound numbers met with in business, if the case of finding the difference between two dates is excepted. 196 PRACTICAL BUSINESS ARITHMETIC 210. The difference between two dates may be found by com- pound, subtraction, or by counting the actual number of days from the given to the required date. In business transactions involving long periods of time, the difference is generally found by compound subtraction ; but in transactions involving short periods of time, the difference is generally found by counting the exact number of days. 211. Examples, i. A mortgage dated Oct. 15, 1915, was paid Apr. 6, 1921. How long had it run ? Solution. Write the later date as the minu- 1921 yr. 4 mo. 6 da, end and the earlier date as the subtrahend. April 1915 IQ 15 being the 4th and October the 10th month, write r 7 K^ t 4 and 10 respectively instead of the names of the J • ' months. Consider 30 da. a month and 12 mo. a year and subtract as usual. 2. Find the difference between Apr. 21 and July 27. Solution. Write the number of 9 J^^ [^i April days remaining in April, the number g| ^.^ ^^ Mav in May and June, and finally the qq j^, :y. June number in July up to and including 97 ^o \r^ Inl v July 27. The sum of these numbers 7_ , . "; -i r»-« ^ t i n^ is the required time expressed with '^^ '^^' ^^^m April 21 to July 27 exactness. Observe that the total time excludes the first and includes the last day of the given dates. ORAL EXERCISE State the exact number of days between : 1. Mar. 12 and Apr. 16. 5. July 1 and Oct. 1. 2. Apr. 27 and May 31. 6. June 30 and Sept. 1. 3. May 31 and July 18. 7. July 31 and Nov. 7. 4. June 7 and Aug. 16. 8. Aug. 31 and Dec. 1. WRITTEN EXERCISE Find the exact number of days between : 1. Apr. 2 and Nov. 25. 5. Mar. 18 and Nov. 27. 2. Mar. 1 and Sept. 18. 6. Mar. 17 and July 28. 3. Mar. 15 and Nov. 2. 7. June 16 and Sept. 18. 4. Apr. 21 and Dec. 31. 8. June 19 and Nov. 29. 9. Find the difference between Jan. 3, 1915, and each of the following dates: May 15, 1912; Sept. 6, 1913; Apr. 8, 1909; Mar. 12, 1897. Find the difference by compound subtraction. DENOMINATE QUANTITIES 197 MULTIPLICATION AND DIVISION ORAL EXERCISE Multiply : Divide : 1. 3 ft. by 6. 7. 27 yd. by 9. 2. IJ mi. by 8. 8. 225 ft. by TJ ft. 3. 9 lb. 4 oz. by 2. 9. 48 ft. 6 in. by 2. 4. 18 lb. 1 oz. by 9. lO. 540 yd. by 18 yd. 5. 17 yd. 2 in. by 9. ii. 164 lb. 12 oz by 4. 6. 19 gal. 1 qt. by 3. 12. 640 mi. 160 rd. by 20. 212. Examples, l. How much hay in 8 stacks each contain- ing 5 T. 760 lb. ? Solution. 8 times 760 lb. = 6080 lb. = 3 T. 80 lb. ; 5 ^ ^qq u^ "write 80 in place of pounds and carry 3. 8 times 5 T. = 40 T. ; 40 T. + 3 T. carried = 43 T. The required result ^ is therefore 43 T. 80 lb. 43 T. 80 lb. 2. An importer paid <£ 87 10s. for 50 pc. of bric-a-brac. What was the cost per piece ? Solution. Since 50 pc. cost £87 10s., 1 pc. costs £ 1 15s. 3*0 of £ 87 10s. -^^ of £ 87 = £ 1 with an undivided re- ^0T£~R7 TO — ' mainder of £ 37 ; write £ 1 in the quotient and add ^ £ 37 to the next lower denomination ; £ 37 10s. = 750s. ^^ of 750s. = 15s. 3. At 10s. 6d. per yard, how many yards can be bought for £ 15 15s. ? Solution. The dividend and divisor are concrete numbers ; therefore reduce them to the <£ 15 15s. = 3780a. same denomination before divid- 10s. Qd. = 126c?. ing. £15 15s. = 3780d, 10s. 6cl gygQ,^. ^ 126c^. = 30, no. of yd. = 126d 87S0d. -r- 126(7. = 30 ; 'J' that is 30 yd. can be bought. ORAL EXERCISE 1. At 72 ^ per gross what will 2 doz. buttons cost ? 4 doz. ? 7 doz. ? 2. How many 3-oz. packages can be put up from 4 lb. of pepper ? 3. Find the cost of 3 T. of bran at 30^ per hundredweight; of 5 T. at 50^ per hundredweight. 198 PRACTICAL BUSINESS ARITHMETIC 4. How many 1-lb. packages can be put up from 15 T. of breakfast food ? 5. When coal is $ 6 per ton what will 7000 lb. cost ? 6400 lb.? 3600 lb.? 6. Find the cost of 2400 lb. of flour at 1 2.25 per hundred- weight; of 4400 lb.; of 3200 lb. 7. At 12| ^ per quire what will 480 sheets of paper cost ? 240 sheets ? 2880 sheets ? 720 sheets ? 8. I buy 3 qt. of milk per day. If I pay 8 ^ per quart, what is my bill for July and August ? 9. I bought 3 gro. pens at 60 p a gross and sold them at the rate of 2 for 1 ^ ; what was my gain or loss ? 10. I bought Z\ bu. of apples at % 1.00 per bu. and sold them at 50 ^ a peck. What was my gain ? 11. I sold 4 J cd. of wood for % 27 and thereby lost $ 9 on the cost. What was the cost per cord ? WRITTEN EXERCISE 1. Find the cost of 10 pwt. 7 gr. of old gold at 11.25 per pennyweight; of 12 pwt. 4 gr. at $1.10 per pennyweight. 2. I bought 3|- A. of city land at $125 an acre and sold it at 50 ^ per square foot. Did I gain or lose and how much ? 3. Give the length of a double-track railroad that can be laid with 352,000 rails 30 ft. long. 4. I bought a barrel of cranberries containing 2\ bu. at $4 per bushel and retailed them at 15^ a quart. Did I gain or lose and how much ? 5. From a farm of 375 A. I sold 25| A. What is the re- mainder worth at $125 per acre ? 6. Find the cost (a) in English money and (5) in United States money of 360 doz. cotton hose at b%. 2d. Solution, (a) 5s. 2d. = 5|s. 360 times 5is. = 1860s. = £ 93, the cost in English money. (6) £1 =.$4.8665. 93 times $4.8665 = $452.58, the cost in United Btates money. DENOMINATE QUANTITIES 199 7. Copy and find the amount of the following invoice : Tgrmg yZj'^^-Y^ ii/^sl^ Bought of E. M. LLOYD & SON ^ ^z. /.r^ a^^--/^.^^^J'€:^^Y?^y^ z^ r^ :;^S^^^Y^^^^^'^!^^r^^-^^->t, ^/j -^Tf^^k 7^^.^^ ^^^^ 5^ ^k jkjutm. 5/2, 4/3, and 12/- in the price column = 55. 2c?., 45. M., and 12s., respectively. 8. Reduce $2500 to English money. Solution. $2500 - $4.8665 =r 513.72, or £513.72. .72 x 20s. = 14.4s. .4 X 12d. r= 4.8d. .8 X 4 far. = 3.2 far. Hence $2500 = £513 14s. 4(Z. 3.2 far. 9. Find the value in United States money of a post-office money order for X5 18s. 6W^ u^^y c ^ ? -^?y . ^^. 200 PRACTICAL BUSINESS ARITHMETIC 11. A druggist bought by avoirdupois weight 5 lb. of pep- permint oil at $ 2.50 per pound and retailed it at 50 ^ an ounce, apothecaries' weight. What was his gain ? 213. Farm products which are handled in bulk are frequently bought and sold by the bushel. The statutory weights of the bushel for some of the common commodities are shown in the following table : Statutory Weights of the Bushel Commodities Weight in AVOIRDITHOIS Poinds Exceptions Barley- 48 Ala., Ga., Ky., and Penn., 47; Ariz., 45; Cal., 50. Beans 60 N. H. and Vt., 62. Clover Seed 60 Corn, Shelled 56 Ariz., 54; Cal. 52. Oats 32 Me.,N.J., Va.,30; Md.,26. Potatoes, Irish 60 Md., Penn., and Va., 56. Rye 56 Cal., 54. Wheat 60 214. Example. What will 4260 lb. of wheat cost at 80 J^ per bushel? Solution. In examples of this character the 71 principles of cancellation may be applied to advan- ^200 X 80^ = ^ 56 80 tage. ^0 In problems 1-4 in the following exercise the price is per bushel in each case. WRITTEN EXERCISE 1. Find the total value of : 66401b. wheat at 84^. 42301b. wheat at 95^. 2. Find the total value of : 32641b. oats at 25^. 24001b. oats at 48^. 25601b. oats at 37^^. 3. Find the total value of : 3660 lb. clover seed at 14.50. 1200 lb. clover seed at 14.75. 2472 lb. clover seed at $4.20. 12601b. wheat at 90^. 61201b. wheat at 871)^. 69511b. oats at 32^. 19201b. oats at 331^. 3840 lb. oats at 29J^. 5040 lb. shelled corn at 47^^. 2800 lb. shelled corn at 56 j^. 2240 lb. shelled corn at 73^. CHAPTER XVI PRACTICAL MEASUREMENTS DISTANCES AND SURFACES Distances 215. An angle is the divergence of two lines from a common ^^^^A point. B^^— C Thus the divergence of the lines BA and BC from the point B is the angle ABC. 216. A right angle is the angle formed when one straight line so meets another as to make the two adjacent angles equal. The lines forming the angles are perpendicular to each other. c- Thus the two angles ABC and ABD are right angles, and the lines AB and CD are perpendicular to each other. 217. An acute angle is less than a right angle ; an obtuse ^ angle is greater than a right angle. __\^ Thus the angle ABC is an acute angle, and the angle ^ ABD is an obtuse angle. 218. A surface is that which has length and width, but not measurable thickness. A level surface, as the surface of still water, is called a plane surface or a plane. 219. A rectangle is a plane figure bounded by four straight lines and having four right angles. A square is a rectangle whose sides are all equal. 201 ■^^^'4^ 202 PRACTICAL BUSINESS ARITHMETIC 220. A triangle is a plane figure bounded by three straight lines and having three angles. A triangle is called equilateral when all its sides are equal ; isosceles when any two of its sides are equal; scalene when no two of its sides are equal. 221. A right-angled triangle is a triangle having a right angle. A triangle containing an acute angle is sometimes called an acute-angled triangle ; a triangle containing an obtuse angle, an obtuse-angled triangle. 222. The perimeter of a plane figure is the distance around it. 223. A circle is a plane figure bounded by a regularly curved line, every point of which is equally distant from a point within called the center. The circumference of a circle is the curved line which bounds it ; the diameter is any straight line passing through the center and terminating in the circumference ; the radius is one half the diameter. An arc is any part of the circumference of a circle. 224. It is proved in geometry that the circumference of a circle is 3.1416 times the diameter. 225. Therefore, to find the circumference of a circle when the diameter is given, multiply the diameter hy 3.1416. 226. And, conversely, to find the diameter of a circle when the circumference is given, divide the circumference by 3.1416. WRITTEN EXERCISE 1. Draw neat figures to represent each of the following: rectangle, triangle, square, circle, right-angled triangle, equi- lateral triangle, isosceles triangle, scalene triangle, radius of a circle, arc of a circle. 2. A parlor is 18 ft. 6 in. long and 12 ft. 3 in. wide. What will be the cost, at 28^ per foot, of a molding extend- ing around the room ? PRACTICAL MEASUREMENTS 203 Trd: 3. The circumference of a circle is 113.0976 ft. What is the length of the longest straight line that can be drawn across the circle? Find the circumference of a circle whose radius is 21 ft. 4. What will be the cost, at 75/ per yard, of carpeting a stairway of 18 steps, the tread of each stair being 12 in. and the riser 8 in. ? (Allow for one extra step and one extra riser.) 5. How many telegraph poles 10 rd. apart will be required for 150 mi. of railroad ? Areas oral exercise 1. What is the area of a square 1 rd. on each side ? 2. How many squares 1 rd. on each side in a rectangle 6 rd. long and 1 rd. wide ? 3. How many rectangles, each 6 rd. by 1 rd., in a rec- tangle 6 rd. by 3 rd. ? 4. How many square rods in the area of a rectangle 6 rd. long and 3 rd. wide ? 5. How many square rods in the area of a rectangle 16 rd. long and 132 ft. wide ? 6?d: Solution. 132 ft. = 8 rd. A rectangle 132 f t. = 8 rd. 1 rd, on a side contains 1 sq. rd. But the 8 X 16 SO rd = 128 SQ rd given rectangle is 16 times 1 rd. long and 8 times 1 rd. wide. Therefore the required area is 16 x 8 x 1 sq. rd., or 128 sq. rd. 227. The product of the length and ividth of a rectangle equals the area. ORAL EXERCISE Find the areas of rectangles having the following dimensions. Make use of the short method explained in §§ 180-182. 1. ^ ft. by ^ ft. 3. 9.5 rd. by 9.5 rd. t 6rd. i. CO 2. 7| rd. by 71 rd. 4. 12.5 ft. by 4.5 ft. 204 PRACTICAL BUSINESS ARITHMETIC 228. The dimensions of a triangle are the base, the side on which the triangle appears to stand ; the altitude, the per- pendicular distance from the base to the highest point of the triangle. Base ORAL EXERCISE 1. How does the area of the triangle on the right compare with the area of a rectangle 8 ft. by 4 ft. ? 2. Compare the area of the triangle on the left with the area of a rectangle 12 rd. by 5i rd. 3. What is the area of a triangle whose base is 8 ft. and whose alti- Dj^dT tude is 9i ft. ? 229. In the above exercise it is clear that one half the product of the base and altitude of a triangle equals the area. ORAL EXERCISE State the areas of triangles whose bases and altitudes, respec- tively, are as follows : 1. 20 ft., 18 ft. 3. 12 ft, 41 ft. 2. 12 ft., 16 ft. 4. 191 ft., 8 ft. 230. If a circle be divided as in the figure on the left and the parts rearranged as in the figure on the right, it will be clear that the area of the circle equals the area of the twelve triangles. The altitude of each triangle is the radius of the circle, and the sum of the bases the circumference. 231. It is therefore clear that one half the product of the circumference and radius of a circle equals the area. PRACTICAL MEASUEEMENTS 205 ORAL EXERCISE 1. Find the area of this triangle: base, 8 in.; height, 11 in. 2. A field contains 1280 sq. rd. If the width is 32 rd., what is the length ? 3. A man sold a lot 10 rd. long and 8 rd. wide at the rate of $260 per acre. How much did he receive ? WRITTEN EXERCISE 1. Find the area of a circular pavilion with a radius of 56i ft. 2. A city lot contains ^ A. If it is 200 ft. long, what is its width, and what is its value at 50 / per square foot ? 3. The floor of a restaurant 50 ft. long and 40 ft. wide is cov- ered with tiles 8 in. square. How many tiles will be required ? 4. A park, 50 rd. long and 40 rd. wide, has a walk 1 yd. wide inclosing it. How many square feet in the walk ? Public Lands 232. In parts of the United States public lands are surveyed by selecting a principal meridian which runs north and south, and a base line which runs east and west. l. ]^ Other lines divide the land into tracts 6 mi. square called townships. Town- ship lines running north and south are called ranges. A in the diagram, may be read as Tp. 1 N., R. 3 W. : the first township north of the base line, in the third range west of the principal meridian. 233. Each townsliip is divided into 36 sections, each 1 mi. square. The numbering of a section is shown in the diagram at the left. Sections are divided into halves and quarters; quarter sections are subdivided into halves and quarters. If diagram 3 is B of diagram 2, and diagram 2 is A of diagram 1, C of dia- W- g 1 ■ 1 Base a Line ^ 1 3 6 5 4 3 2 1 r 8 9 10 11 12 18 17 16 15 14 13 B 20 21 22 23 24 80 29 28 27 2C 25 31 32 33 34 35 36 3 N. i Section (320 A.) S.W. i (160 a.) li Township Section gram 3 may be described as the S. E. 1 of S. E. i, Sec. 19, Tp. 1 N., R. 3 W. 206 PRACTICAL BUSINESS ARITHMETIC ORAL EXERCISE 1. How many chains *n a mile ? liow many rods ? how many feet ? How many rods in a chain ? how many feet? 2. How many acres in a field 50 ch. by 40 ch.? in a field 40 ch. square ? in a field 80 ch. by 80 ch. ? 3. A field has an area of 4 A. If it is 10 ch. long, how wide is it and what will it cost to fence it at 50 ^ per rod ? at 60 ^ ? WRITTEN EXERCISE 1. Make a diagram of a township and locate N. J, Sec. 20. 2. Draw a diagram illustrating principal meridian, base line, range line, and township lines, and mark Tp. 2 S., R. 2 E. and Tp. 1 N., R. 3 W. 3. Find the value, at 112.50 per acre, of Tp. 2 N., R. 3 W. 4. Find the cost at S25 per acre of the E. h of N.W. i, Sec. 20, Tp. 1 N., R. 4 W. Squaiie Root and Its Applications oral exercise 1. What is meant by factor^ by exponent P by power of a number f 2. State the second power of each of the following numbers : 1, 2, 3, 4, 5, 6, 7, 8, 9. How much is 122, 132^ 142^ 152^ 162? 3. Name one of the two equal factors of each of the following numbers: 2, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196. 234. The square of a number is the product arising from using the number twice as a factor. The square root of a number is one of the two equal factors of the number. 235. The square root of a number may be indicated by writ- ing the number under the radical sign ■y/~ or by placing the fraction ^ above and to the right of the number. Thus, \/l96 or 1965 indicates the square root of 196. 236. The square root of a number is readily derived from the process by which the square is formed. PRACTICAL MEASUREMENTS 207 237. Example. What is the square of 42 ? Solution. Since 42 = 40 + 2, the square of 42 may be found as follows : 40 + 2 40 + 2 . 402=1600 ( 40x2 ) + 22 2(40x2)= 160 402 ■!_ (40x2) 22 = 4 402+ 2(40x2) + 22= 17(54- 238. In the preceding process it is shown that the square of a number is equal to the square of the tens plus twice the product of the tens hy the units, plus the square of the units. 239. 12 = 1 , 102 ^ 100, 1002 = 10000, and so on ; 92 = 81, 992 ^ 9801, 9992= 998001, and so on. If is therefore evident that the square of an integral number contains twice as many figures or one less than twice as many figures as the number. Hence, if an integral number be separated into groups of two figures each, from right to left, there will be as many figures in the square root as there are groups of figures in the number. 240. Examples. 1. What is the square root of 529 ? Solution. Beginning at the right, separate the number into 5 29(23 periods of two figures each. The greatest square in 5 is 4 and a the square root of 4 is 2, the tens' figure of the root. Find the — — -— remainder, affix the second period, and the result is 129. This ^"^J^ remainder is equal to twice the product of the tens by the units, 1 29 plus the square of the units (§ 242). Twice 2 tens is 4 tens (40) and 4 tens (40) is contained in 129, 3 times ; hence, 3 is the units' figure of the root. Twice the tens multiplied by the units plus the square of the units is the same as twice the tens plus the units multiplied by the units. Therefore, annex 3 units to the 4 tens and multiply by 3 ; the result is 129. The square root of 529 is thus shown to be 23. 2. What is the square root of (a) 13.3225; (5) of .0961 ? 13 .32 25(3.65 .09 61(.31 9 .09 6.6)4 .32 .61). 00 61 3 .96 .00 61 7.25) .36 25 .36 25 208 PRACTICAL BUSINESS ARITHMETIC 241. The process of finding the square root of a number may be summarized as follows : Beginning at the units, sejparate the number into groups of two figures each. Find the greatest square in the left-hand group and write its root for the first figure of the required root. Subtract the square of the root figure from the left-hand period and annex the second period for a dividend. Take twice the root figure already founds considered as tens^ and divide the dividend by it. Annex the quotient to both the root ayid the trial divisor and multiply by the units. Continue in like manner until all the periods have been used. The result will be the square root. If a number contains a decimal, begin at the decimal point and indicate groups to the left for the integral part of the root, and to the right for the decimal part of the root. If the last period on the right of the decimal point has but one figure, annex a decimal cipher, as each decimal period must contain two figures. To find the square root of a common fraction, extract the square root of the numerator and denominator separately. If the terms of the fraction are not perfect squares, reduce the fraction to a decimal and then extract the square root. WRITTEN EXERCISE Find the square root of: 1. 324. 5. 576. 9- 9025. 13. II- 2. 484. 6. 1024. 10. 3364. 14. Ml- 3. 676. 7. 7225. 11. 70.56. 15. MM- 4. 729. 8. 3969. 12. 150.0625. 16. fitffi- 242. It has been seen that the area of a square is the product of its two equal sides. It therefore follows that the square root of the area of a square equals one of its sides. 243. The hypotenuse is the side opposite the right angle in a right triangle. PRACTICAI^ MEASUREMENTS 209 244. In the accompanying illustration it will be seen that the square on the hypotenuse is equal to the sum of the squares on the other sides. Hence, 245. To find the hypotenuse take the square root of the sum of the squares of the base and altitude; and 246. To find the base or the altitude take the square root of the difference he- tiveen the squares of the hypotenuse and the other side. WRITTEN EXERCISE 1. A square field contains 6.625 A. What is the length of one of its sides ? 2. Find the side of a square containing the same area as a field 160 rd. long by 90 rd. wide. 3. What is the hypotenuse of a right-angled triangle, the base of which is 30 ft. and the altitude 40 ft. ? 4. The accompanying diagram, represents a piece of land. It is drawn on the scale of -^-Q in. to the rod. The land is divided into two fields by the line AB. Find the cost, at 50 ^ per rod, of fencing the two fields. 5. What will be the cost, at $1.75 per chain, of fencing a square field containing 1.6 A.? Roofing 247. Roofing is usually measured by the square of 100 sq. ft. 248. The size of slates used for roofing varies from 6 in. by 12 in. to 16 in. by 24 in. Contractors and builders generally use prepared tables for estimating the amount of slate to be used. The number of slates per square varies with the size of the slate. Thus, slates 16 in. by 24 in. require 86 per square; slates 6 in. by 12 in. require 533 per square ; etc. 210 PRACTICAL BUSINESS ARITHMETIC ' 249. All shingles average 4 in. in width and are put up in bundles of 250. The shingles most commonly used are 16 in. or 18 in. long. 16-inch shingles are generally laid 4^ in. and 18-inch shingles 5^ in. to the weather. 250. A shingle 4 in. wide laid 41 in. to the weather will cover 18 sq. in. A square contains 14,400 sq. in. 14,400 sq. in. 'T- IS sq. in. = 800. It is therefore clear that 800 16-inch shingles will cover a square of roof. 251. A shingle 4 in. wide laid 5 1- in. to the weather will cover 22 sq. in. 14,400 sq. in. -^ 22 sq. in. = 655. It is therefore clear that 655 IS-inch shingles will cover a square of roof. In practice 655 per square is called 700 per square. in 7500 shingles? ORAL EXERCISE 1. How many bundles in 1000 shingles in 26,000 shingles ? 2. What will be the cost, at 14 per square, of tinning a roof 20 ft. by 15 ft. ? 3. A certain roof requires 7610 shingles. How many bundles of shingles must be bought to cover it? A dealer will not sell a fractional part of a bundle of shingles. 4. How many slates at 300 to the square will be required for a flat roof 30 ft. by 20 ft. ? 252. The rise in the -rafters for each foot in the base of the gable is called the pitch of the roof. 253. When the rise of the roof is 6 in. per foot, the roof is said to have one-fourth pitch. 254. When the rise of the rafters is 12 in. per foot, the roof is said to have one-half pitch. Gothic Pitch PRACTICAL MEASUREMENTS 211 255. When the rise of the rafters is 15 in. per foot, the roof is said to have five-eighths, or Gothic pitch. When the rise of the rafters is 6 in. per foot, the perpendicular height of the gable is i of the width of the building ; when the rise is 12 in. per foot, the height of the gable is ^ the width of the building; when the rise is 15 in. per foot, the height of the gable is f of the width, or 1^ times | the width of the building. Hence the names one-fourth pitch, one-half pitch, etc. Find the height of the gable : Width of Building Pitch of Roof Width of Building Pitch of Roof 1. 30 ft. 1 3. 24 ft. Gothic 2. 50 ft. 12 in. per ft. 4. 36 ft. i WRITTEN EXERCISE 1. The accompanying diagram represents the roof of a shed 16 ft. wide. If the ridge- pole is 68 ft., the pitch of the roof one half, and the projection of the rafters 18 in., how many shingles 16 in. long, laid ^ in. to TfilillPlIi™ the weather, will be re- |ll|jl quired to cover the roof ? Solution \ of 16 ft. = 8 ft. = the base of the triangle ABC. The pitch of the roof is \ ; ^ of 16 ft. = 8 ft. = the altitude of the triangle ABC. 82 + 82 = 128 ; 128^ = 11.31, number of feet in the hypothenuse of ABC. 18 in. = 1.5 ft. ; 11.31 ft. + 1.5 ft. = 12.81 ft. = the length of the rafters or the width of each side of the roof. 2 X 68 X 12.81 ft. = 1742.16 sq. ft. = the entire surface of the roof. 1742.16 sq. ft. = 17.4216 squares ; 17.4216 x 800 shingles = 13937 shingles. As bundles of shingles are not broken it will be necessary to buy 14000 shingles. 2. A building is 40 ft. wide. If the length of the ridge- pole is 80 ft. and the projection of the rafters 20 in., how many shingles 18 in. long and laid 5^ in. to the weather will be required for the roof, the pitch being | ? 212 PRACTICAL BUSINESS ARITHMETIC 3. A building is 30 ft. wide. If the length of the ridge- pole is 60 ft. and the projection of the rafters 15 in., how many shingles 16 in. long and laid 4^ in. to the weather will be required for the roof, the pitch being ^? Plastering 256. Plastering is usually measured by the square yard. 257. There is no uniform rule with respect to the allowance to be made for doors, windows, and other openings. What Allowance, if any, shall be made for openings is usually stated in the contract covering the work. In some sections it is customary to make allowance for one half the area of the openings ; in others, for the full area of the openings ; in still others, for a stated number of square feet. In giving the dimensions of a room carpenters, architects, and mechanics write the length first, then the width, and finally the height. They also usually write 5" for 5 in., 5' for 5 ft., and 5' x 5' for 5 ft. by 5 ft, ORAL EXERCISE 1. What is the perimeter of a square room 20' on a side ? 2. What is the perimeter of a dining room 18' x 12' x 9'? 3. How many square feet in the four walls of the room in problem 2, not allowing for openings ? in the ceiling ? in the four walls and the ceiling ? 4. How many square yards in the four walls of a room 24' x 16' X 9', not allowing for openings? 5. At 25^ per square yard, what will it cost to plaster 945 sq. ft. ? 1080 sq. ft. ? 1440 sq. ft. ? WRITTEN EXERCISE 1. What will it cost, at 27 ^ per square yard, to plaster the walls and ceiling of a hall 60' x 40^ x 24', making an allow- ance of 40 sq. yd. for openings ? 2. Find the cost, at 26^ per square yard, of plastering the walls and ceiling of a room 18' x 16' 6" x 8' 6'^ making full allowance for 2 doors each 7' 6" x 4', 3 windows 6' x 4', PEACTICAL MEASUREMENTS 213 3. What will be the cost of plastering, with hard finish, at 34 ^ per square yard, the walls of the rooms in the following dwelling ? First Floor. Parlor, 14' x 12' ; sitting room, 12' x 12' ; dining room, 12' x 10' ; kitchen, 12' x 10' ; pantry, 8' x 6'. All rooms on this floor are uniformly 8' 6" high. Second floor. Front chamber, 14' x 12' ; back chamber, 12' X 12' ; middle chamber, 10' x 9' ; hall, 23' x 4'. All rooms on this floor are uniformly 8' high. Allowance is made for 40 openings of 17 sq. ft. each. Painting 258. Painting is usually measured by the square yard. 259. It is customary to make no allowance for windows, the painting of window sills and sashes being considered as expen- sive as the painting of the surface area of the entire window. WRITTEN EXERCISE 1. What will it cost, at 25^ per square yard, to paint the walls of a room 20' x 16' x 12', no allowance being made for doors or windows ? 2. At 6J^ per square yard, what will it cost to kalsomine the walls and ceiling of a room 24' x 18' x 12', allowing for a door 9' X 4', 2 windows 7' x 4', and a wainscot 3' high around the regular surface of the room ? 3. Find cost, at 24^ per square yard, of two coats of paint on the outside walls of a tobacco barn 68' x 20' x 25' with gables extending 10' above the ends of the walls. 4. What will be the cost, at 22^ per square yard, of painting the outside walls of a barn 100' x 40' x 20' with gables extending 10' above the walls ? with gables extending 12|' above the walls ? 214 PRACTICAL BUSINESS ARITHMETIC Flooring 260. Flooring is measured by the square (100 sq. ft.) or by the thousand square feet. Professional floor layers charge by the square, the price being from 75^ to $ 1.50 per square. Carpenters usually work by the day in laying floors. Spruce flooring is 4" or 5^" in width; hardwood flooring is 2" or 2^" in width. In flooring there is considerable waste in forming the tongue and the groove of the boards. When flooring is 3" or more in width, it requires about 1^ sq. ft. of material for every square foot of surface to be covered; when flooring is less than 3" in width, it requires 1^ sq. ft. for every square foot of surface to be covered. 261. Example. How many feet of spruce flooring will be required for a room 32' x 24'? Solution. 32 x 24 = 768, the number of square feet to be covered. 1^ X 768 sq. ft. = 060 sq. ft., the quantity of flooring required. WRITTEN EXERCISE 1. Find the cost at 845 per thousand square feet of a hard- wood floor for a room 20' x 16'. 2. A pavilion is 70' x 50'. If the flooring is of spruce, what will be the cost at $ 27 per thousand square feet ? 3. In a two-story dwelling the floor area measures S5'6" x 26'. The first floor is to be of hardwood and the second floor of spruce. Find the quantity of flooring needed. 4. What will be the cost of a hardwood floor in a room 30' X 28', if the labor and incidentals cost 825.50, the lumber S48perM.? 5. Find the cost of laying an oak floor 20' x 15', reckoning the labor and incidentals at $ 9.50, the floor boards at $ 83|^ per thousand. 6. The floors in a three-story dwelling are each 55' 4" x 33' 10". The first floor is to be of hardwood worth 1 50 per thousand square feet and the other floors of spruce worth $27 per thousand square feet. If it costs 11.10 per square for labor, what will be the total cost of laying the three floors ? PRACTICAL MEASUREMENTS 215 Carpeting 262. Carpet is sold by the yard. Such floor covering as oilcloth and linoleum are frequently sold by the square yard. 263. In determining the number of yards of carpeting re- quired for a room it is necessary to know whether the strips are to run lengthwise or crosswise. Carpets are generally laid lengthwise of a room ; but when the matter of expense is an item, it is sonxetimes more economical to lay the strips cross- wise. When the length of the strips required is not an even number of yards, there is usually some waste in matching the pattern. Merchants will cut fractional lengths but not fractional widths of carpeting. It is therefore frequently necessary to cut off or turn under a part of a strip. ORAL EXERCISE 1. How many yards of carpet, 1 yd. wide, must be purchased for a room 5 yd. long by 4 yd. wide ? 2. The accompanying diagram represents a room drawn on the scale of 21 of an inch to the foot. Find the dimensions of the room. 3. How many strips of carpet, 1 yd. wide, laid lengthwise of the room, will be required for problem 2 ? How many feet in each strip ? How many yards of carpet will be required for the room ? 4. The accompanying diagram represents a room drawn on the scale of ^ in. to the foot. How many strips of carpet, 1 yd. wide, laid lengthwise of the room, will be required to cover it ? What part of a strip must be cut off or turned under in this case? 5. How many feet in each strip in problem 4 ? If there is 1 . 1 2 in. no waste in matching the pat- tern, how many feet of carpet will be required ? how many yards ? lin. 216 PRACTICAL BUSINESS ARITHMETIC WRITTEN EXERCISE 1. How many yards of carpeting 1 yd. wide will be required to cover the chamber in the accompanying floor plan if the strips are to run lengthwise and there is no waste in matching the pattern ? 2. Find the number of yards of carpet required to cover the room in problem 1 if the strips run across the room and there is a waste of 6 in. per strip in matching the pattern. 3. If the chamber is carpeted in the more economical way, what will be the cost at $ 1.25 per yard ? 4. How many yards of carpet I yd. wide will be required for the parlor in the foregoing floor plan ? The strips are to run lengthwise, and there is no waste in matching the pattern. The cheaper grades of carpet are usually 1 yd. wide. The expensive grades, such as Brussels, Wilton, etc., are | yd. wide. 5. How many yards of carpet | yd. wide will be required for the dining room in the foregoing floor plan ? The strips are to run lengthwise, and there is a waste of 6 in. per strip in match- ing the pattern. Papering 264. Wall paper is usually sold in double rolls 18 in. wide and 16 yd. long. Single rolls 18 in. wide and 8 yd. long are sometimes used, but it is generally found more economical to use double rolls. These dimensions vary more or less. Allowances for openings, such as doors and windows, are made in dif- ferent ways by different paper hangers. Some make a uniform allowance for each opening, while others make allowance for the exact measurements of the openings. Any whole rolls left over after papering may usually be returned to the dealer. PRACTICAL MEASUREMENTS 217 ORAL EXERCISE 1. What will the border for a room 15' x 18' cost at 33^ f per yard? 2. 18 in. = f ft. 30 ft -^ f ft. = 30 ft. x | ft. = 20. Divide 21 ft. by 18 in. 3. A wall is 15 ft. long and 9 ft. high. If there are no openings, how many strips will be required to cover it ? How many full strips can be cut from each double roll of paper? What part of a strip will run to waste? How many rolls will be required for the wall ? 4. Suppose that in problem 2 there is a door 3' x 8'. What is the length of the regular surface of the wall ? Fractional strips must be counted as full strips. Why ? How many strips of paper will be required to cover the regular surface of the wall ? Will dealers sell a fractional part of a roll of paper? How many rolls, then, will be required for the regular surface of the walls? 5. There is a small surface over the door in problem 5 that has not been considered. What may be used to cover this surface ? 265. Obviously, to estimate the quantity of paper required for a room: From the perimeter of the room subtract the width of the open- ings. Find J of this remainder and the result will be the number of strips required. Divide the number of strips required by the number of full strips that can be cut from each roll of paper and the result is the required number of rolls. By this method the ends of the rolls are supposed to be utilized for the surface above the doors and above and below the windows and other irregu- lar places. The height of the room, in papering, will be understood to mean the distance from the baseboard to the frieze. To estimate the paper required for a ceiling, take -| of the width of the room for the number of strips required. Divide the number of strips re- quired by the number of full strips that can be cut from each roll and the result is the number of rolls of paper required. 218 PEACTICAL BUSINESS AEITHMETIC 266. Example. How many double rolls of paper will be required for the walls and ceiling of a room 21' x 18' x 8', al- lowing for 2 doors and 3 windows, each 3|- ft. wide? Solution (21' + 18') X 2 = 78', the perimeter of the room. 5x3^' = 17|', the total width of the openings. 78' — 17|' = 601' , the perimeter of the reguLar surface of the walls. I of 60| = 40i, the number of strips of paper necessary for the regular surface. 48' -f- 8' = 6, the number of- strips in each roll. 40i strips -=- 6 strips = 6 if, or practically 7 rolls of paper required for the walls. I of 18 = 12, the number of strips required for the ceiling. 48' -4- 21' = 2f , or practically 2, the number of strips in each roll. 12 strips H- 2 strips =6, the number of rolls required for the ceiling. 6 rolls + 7 rolls = 13 rolls required for the walls and ceiling. WRITTEN EXERCISE 1. The rooms in the floor plan, page 216, are 9' high. What will it cost, at 93^ sl roll, to paper the walls and ceiling of the parlor, making allowance for 2 double doors, each 6' wide, 1 single door S^' wide, and 2 windows, each 3 J' wide? 2. How many rolls of paper will be required for the walls and ceiling of the dining room in the floor plan, page 216, al- lowing for 1 double door 6' wide, 1 single door 3^-' wide, and 2 windows each 3| ' wide ? 3. At 43^ per roll how much will it cost to paper the walls and ceiling of the chamber in the floor plan, page 216, allowing for 2 windows, each 3 J' wide, 1 double door 6' wide, and 1 single door 3|^' wide. SOLIDS Rectangular Solids 267. A solid is that which has lengthy width, and thickness. 268. A rectangular solid is a solid bounded by six rectangular surfaces. 269. A cube is a rectangular solid having six square faces. PRACTICAL MEASUREMENTS 219 ORAL EXERCISE 1. If A in the accompanying series of diagrams is 1 cu. ft., how many cubic feet in B ? in C ? in D ? 2. How many cubic feet in a block of granite 6 ft. long, 1 ft. wide, and 1 ft. high ? in a block 6 ft. long, 3 ft. wide, and 1 ft. high ? in a block 6 ft. long, 3 ft. wide, and 3 ft. high? 3. Find the volume of a rectangular solid 6 ft. by 4 ft. by 2 ft. ; a rectangle 10 ft. by 9 ft. by 9 ft. - 4. A cellar is 40 ft. square and 6 ft. deep. How many cubic yards of earth were removed in excavating it ? SoLTTTiON. A cube 1 ft. on 6 X 40 X 40 X 1 CU. ft. = 9600 cu. ft. the side contains ] cu. ft. The qqqq ^^^ f^.^ - 27 = 355| CU. yd. given cube is 40 x 1 ft. long, ^ '' 40 X 1 ft. wide, and 6 x 1 ft. high. Therefore, it Contains 6 x 40 x 40 x 1 cu. ft., or 9600 cu. ft. ; and 9600 cu. ft. = 355f cu. yd, , the required result. 270. In the foregoing exercises it is clear that the product of the three dimensions of a solid equals the volume or solid contents. WRITTEN EXERCISE 1. A box car is 50 ft. 6 in. long, 8 ft. 4 in. wide, and 3 yd. high. What is its volume ? 2. A piece of timber is 60 ft. long and 18 in. square. How many cubic feet does it contain ? 3. A village constructs a reservoir for a water supply. The length is 100 yd., the width 70 yd., and the depth 15 ft. What will be the cost, at 23^ per cubic yard, of excavating the reservoir ? 220 PEACTICAL BUSINESS ARITHMETIC Wood 27^1. Wood is measured by the cord. 272. A cord of wood or stone is a pile 8 ft. long, 4 ft. wide, and 4 ft. high. It con- tains 128 cu. ft. The word "cord," as prac- tically used in wood measure, generally means a pile 8 ft. long and 4 ft. high, the price depend- ing on the length of the stick. ■^-a/m'C^- 273. Example. How many cords of wood in a pile 32 ft. long, 8 ft. wide, and 4 ft. high ? Solution. ^toQ^ ~ ^ ' ^^^* ^^' there are 8 cd. in the pile. WRITTEN EXERCISE 1. How many cords in a pile of wood 60 ft. long, 4 ft. wide, and 6 ft. high? 2. A pile of wood contains 5 cd. If it is 4 ft. wide and 4 ft. high, how long is it ? 3. A pile of tan bark contains 150 cd. If it is 4 ft. wide and 8 ft. high, how long is it ? 4. A pile of wood .contains 8 cd. It is 64 ft. long and as high as it is wide. What is the height of the pile ? Lumber 274. A foot of lumber, sometimes called a board foot, is a board 1 ft. long, 12 in. wide,- and 1 in. thick, or its equivalent. An exception to this is made in the measurement of boards less than 1 in. in thickness. A square foot of the surface of such boards is regarded as a foot of lumber regardless of the thick- ness. Boards more than one inch in thickness, planks, joists, beams, scantling, and sawed timber are generally measured by the board foot. PEACTICAL MEASUEEMENTS 221 Thus, a board 12 ft. long, 12 in. wide, and 1 in. thick contains 12 sq.ft. of surface, or 12 hoard feet ; a board 12 ft. long, 12 in. wide, and \, |, or | in. thick contains 12 sq.ft. of surface, or 12 hoard feet; but a board 12 ft. long, 12 in. wide, and 2| in. thick contains 30 hoard feet. Scantling is timber 3|^ in. wide and from 2 in. to 4 in. thick; joists are narrow and deep sticks of lumber ; planks are thick boards ; lumber heavier than joists or scantling is usually called timber. Except when sawed to order and in cherry, black walnut, etc., where the price is 15 ^ a board foot and upward, the width of a board is reckoned only the next smaller half inch. Thus, a board 10 J in. wide is reckoned as 10 in., and a board lOf in. wide is reckoned as 10^ in. The average width is used in measuring boards that taper uniformly. Thus, a tapering board 12 ft. long, 8 in. wide, at one end and 6 in. wide at the other and 1 in. thick averages 7 in. wide and contains 7 ft. of lumber. ORAL EXERCISE 1. How many square feet in the surface of a board 12 ft. long, 8 in. wide, and 1 in. thick ? How many board feet ? 2. How many board feet in a board 12 ft. long, 4 in. wide, and I in. thick ? 3. How many feet, board measure, in a board 12 ft. long, 12 in. wide, and 2 in. thick ? 4. How many feet of lumber in 65 boards each 12 ft. long, 6 in. wide, and 1 in. thick ? 275. In charging or billing lumber the number of pieces is entered first ; then the thickness and width in inches and the length in feet; and finally, the article. Thus, in billing 12 pc. hemlock, 2 in. thick, 6 in. wide, 12 ft. long, the form would be : 12 pc. 2" x 6", 12', hemlock. ORAL EXERCISE 1. How many board feet in 6 planks, 1|" x 12", W 2 Suggestion. By inspection eliminate 12 in the dividend. Then, 1^ x 6 x 14 = 126, the required number of board feet. 2. How many feet, board measure, in 6 planks 2'' x 8'', 18' ? Suggestion. By inspection cancel a 12 in the dividend (6 x 2). Then, 8 x 18 = 144, the required number of feet, board measure. 222 PRACTICAL BUSINESS ARITHMETIC 3. How many feet of lumber in 6 pc. of scantling 4'^ x 4'^ 16' ? Suggestion. Mentally picture the problem arranged, in form for cancellation / 6 X 4 X 4 X 16 \ ^ Cancel a 12 in the dividend (^V of Fx4). Then, 2 x 4 x 16, or 128, equals the required number of feet of lumber. 4. How many feet of lumber in 5 sticks, 2'' x 6", 16'? Suggestion. Mentally picture the problem in form for cancellation / 5 X 2 X 6 X 16 \ ^ Q^^QQi a 12 in the dividend (J- of 2ir6). Then, 5 x 16, or 80, equals the required number of feet of lumber. 5. How many feet of lumber in a plank 3'' x 12'', 16'? in 6 planks ? in 10 planks ? How many feet of lumber in a plank 2" X 6", 12' ? in 5 planks ? in 20 planks ? 276. Obviously, the number of board feet in lumber 1 in. or less in thickness is -^^ ^f ^^^ product of the length in feet hy the width in inches ; and the number of board feet in lumber more than 1 in. in thickness is -^^ of the product of the length in feet hy the width and thickness in inches. But the work may be materially shortened by mentally cancelling 12 from the divi- dend as illustrated in the foregoing exercise, ORAL EXERCISE State the number offeet^ hoard measure^ in the following hemlock: 1. 5 pc, 3" X 4", 14'. 13. 12 PC 2" x 8", 18'. 2. 6 pc, 2" X 4", 20'. 14. 6 pc, 8" x 10", 20'. 3. 6 pc, 2" X 6", 20'. 15. 30 pc, 2" x 6", 20'. 4. 20 pc, 2" X 6", 14'. 16. 6 pc, 8" x 10", 21'. 5. 12 PC 2" X 8", 14'. 17. 25 pc, 3" x 8", 14'. 6. 25 PC 3" X 4", 12'. 18. 10 PC 2" x 6", 13'. 7. 25 pc, 2" X 6", 20'. 19. 15 pc, 2" x 6", 18'. 8. 25 PC 3" X 8", 16'. 20. 15 PC 2" x 6", 12'. 9. 10 PC 3" X 4", 14'. 21. 16 pc, 2" X 6", 10'. 10. 10 pc, 2" X 8", 18'. 22. 10 PC 8" X 10", 15'. 11. 14 PC 2" X 6", 20'. 23. 15 PC 8" x 10", 12'. '12. 10 pc, 3" X 6", 20'. 24. 200 PC 2" X 6", 20'. PRACTICAL MEASUREMENTS 223 WRITTEN EXERCISE How many feet ^ hoard 7neasure, in each of the following f 1. 100 joists, 4:" X 4'^ 16'. 4. 70 joists, 2" x 10", 32'. 2. ^^ boards, {" x 6'', 12'. 5. 8 beams, 10" x 10", 24'. 3. 12 timbers, 8" x 8", 40'. 6. 10 beams, 12" x 12", 30'. 7. At $ 19 per M, find the total cost of : 6 joists, 2" X 8", 12'. 5 joists, 2" x 8", 18'. 12 joists, 2" X 8", 13'. 17 joists, 2" x 6", 16'. 30 joists, 2" X 8", 15'. 30 joists, 2" x 8", 16'. 8. At $ 26 per M, find the total cost of : 7 beams, 9" x 9", 20'. 16 beams, 9" x 9", 18'. 24 joists, 2" X 10", 18'. 75 planks, 21" x 8", 12'. 150 boards, |" x 5", 12'. 576 boards, 1" x 9", 16'. Cylinders 277. A cylinder is a solid bounded by a uniformly curved surface and two equal parallel circles. ^,,g|j|||[||^^ Two circles are parallel when all the points of |||II |B one are equally distant fi-om all the points of the liii^^^ H i IIBI i ■ ' other. The curved surface of a cylinder is called i" ' ''^' ||ii|HH|^^ its lateral surface ; the parallel circles its bases. ^ v ^tHI^^BRP™^ 278. If the lateral surface of a cylinder be exactly covered with paper, it will be found that the paper is in the form of a rectangle whose length and width are equal to the circumfer- ence and height, respectively, of the cylinder. Hence, The product of the circumference and height of a cylinder equals the area of its lateral surface. ORAL EXERCISE 1. If the accompanying diagram is a solid 4 ft. square and 12 ft. high, what is the area of its six sides? 2. Give a brief rule for finding the entire surface (lateral surface and bases) of a rectangular solid ; of a cylinder. 3. How many cubic inches in a block 2 in. square and 1 in. high? in a block 2 in. square and 10 in. high? lare ana 224 PRACTICAL BUSINESS ARITHMETIC 279. In the foregoing exercise it is clear that the area of the base multiplied hy the height of the cylinder equals the volume. WRITTEN EXERCISE ■ 1. What will be the cost, at 40^ per cubic yard, of excavat- ing for a cistern 10 ft. in diameter and 23 ft. deep ? 2. A man dug a well 6 ft. in diameter and 38 ft. deep. How much should he receive if he was paid |1 for each cubic yard of earth removed ? 3. What will be the cost, at 12 J ^ per square foot, of a sheet- iron smokestack 2^ ft. in diameter and 30 ft. high ? Cisterns 280. A gallon equals 231 cu. in. ORAL EXERCISE 1. How many gallons in 462 cu. in. ? in 1386 cu. in. ? 2. How many gallons of water in a vat 22 in. long, 7 in. high, and 3 in. wide ? 3. Give a rule for finding the exact number of gallons in a vessel. How many gallons in a cubic foot ? Solution. 231 cu. in. = 1 gal. 1728 cu. in. = 1 cu. ft. Therefore, 1 cu. ft. = yg^jS- gal. = 7.48 + gal., or approximately 7| gal. 4. Find the approximate capacity, in gallons, of a vat 5 ft. square and 4 ft. high. Solution. 5 f t. x 5 ft. x 4 f t. = 100 cu. ft. 100 times 71 gal. = 750 gal. 5. State a rule for finding the approximate capacity, in gal- lons, of a vessel. WRITTEN EXERCISE Find the capacity (^approximate and exact^, in gallons, of: 1. A cistern 6 ft. square and 12 ft. deep. 2. A cistern 6 ft. in diameter and 10 ft. deep. 3. A tank 5 ft. long, 4 ft. wide, and 6 ft. deep. 4. A cistern 15 ft. in diameter and 20 ft. deep. PRACTICAL MEASUREMENTS 225 Stone Work 281. Stone work is usually measured by the perch, which is a mass of stone 16| ft. long, 1-|- ft. wide, and 1 ft. high, contain- ing 24| cu. ft. In some localities the perch contains 16^ cu. ft. 282. Masonry is measured by the cubic yard or the perch. In measuring stone work, such as the walls of cellars and buildings, masons take the distance around the outside of the wall (the girt) for the length. In this way the corners are measured twice, but this is considered offset by the extra work required in building the corners. The work around openings, such as doors and windows, is also more difficult than the straight work and on this account no allowance is usually made for openings, unless they are very large. WRITTEN EXERCISE 1. How many perches of stone will be required for an 18-in. foundation 72' X 40' x 10'? 2. How many perches of masonry in the 18-in. walls of a cellar 40' X 30' x 8' ? 3. How many cubic yards of masonry in the foundation walls of a house 42' x 32' if the walls are 21 ft. wide and 8 ft. high? (Solve (a) by mason's and (^) by actual measure.) Brick Work 283. A common brick is 8 in. long, 4 in. wide, and 2 in. thick. Bricks vary in size, but the common brick may be taken as a unit for measuring brick work. Contractors and builders do not follow any uniform rule for estimating the number of bricks required for a wall. It is suffi- ciently accurate, however, to reckon 22 common bricks, laid in mortar, for each cubic foot of wall. In estimating material for a brick wall actual measurements are taken and an allowance made for doors and windows and other openings. In estimating labor girt measurements are taken and usually a stated allowance made for openings such as doors and windows. The allowance to be made for openings is generally covered by contract In some localities a uniform number of cubic feet is deducted for each open- ing ; in others one half the volume of all openings is deducted ; in still others nothing whatever is deducted. , 226 PRACTICAL BUSINESS ARITHMETIC WRITTEN EXERCISE 1. How many common bricks will be required for a wall 84 ft. long, 161 ft. high, and 1|- ft. thick ? 2. Find the cost of the bricks required to build a wall 300 ft. long, 12 ft. high, and 18 in. thick, at $6 per thousand. 3. How many bricks will be required for the four walls of a building 80' x 50' x 25' if the walls are 18 in. thick and 500 cu. ft. is allowed for openings ? (Solve (6?) by mason's measure, making allowance for the openings, and (6 ) by actual measure.) CAPACITY Bins 284. The stricken bushel is used in measuring grain. The heaped bushel is used in measuring such things as large fruits, vegetables, coal, and corn on the cob. A stricken bushel equals 2150.42 cu. in. A heaped bushel equals 2747.71 cu. in. ORAL EXERCISE 1. How many bushels of wheat in 2,150,420 cu. in. ? 2. State a rule for finding the exact number of stricken bushels in a bin. What part of a stricken bushel is 1 cu. ft.? 8-4- SoLUTioN. 2150.42 cu. in. = 1 bu., stricken measure. ! _ 1728 cu. in. = 1 cu. ft. Therefore, 1 cu. ft. = 172800- 2150.42)1728.000 215042, or approximately .8 of a bushel, stricken nieas- ITzO oob ure. 7664 3. Find the approximate capacity, in stricken bushels, of a cubical bin the inside of which measures 10 ft. on a side ; in cubic inches of 800 bu. of wheat. 4. State a brief rule for finding the approximate number of stricken bushels in a bin; the approximate number of cubic feet in any number of stricken bushels. 5. How many bushels of potatoes in a bin containing 2,747,710 cu. in. ? State a rule for finding the exact number of heaped bushels in any number of cubic inches. Reduce a cubic foot to a decimal of a heaped bushel. PEACTICAL MEASUEEMENTS 227 .63- SoLUTiON. 2747. 71 cu. in. = lbu., heaped measure. 2747.71)1728.0000 Therefore 1 cu. ft. = 172800 -h 274771, or approxi- 1648 626 mately .63 of a bushel, heaped measure. ■ — oTAri 82 4313 6. Find the approximate capacity, in heaped bushels, of 1000 cu. ft. ; in cubic feet, of 630 bu. 7. State a short method of reducing cubic feet to heaped bushels; heaped bushels to cubic feet. 8. Find («) the exact capacity and (6) the approximate capacity, in stricken bushels, of a bin 10^ X 5' x 4^ Solutions (a) 10' X 5' X 4' = 200 cu. ft. (6) 10' x 5' x 4' = 200 cu. ft. 200 X 1728 cu. in. = 345,600 cu. in. .8 of 200 cu. ft. = 160 bu. 345,600 cu. in. -- 2150.42 = 165.31 + bu. ORAL EXERCISE 1. Find the approximate capacity in bushels of a wheat bin 10 ft. long, 8 ft. wide, and 5 ft. high. 2. A square bin 10 ft. high contains, by approximate measure- ments, 800 bu. What is its width ? 3. Approximately, how many bushels of potatoes may be stored in a bin 10 ft. long, 5 ft. wide, and 4 ft. high ? WRITTEN EXERCISE Find the approximate capacity in stricken bushels, of : 1. A bin 12 ft. square and 4 ft. deep. Inside dimensions are given in all the problems of this and similar exercises. 2. A box 6 ft. long, 2i ft. wide, and 3i ft. deep. 3. A farmer wishes to construct a square granary 15 ft. on each side that will hold 800 bu. of grain. How deep must the bin be made ? (Approximate rule.) 4-5. Find the exact capacity, in stricken bushels, of prob- lems 1-2. 6-7. Find the approximate capacity, in heaped bushels, of problems 1-2. 228 PRACTICAL BUSINESS ARITHMETIC CALCULATION TABLES 285. Persons who have a great deal of computing to do frequently use machines (see Appendix A) and calculation tables to aid them in their work. The table on page 229 will give a good idea of the arrangement of calculation tables that are used in making up and proving bills and invoices, comput- ing wages, finding percentages, etc. The following examples will illustrate a few of the many uses of such tables. 286. Examples, i. Multiply 58 by 42. Solution. Under 58 and opposite 42 find 2436. 2. How many square feet in a floor 88' x 46' ? Solution. Under 46 and opposite 38 find 1748 ; that is, 1748 sq. ft. 3. Find the cost of 495 yd. wash silk at 39^. Solution. Under 495 and opposite 39 find 19,305 ; that is, $ 193.05. 4. Find the cost of 48,000 bricks at 14.95 per M. Solution. Under 495 and opposite 48 find 23,760. Since the zeros in 48,000 have been rejected, there are but two places to point off. Result $ 237.60. 5. Find the cost of 46 hr. of labor at 25| ^ per hour. Solution. Under 46 and opposite 25 find 1150 ($11.50); under 46 and opposite I find 34.50 (35 ;*). $ 11.50 + 35 ^ = $ 11.85, the required result. ORAL EXERCISE By the aid of the table state the product of: 1. 27 X 26. 5. 39 X 27. 9. 87 x 46/. 2. 27x58. 6. 45x58. lo. 93x32/. 3. 45x46. 7. 37x46. ii 48x93/. 4. 47x39. 8. 49x58. 12. 47x87/. 17. Find the cost of 49,500 lb. of old rags at |/. 18. Find the cost of 93,000 bricks at 'f 5.25 per M. 19. Find the cost of 37 days' labor at $1.35 per day ; at 15.25. 20. Find the cost of 109 hours' labor at 27/; at 39jZ^; at 46 /. 21. Find the cost of 49,500 lb. freight at 31 / per hundred- weight ; of 46,000 lb. at 27 / per hundredweight. 13. 35 x 93/. 14. 93 X 42/. 15. 46x87^. 16. 38 X 93/. PRACTICAL MEASUREMENTS 229 CALCULATION TABLE lulti- plier 27 39 46 68 Multi- plier 87 93 109 128 Multi- plier 135 147 495 625 Multi- plier 1 27 39 46 58 1 87 93 109 128 1 135 147 495 4 1 2 54 78 92 116 2 174 186 218 256 2 270 294 990 1050 2 3 81 117 138 174 3 261 279 327 384 3 405 441 1485 1575 3 4 108 156 184 232 4 348 372 436 512 4 &40 588 1980 2100 4 6 135 195 230 290 5 435 465 545 640 5 675 735 2475 2625 5 6 162 234 276 348 6 522 558 654 768 6 810 882 2970 3150 6 7 189 273 322 406 7 609 651 703 896 7 045 1029 3465 3675 7 8 216 312 368 464 8 696 744 872 1024 8 1080 1176 3%0 4200 8 9 243 351 414 522 9 783 837 981 1152 9 1215 1323 4455 4725 9 10 270 390 460 580 10 870 930 1090 1280 10 1350 1470 4950 5250 10 11 297 429 506 638 11 957 1023 1199 1408 11 1485 1617 5445 5775 11 13 324 468 552 696 12 1044 1116 13(»8 1536 12 1620 1764 5940 6300 12 13 351 507 598 754 13 1131 1209 1417 1664 13 1755 1911 6435 6825 13 14 378 546 644 812 14 1218 1302 1526 1792 14 1890 2058 6930 7350 14 16 405 585 690 870 15 1305 1395 1635 1920 15 2025 2205 7425 7875 15 16 432 624 736 928 16 1392 1488 1744 2048 16 2160 2a52 7920 84(10 16 17 459 663 782 986 17 1479 1581 1853 2176 17 2295 2499 8415 8925 17 18 486 702 828 1044 18 1506 1674 1962 2304 18 2430 2646 8910 9450 18 19 513 741 874 1102 19 1653 1767 2071 2432 19 2565 2793 9405 9975 19 20 540 780 920 IIGO 20 1740 1860 2180 2560 20 2700 2940 9900 10500 20 21 567 819 966 1218 21 1827 1953 2289 2688 21 2835 3087 10395 11025 21 22 594 858 1012 1276 22 1914 2046 2398 2816 22 2970 3234 10890 11550 22 23 621 897 1058 1334 23 2001 2139 2507 2944 23 3105 3381 11385 12075 23 24 648 936 1104 1392 24 2088 2232 2616 3072 24 3240 3528 11880 12600 24 25 675 975 1150 1450 25 2175 2325 2725 3200 25 3375 3675 12375 13125 25 26 702 1014 1196 1508 26 2262 2418 28^4 3328 26 3510 3822 12870 13650 26 27 729 1053 1242 15^56 27 2349 2511 2943 3456 27 3645 3969 13365 14175 27 28 756 1092 1288 1624 28 2436 2604 3052 3584 28 3780 4116 13860 14700 28 29 783 1131 ia34 1682 29 2523 2697 3161 3712 29 3915 4263 14355 15225 29 30 810 1170 1380 1740 30 2610 2790 3270 3840 30 4050 4410 14850 15750 30 31 837 1209 1426 1798 31 2697 2883 3379 3968 31 4185 4557 15345 16275 31 32 864 1248 1472 1856 32 2784 2976 3488 4096 32 4320 4704 15840 16800 32 33 891 1287 1518 1914 33 2871 3069 3597 4224 33 4455 4851 16335 17325 17850 18375 33 34 918 1326 1564 1972 34 2958 3162 3706 4352 34 4590 4998 16830 34 35 945 1365 1610 2030 35 3045 3255 3815 4480 35 4725 5145 17325 35 36 972 1404 1G56 2088 36 3132 3348 3924 4608 36 4860 5292 17820 18900 19425 19950 36 37 999 1443 1702 2146 37 3219 3441 4033 4736 37 4995 5439 18315 37 38 1026 1482 1748 2204 38 a306 3534 4142 4864 38 5130 5586 18810 38 39 1053 1521 1794 2262 39 3393 3627 4251 4992 5120 39 5265 5733 19305 20475 39 40 1080 1560 1840 2320 40 3480 3720 4360 40 5400 5880 19800 21000 40 41 1107 1599 1886 2378 41 3567 3813 4409 5248 41 5535 6027 20295 21525 41 42 1134 1638 1932 2436 42 36&4 3906 4578 5376 42 5670 6174 20790 22050 42 43 1161 1677 1978 2494 43 3741 3999 4687 5504 43 5805 6321 21285 22575 43 44 1188 1716 2024 2552 44 3828 4092 4796 5632 44 5940 6468 21780 23100 44 45 1215 1755 2070 2610 45 3915 4185 4905 5760 45 6075 6615 22275 23625 45 46 1242 1794 2116 2668 46 4002 4278 5014 5888 46 6210 6762 22770 24150 46 47 1269 1833 2162 2726 47 4089 4371 5123 6016 47 6345 6909 23265 24675 47 48 1296 1872 2208 2784 48 4176 4464 5232 6144 48 6480 7056 23760 25200 48 49 1323 1911 2254 2842 49 4263 4557 5341 6272 49 6615 7203 24255 25725 49 50 1350 1950 2300 2900 60 Multi- plier 4350 4650 5450 6400 60 6750 7350 24750 26250 60 Multi- plier 27 39 46 68 87 93 109 128 Multi- plier 135 147 495 525 Multi- plier Vs 3 38 488 5 75 7 25 Vs 10 88 1163 13 63 16 00 Vs 16 88 18 38 6188 65 63 Vs V4 6 75 9 75 1150 14 50 ¥4 2175 23 25 27 25 32 00 V4. 33 75 36 75 123 75 13125 V4 % 10 13 14 63 17 25 2175 % 32 63 34 88 40 88 48 00 % 50 63 5513 185 63 196 88 //« V2 13 50 19 50 23 00 29 00 H 43 5C 46 50 54 50 64 00 V2 67 50 73 50 247 50 262 50 V2 % 16 88 24 38 28 75 36 25 % 54 38 58 13 6813 80 00 % 84 38 9188 309 38 328 13 % % 20 25 29 25 34 50 43 50 50 75 % 65 2S 69 75 8175 96 00 % 10125 110 25 37125 393 75 »/4 Vs 23 63 3413 40 25 % 76 13 1 81 38 95 38 112 00 % ,118 13 128 63 43313 459 38 Vs 230 PEACTICAL BUSINESS ARITHMETIC 22. Find the cost of 48,000 ft. of lumber at f 16 per M ; of 93,000 ft. ; of 52,500 ft. ; of 49,500 ft. ; of 58,000 ft. 23. An agent sold 240 (10 x 24) excursion tickets at $4.95. How much did he receive ? 360 x 15.25 = ? 310 x il.47 = ? 24. Find the cost of 45 rm. of paper at 11.35 ; at 1 1.28 ; at $1.09; at 93^; at $4.95. Also find the cost of 38 rm. at each of the above prices ; of 29 rm. ; of 37 rm.; of 46 rm. 25. Find the Cost of 4600 lb. of coal at $6.40 per ton ($3.20 per thousand pounds) ; at $8.40; at $4.60; at $6.80 ; at $7.20; at $7.40; at $9.20; at $5.60. Also find the cost of 2700 lb. at each of the above prices ; of 3900 lb. ; of 8700 lb. ; of 9300 lb.; of 10,900 lb,; of 12,800 lb.; of 13,500 lb.; of 14,700 1b.; of 49,500 1b.; of 52,500 lb. 26. By the aid of the table find the total cost of : 525 bolts at S1.70 per C. 128 bolts at S1.90 per C. 495 bolts at S2.40 per C. 525 bolts at S2.70 per C. 135 bolts at $1.60 per C. 495 bolts at $3.50 per C. 27. By the aid of the table find the total cost of : 1280 ft. lumber at $ 28 per M. 5250 ft. lumber at $ 27 per M. 1350 ft. lumber at $29 per M. 3800 ft. lumber at $27 per M. 4950 ft. lumber at $19 per M. 4600 ft. lumber at $18 per M. A REVIEW EXERCISE 1. Without copying, extend and find the total of each invoice on pages 189 and 190. Time for each invoice, approximately, 3 min. 2. How many acres in each of the following fields : a. A field 60 rd. long and 40 rd. wide. ' Suggestion. As the field is 40 rd. wide, each 4 rd. of length makes an acre ; hence, there are as many acres as 4 is contained times in 60. Ans. 15 A. h. A field 50 rd. long and 32 rd. wide. c. A field 80 rd. long and 16 rd. wide. d. A field 96 rd. long and 20 rd. wide. e. A field 75 rd. long and 531 rd. wide. /. A field 80 rd. long and 80 rd. wide. g. A field 120 rd. long and 40 rd. wide. PERCENTAGE AND ITS APPLICATIONS CHAPTER XVII PERCENTAGE ORAL EXERCISE 1. .50 may be read fifty hundredths^ one half or fifty per cent. Read each of the following in three ways : . 25, . 30, 12 J % . 2. Read each of the following in three ways : -J, J, \^ ^, gV' h h h h h 2 %' H% 125%, 61%., 81%, mi% 250%, 375%. 3. 50 % of a number is .50 or ^ of the number. What is 50% of 1600? 25%? 121%? 10%? 40%? 20%? 75%? 287. Per cent is a common name for hundredths. 288. The symbol % may be read hundredths ov per cent. 289. Percentage is the process of computing by hundredths or per cents. ORAL EXERCISE Express as per cerits : 1. .28. 3. .00^. 5. .33J. 7. .621 9. .5. 2. .37. 4. .14f 6. .28|. 8. .0075. 10. .2. Express as decimal fractions : 11. 20%. 13. 72%. 15. 1%. 17. 125%. 19. ^V%- 12. 45%. 14. 18%. 16. 1%. 18. 250%. 20. 375%. Express as common fractions : 21. 1%. 23. 2|%. 25. 1331%. 27. 871%. 29. 1%, 22. 2%. 24. 31%. 26. 26Gf%. 28. 1121%. 30. 175%. Express as per cents : 31. 1 33. -^y 35. !{. 37. |. 39. |. 32. 1 34. ^^. 36. 2f. 38. If 40. ^^K 231 232 PRACTICAL BUSINESS ARITHMETIC Important Per Cents and their Fractional Equivalents Per Fkaotional Per Fractional Per Fractional Per Fractional Cent Value Cent VALUE Cent Value Cent Value i2r/o i 75% 1 831% 1 6i% h 25% \ 100% 1 20% I 6f% iV 37r/o f 16f% I 40% I 8i% 1^1 50% 1. 33|% \ G0% f 1H% \ 62i% f 66f% ^ 80% f in% \ 290. The terms used in percentage are the base, the rate, and the percentage. The base is the number of which a per cent is taken ; the rate, the number of hundredths of the base to be taken ; the percentage, the result obtained by taking a certain per cent of the base. In the expression "12 % of ^50 is 1 6," % 50 is the base, 12 %, the rate, and $6, the percentage. 291. The base plus the percentage is sometimes called the amount ; the base minus the percentage, the difference. FINDING THE PERCENTAGE 292. Example. What is 15 % of % 660 ? Solution. 15% of a number equals .15 of it. .15 of $660 % 99, the required result. 1660 .15 199.00 293. Obviously, the product of the base and rate equals the percentage. The base may be either concrete or abstract. ^ The rate is always abstract. The percentage is always of the same name as the base. ORAL EXERCISE 1. Whataliquotpartof lis .121? .25? .50? .16| ? .33J? .20? Ml? .06|? .081? .111? .142? 371^^? 62-i-%? 66f%? 2. Formulate a short method for finding 12J% of a number. Solution. 12| % = .121 = i j hence, to find 12i % of a number, divide by 8. 3. State a short method for finding 25 % of a number ; .3/.; 20%; 61%; 6|%; 81%; 111%. 50%; 16|%; 331 PERCENTAGE 233 To guard against absurd answers in exercises of this character estimate the results in advance as explained on pages 58 and 146. 4. Find 50% of 960. Also 25%; 37-1%; I2i%; 621%; 75%; 16f%; 331%; 66|%; 831%; 20%; 40%; 60%; 6^%. 5. By inspection find : a. 50 % of 1792. e, 25% of S1729. i. 66f % of 2460. b. 371% of 1320. /. 6f% of 16600. j, 331% of 2793. c. 121% of $880.- g, 61% of 3296. Jc. 81% of 24,960. d. 16f % of 1669. h. 831% of 4560.. I 20% of 12,535. ORAL EXERCISE 1. Find 10% of 720; of 115.50; of 120 men; of 1127.50. 2. What aliquot part of 10% is 5% ? 21% ? li % ? 31% ? If % ? 3. Formulate a short method for finding 1^ % of a number. Solution. 1 J% of a number is i of 10 % of the number ; hence, to find 1^% of a number, point of one place to the left and divide by 8. 4. State a short method for finding 5 % of a number ; 21 % ; 5. By inspection find : a. 5% of 720. d. 11% of 1840. g. 31% of 13900. h. 21% of 840. e. If % of $366. h. 1| % of 120 mi. c. 31% of 1560. /. 21% of $720. ^. IJ % of 1632 A. ORAL EXERCISE 1. Compare 24% of $25 with 25% of $24; 24% of $2500 with 25 % of $2400. What is 32 % of $25 ? Solution. 32% of § 25 = 25% of |32 = ^ of $32 = $ 8, the required result. 2. What is 125% of $880? Solution. 125% = 1.25 = 1 of 10 ; i of $8800 (10 times $880) =$1100. 3. Find 125% of 400; of 640; of 3200 ; of 160; of 1280. 4. Formulate a short method for finding 166f % of a num- ber ; 3331 % of a number ; 250 % of a number. 5. Compare 88 % of 12,500 bu. with 125 % of 8800 bu. 6. Find 32% of $125; of $1250; of $12,500; of $125,000. 7. Find 250% of $720; of $3200; of $28,800; of $64,800. 234 PRACTICAL BUSINESS ARITHMETIC ORAL EXERCISE By inspection find : 1. 48% of 250. 5. 180% of 625. •2. 32% of 125. 6. 160% of 875. 3. 128% of 250. 7. 240% of 7500. 4. 16 % of 2500. 8. 125 % of f 240.40. WRITTEN EXERCISE 1. A farmer sold 640 bu. wheat, receiving f 1.05 per bushel for 87|% of it and 85)^ per bushel for the remainder. What was the total amount received ? 2. A grocer compromised with his creditors, paying 60 % of the amount of his debts. If he owed A i 756, B »$ 1250, and C $3750, how much did each receive ? 3. A merchant sold 360 bbl. apples for $1200. If he re- ceived $3.50 per barrel for 6Q^% of the apples, what was the price received per barrel for the remainder ? 4. A man bought a house for $12,864.75; he expended for improvements 331 % of the first cost of the property, and then sold it for $20,000. Did he gain or lose, and how much ? 5. A commission merchant bought 1200 bbl. apples and after holding them for 3 mo. found that his loss from decay was 10%. If he sold the remainder at $3.75 per barrel, how much did he receive ? 6. A merchant prepaid the following bills and received the per cents of discount named: 4% on bill of $875.50; 6% on bill of $378.45; 2% on bill of $940.50; 3| % on bill of $400. What was the net amount paid ? FINDING THE RATE ORAL EXERCISE 1. 8 is what part of 40 ? what per cent of 40 ? 2. 90 is what per cent of 270 ? of 360 ? of 450 ? 3. 70 is what per cent of 560? of 630 ? of 700 ? 4. The base is 900 and the percentage 450 ; what is the rate ? PEECENTAGE 235 294. Example. $35.50 is what per cent of 8284 ? Solutions, a. $35.50 is ^^^^.o^ or \ of {a) $284. $284 is 100% of itself; hence, _3_55JL _. i _ J^21 ^ $85.50, which is \ of $284, must be ^ of 2 810 8 2 / 100%, or 121%. Or, Q>) h. Since the product of the base and __J^5 = 12^ffo the rate is the percentage, the quotient 284)35.50 obtained by dividing the percentage by the base is the rate. 295. Obviously, the percentage divided hy the base equals the rate. ORAL EXERCISE What per cent of: 1. 95 is 19? - 7. 1.6 is .008? 2. 4.8 is 1.2? 8. 1yd. is 1ft. ? 3. $35 is 1171 ? 9. 2 da. are 8 hr. ? 4. 225 A. are 75 A. ? lo. 4 T. are 3000 lb. ? 5. 34 bu. are 34 bu. ? ii. 1 yr. are 4 mo. ? 6. 34 bu. are 68 bu. ? 12. 2 mi. are 80 rd. ? WRITTEN EXERCISE 1. A man bought a house for §7500 and sold it for 18700. What per cent did he gain ? 2. In a certain city, school was in session 190 da. A lost 38 da. What per cent of the school year did he attend? 3. An agent sold a piece of property for $8462.50 and re- ceived $338.50 for his services. What per cent did he receive ? 4. A commission agent sold 28,600 bu. of grain at 50 ^ per bushel and received for his services $357.50. What per cent did he receive on the sales made ? 5. Smith and Brown engaged in business, investing $18,000. Smith invested $10,440, and Brown the remainder. What per cent of the total capital did each invest ? 6. An agent for a wholesale house earned $165.55 during the month of May. If the goods sold amounted to $ 1505, what per cent did he receive on the sales made ? 236 PEACTICAL BUSINESS ARITHMETIC FINDING THE BASE ORAL EXERCISE 1. What is 5% of 240 bu. ? 2. 12 bu. is 5 % of how many bushels ? 3. 160 is8% of what number ? 4%? 2%?1%?|%? i%? 4. The multiplicand is 400 and the multiplier 10; what is the product? The product is 2000 and the multiplicand 100; what is the multiplier? The product is 4000 and the multi- plier 20 ; what is the multiplicand ? 5. In percentage what name is given to the product ? to the multiplicand ? to the multiplier ? When the base and rate are given, how is the percentage found ? When the percentage and base are given, how is the rate found ? When the per- centage and rate are given, how is the base found ? 296. Example. 37.5 is 25% of what number? Solution. 25% or I of the number = 37.5 . •. the number = 37.5 -^ ^ = 150. 297. Obviously, the quotient of the percentage divided hy the rate equals the base. WRITTEN EXERCISE 1. N invested 30% of the capital of a firm, H 35%, and W the remainder, $1400. What was the capital of the firm? 2. During the month of May the sales of a clothing mer- chant amounted to $4864.24, which was 8 % of the total sales for the year. What were the total sales for the year? 3. B sold his city property and took a mortgage for $4375, which was 1TJ% of the value of the property. If the balance was paid in «ash, what was the amount of cash received ? 4. In compromising with his creditors, a man finds that his assets are 1270,900, and that this sum is 43% of his entire in- debtedness. What will be the aggregate loss to his creditors? 5. The aggregate attendance in the schools of a certain city for 1 da. was 43,225 students. If this number was 95% of the number of students belonging, how many students were absent? PERCENTAGE 237 PER CENTS OF INCREASE ORAL EXERCISE 1. If 2| times a number is 50, what is the number? 2. If 2.5 times a number is 75, what is the number? 3. If 250% of a number is $1250, what is the number? 4. If 250% of a number is 150, what is the number? If 250% is 125, what is the number? 5. If 300% of a number is $5400, what is the number? 298. Examples, i. A man sold a farm for $3900 and thereby gained 30%. How much did the farm cost? Solution. 1.30 of the cost = $3900. . • . the cost = $ 3900 -T- 1 .30 = $ 3000. 2. What number increased by 33^% of itself equals 180? Solution. | of the number = 180. . •. the number = 180 h- | = 135. ORAL EXERCISE What number increased by: 1. 10% of itself is 220? 8. 6f % of itself is 480? 2. 25% of itself is 125? 9. 125% of itself is 900? 3. 50% of itself is 300? 10. 37^% of itself is 440? 4. 75% of itself is 700? ' li. 11^% of itself is 300? .5. 6|% of itself is 170? 12. 14f % of itself is 328? 6. 121% of itself is 180? . 13. 200% of itself is 2700? 7. 661% of itself is 135? 14. 300% of itself is 2800? WRITTEN EXERCISE 1. I sold 375 bu. of wheat for $427.50, thereby gaining 20%. How much did the wheat cost me per bushel? 2. A fruit dealer sold a quantity of oranges for $6.75. If his gain was 121%, what did the oranges cost him? 3. My savings for March increased 33^% over February. If my savings for March were $84.36, what were my savings for February and March? 238 PEACTICAL BUSINESS AKITHMETIC PER CENTS OF DECREASE ORAL EXERCISE 1. What per cent of a number is left after taking away 331% of it ? What fractional part? 2. If I of a number is 600, what is the number ? If G6| % of a number is 75, what is the number ? 3. A man spent 40 % of his money and had $60 remaining. How much had he at first ? How much did he spend? 299. Examples, l. A man sold a horse for $332, thereby losing 17 %. What was the cost ? Solution. 0.83 of the cost = $332. . •. the cost = f 332 -- 0.83 = $ 400. • 2. What number decreased by 25 % of itself equals $375? Solution. | of the number = $ 375. . •. the number = $ 375 -=- f = $ 500. ORAL EXERCISE What number diminished hy: 1. 61 % of itself equals 75 ? 4.-1 of itself equals 750 ? 2. 81% of itself equals 440? 5. 1% of itself equals 99.5? 3. 6|% of itself equals 280? 6. 1% of itself equals 49.5? WRITTEN EXERCISE 1. Of what number is 9581.88 77 % ? 2. A merchant sold 1200 bu. of potatoes for $640, which was 16|% less than he paid for them. What was the cost per bushel? 3. In selling a carriage for f 75 a merchant lost 25% on the cost. What was the asking price if the carriage was marked to gain 25 % ? 4. A newsboy sold 92 papers on Tuesday. If this number was 23J% less than the number sold on Monday, how many papers were sold on the two days ? 5. A dealer sold a quantity of apples at $6 per barrel, and by so doing lost 16|%. If he paid $309.60 for the apples, how many barrels did he buy ? PEECENTAGE 239 ORAL REVIEW EXERCISE 1. By inspection find 12| a. ^872. e. 12464. h. 648 bu. /. 2696 A. c. 1264 A. g. 1624 ft. d. 960 mi. h. 1832 mi. 2. By inspection find 10 25% ; 125% ; 20%. of the following numbers : i, 11688. m. I24.T2. j. 2072 A. 7u 1168.48. h, 11,464 mi. 0. $176.24. I. 37,128 mi. p. 12184.32. of each of the above numbers : 3. State the missing term in each of the following : No. Base Kate Percentage ■■ No. Base Rate Percentage a. $600 7^% v /. 906 16f% ? h. §650 ? ^ ;39 9- ? 8i% 15 bu. c. ? 4% $1^ h. 1275 61% ? d. 900 ? 720 i. ? 6|-% 21 mi. \ e. ? 4% 20 J- 400 ? 600 \\' 4. By inspection find 10 ^ a. 8264. d. 1840. h. 1920. e. 1750. (?. 1720. /. $364. 5. By inspection find 1-| ^ of each of the following : ff. 1232. y. 12448. ^. 1144. h 11432. z. $288. L $3624. % of each of the above numbers ; 1|%; 1000%; 125%; 166f%. WRITTEN REVIEW EXERCISE 1. A collector charged 4 % on all amounts collected. If he remitted to his customers in one month $3720.48, how much did he receive for his services? 2. A father left to his son 60 % of his estate and to his daughter the remainder, $9390.88. What was the value of the estate and how much did the son receive? 3. A farmer planted Wbrrr-fe'pk. of oats on an acre of ground and harvested 56 bu. What per cent of the yield was the planting? What per cent of the planting was the yield? 4. A merchant paid the following charges on a bill of goods : cartage $12.45, freight $65.32, insurance $41. If the charges represent 5 % of the face of the bill, what was the gross cost of the goods? 240 PRACTICAL BUSINESS ARITHMETIC 5. A man had 6 Ai^ of land; to one party he sold a piece 25 rd. by 20 rd., and to another party 140 sq. rd. What per cent of the field remained unsold? 6. In a recent year 191,571,750 lb. of fish were landed in Boston and Gloucester, and of this quantity 103,460,410 lb. were landed in Gloucester and 88,111,340 in Boston. What per cent of the total was furnished by each city ? (Correct to the nearest .01.) 7. A owned property valued at $12,000 from which he received a yearly rental of S960. If he paid taxes amounting to $160, insurance $75.50, and made repairs amounting to $184.50, what per cent net income did he receive? 8. B owns a field 80 rd. square. During a certain year this field yielded on an average 25 bu. of wheat to an acre. The wheat when sold at $1 a bushel produced an amount equal to 25 % of the value of the field. What was the value of the field ? . 9. A landowner rented a field to a tenant and was to receive as rent 16|% of the grain raised. The owner of the field sold his share of the grain for 84/ per bushel, receiving $298.20. If the, tenant sold his share of the grain for the same price per bushel, how much did he receive ? 10. In a single year the cost of the cotton yarn used in the manufacture of hosiery and knit goods in the state of New York, in round numbers, was $13,825,000; in the state of Illinois, $1,550,000. The cost of the cotton yarn used in Illinois was what per cent less than the cost of the cotton yarn used in New York, in a year? (Correct to the nearest .01.) - 11. By a recent census report it was shown that the value of all personal property in the state of New York was approximately $500,000,000 and the value of all the real estate approximately $10,000,000,000. Draw parallel lines making a comparison of the personal property and the real estate. The real estate is what per cent greater than the personal property ? The personal property is what per cent less than the real estate ? PERCENTAGE 241 12. A young man entered a bank as cashier and at the end- of the first year his salary was increased 25% ;.at the end of the second year he was given an increase of 20 % ; and at the end of the third year he was given an increase of 25%, which made his salary f 4500. What salary did he receive at first ? 13. A government statistician collected facts regarding wages and income from nearly two thousand private manufacturing concerns, and reported the following : the average wages of all employees, men, women, and children, per year was $ 263.06, and the average net profit for each employer was $ 2273. What per cent greater was the income of each employer than of each em- ployee ? (Correct to the nearest .01.) 2 14. The population of three 1 1 1 h M 1 1 1 1 1 1 1 1 1'l 1 1 1 1 1 1 1 1 iTtm- cities during a certain year is At^^ma^^^^t^^mma^m^^ illustrated by the accompany- Bm^^mt^m^^mK^m^^m ing lines, which are drawn on ciMHBiiH^HaMMHii a scale of 12,500 inhabitants to each -| of an inch. What is the population of A, B, and C, respectively ? The population of each city is what per cent of the population of the three cities ? 15. The annual coal production in the United States, Great Britain, Germany, and France for a certain year is illustrated h I i 1 1 1 1 I i 1 1 I 1 1 1 h 1 1 1 1 1 1 1 1 1 1 I 1 1 i in the accompanying rectan- United states gles, drawn on the scale of 50,000,000 short tons to each £SiSlSilM ^ of an inch. During that oermaiy^ year, how many tons did the jYanoe United States, Great Britain, "• Germany, and France, respectively, produce? The produc- tion of each country is what per cent of the production of the four countries ? In the same ,year the rest of the world pro- duced approximately 200,000,000 short tons. Illustrate graph- ically the world's coal production for that year. What was the world's approximate production this year ? 242 PEACTICAL BUSINESS AEITHMETIC * 16. The total value of the cotton crop to farmers in a recent year was S 920,630,000 and the value of the cotton exported to Great Britain in the same year was $ 231,817,000. What per cent was exported to Great Britain? (Correct to the nearest .01.) 17. A saleswoman in a city store receives $9 per week. She pays S3.50 per week for board and room, 10/ per day for car fare 6 da. of the week, 20/ per day for 6 da. of each week for luncheon, and has incidental expenses amounting to S1.70. If she saves the remainder, what per cent of her weekly wages does she save ? What per cent does she spend ? j 18. The production, in bushels, of grain in the Uiiited States in two recent years was approximately as follows : Cereals 1912 1913 Corn 3,124,000,000 2,370,000,000 Wheat 730,000,000 753,000,000 Oats 1,418,000,000 1,122,000,000 Barley 223,000,000 175,000,000 Rye 35,000,000 34,000,000 Buckwheat 19,000,000 14,000,000 Find the per cent of increase or decrease of each cereal for 1913 as compared with the previous year. Then draw a series of parallel rectangles to compare the production of 1913 with the production of 1912. Also draw a series of rectangles to com- pare the production of 1913 with the production of a later year. Suggestion. This may be represented by one series of rectangles. Each rectangle may be divided, into two parts — one shaded and the other unshaded. The shaded part may be made to represent the yield for 1913 and the unshaded part the yield for 1912. 19. The silver produced by the leading sources in a recent year was approximately as follows : 32,000,000 oz. 6,000,000 oz. 4,000,000 oz. 4,500,000 oz. Austria-Hungary 1,500,000 oz. Draw a set of parallel rectangles to represent graphically the above numbers. Mexico 80,000,000 oz. Canada United States 60,000,000 oz. Peru Turkey 1,500,000 oz. Spain Australia 16,000,000 oz. Japan Germany 6,000,000 oz. Austria PERCENTAGE 243 20. In the following table is shown the population in the United States in a certain year, men and women, engaged in gainful occupations, classified according to geographic divisions. Supply the missing terms. Check the work. Engaged in Gainful Occupations Geogkaphic Divisions Number Per Cent of Total Total Men Women Total Men Women North Atlantic . . . South Atlantic . . . North Central . . . South Central . . . Western 8,274,869 3,553,985 9,211,119 4,610,924 1,672,158 6,539,941 2,781,825 7,895,395 3,792,422 1,479,842 1,734,928 772,160 1,315,724 818,502 192,316 30.3 ? ? ? ? 29.1 9 9 9 9 35.9 ■ ? ? ? ? Totals ? ? ? 100.0 100.0 100.0 Public 21. Suppose the accompanying diagram illustrates the distri- bution of school enrollment in the public, private, and parochial schools of the United States during a certain year. The private and parochial schools are what per cent of the public schools? of the en- tire school enrollment ? The public schools are what per cent of the total enrollment ? of the private and parochial schools combined ? 22. The gold production in the eight principal gold-producing states in the United States in a recent as follows: Colorado, 900,000 oz. Arizona, 180,000 oz. ; Montana, 170,000 oz. ; Nevada, 800,000 oz. ; South Dakota, 350,000 oz. ; Utah, 200,000 oz. ; Idaho, 60,000 oz. Compare these values by drawing a series of parallel rectangles. Parochial Private year was approximately California, 960,000 oz. ; 244 PEACTICAL BUSINESS ARITHMETIC A REVIEW EXERCISE Illustrate the following problems by the use of graphs. Graph forms are given on pages 144, 153, 243. Use the form suggested by the instructor. 1. Illustrate graphically problem 3, page 85. Use the even number of thousands for each month. 2. In a recent year the railway mileage, single-track, of the world was as follows : America, 325,000 mi. ; Europe, 200,000 mi. ; Asia, 63,000 mi. ; Africa, 23,000 mi. ; Austraha, 19,000 mi. Illus- trate graphically, showing the total mileage, and the relation that each country bears to the total. 3. In a recent year there were enrolled in the schools and col- leges of the United States 20,000,000 students, grouped accord- ing to ages as follows: 5 yr., 400,000; 6 to 9 yr., 6,200,000; 10 to 14 yr., 9,000,000; 15 to 17 yr., 3,000,000; 18 to 20 yr., 1,000,000 ; 21 to 24 yr., 400,000. Illustrate graphically. Each group is what per cent of the total ? 4. The number of cattle, other than milch cows, on farms and ranches in the United States, as reported by the decennial cen- suses, for the years named were as follows: 1870, 13,500,000; 1880, 22,500,000; 1890, 33,500,000; 1900, 50,000,000; 1910, 41,000,000. Illustrate graphically. What do these figures sug- gest regarding the cost of living as applied to beef ? 5. The following figures represent the latest estimates of the wealth of the nations named. The figures given represent bil- lions of dollars: United States, 130; Great Britain and Ireland, 80; France, 65; Germany, 60; Russia, 40; Austria-Hungary, 25; Italy, 20; Belgium, 9; Spain, 5i; Netherlands, 5; Portugal, 2|-. Switzerland, 21. Illustrate graphically. 6. In a recent year the cities of the United States which had a population of over 100,000 expended $100,000,000 in various school expenses, according to the following geographical divisions: North Atlantic Division, $54,000,000; North Cen- tral Division, $30,000,000; South Atlantic Division, $2,700,- 000; South Central Division, $3,000,000; Western Division, $10,300,000. Illustrate graphically. PERCENTAGE 245 A WRITTEN REVIEW TEST (Time, approximately, forty minutes) 1. A gardener planted 1 qt. of corn and harvested 5 bu. What per cent of the planting was the harvest ? 2. A bookkeeper made an investment on which he lost 15%. If the sum returned to him was S 1912.50, what was the investment ? 3. A piece of cloth, unfinished, cost 6/ per yard. It costs .0075/ per yard to bleach it, and then it sells for 7|/ per yard. The selling price is what per cent advance over the total cost ? 4. A merchant paid the following bills less the discounts named: S85.50 less 2% ; S141.50 less 3% ; $117.95 less 1% ; S225.40 less li% ; S47.50 less 2i%. What was the total sum paid ? . What was the total discount allowed ? 5. On Monday a man deposited in the bank S 184.96. On Wednesday he deposited a sum 12| % greater than the deposit of Monday ; he then drew a check for 50 % of his total deposit. What was the amount of the check ? 6. A merchant's sales mcreased the second month of his business 25% over the first naonth; the third month they in- creased 20% over the second month; the fourth month they decreased 10% from the sales of the third month. What were the sales for each month if they were S 3240 for the fourth month ? 7. A farmer used 1200 lb. of potato fertilizer per acre, on a 16-acre field of potatoes. The fertilizer cost $24,125 per ton, less 5% for cash payment. If the unfertilized land produced 60 bu. of potatoes per acre, and the fertilized land produced 150 bu. per acre, what per cent of increase was realized by using the fertilizer if the potatoes sold for 80/ per bushel? 8. A man bought a piece of land, and at the end of the first year it had increased in value 25% ; at the end of the second year it had increased an additional 8 % in value ; at the end of the third year it had increased an additional 5% in value. What did he pay for the property if at the end of the third year it was worth $2551.50? CHAPTER XYIII COMMERCIAL DISCOUNTS ORAL EXERCISE 1. A set of Scott's works is marked $12. If I buy it at this price, less 16|%, what does it cost me? 2. I buy $90 worth of goods on 30 da. time, or 5% off for cash. What cash payment will settle the bill ? 3. I owe B $600, due in 30 da. He offers to allow me 5% discount if I pay cash to-day. I accept his offer and give him a check for the amount. What was the amount of the check ? 300. A reduction from the catalogue (list) price of an article, from the amount of a bill of merchandise, or from the amount of a debt, is called a commercial or trade discount. Business houses usually announce their terms upon their bill heads. The space allowed for recording the terms is usually limited, and bookkeepers find it necessary to use symbols and abbreviations to indicate them. Thus, if a bill is due in 30 da. without discount, the terms may be written ^/soj or Net 30 da. ; if the bill is due in 30 da. without discount, but an allowance of 2% is made for payment within 10 da., the terms may be written ^/jq, ^/^, or 2 % 10 da., net 30 da. 301. Manufacturers, jobbers, and wholesale dealers usually have printed price lists for their goods. To obviate the neces- sity of issuing a new catalogue every time the market changes, these lists are frequently printed higher than the actual selling price of the goods, and made subject to a trade discount. 302. The fluctuations of the market and the differences in the quantities purchased by different customers frequently give rise to two or more discounts called a discount series. Large purchasers sometimes get better prices and terms than small pur- chasers. Thus, the average customer might be quoted the regular prices less a trade discount of 25 %, while an especially large buyer might be quoted the regular prices less trade discounts of 25 % and 10 %. 246 COMMERCIAL DISCOUNTS 247 303. When two or more discounts are quoted, one denotes a discount oil the list price, another, a discount off the remainder, and so on. The order in which the discounts of any series is considered is not material. Thus, a series of 25 %, 20 %, and 10 % is the same as one of 20 %, 10 %, and 25 %, or one of 10 %, 25 %, and 20 %. 304. Catalogue prices are generally estimated on the basis of credit sales, and a cash purchaser is given the usual trade dis- count and a special discount for early payment. This latter discount has the effect of encouraging prompt payments. The list price is sometimes called the gross price and the price after the discount has been deducted the net price. FINDING THE NET PRICE 305. Example. The list price of a dozen pairs of shoes is $45. If this price is subject to a discount series of 20% and 10%, what is the net selling price? Solution. 20% or ^ of $45 = $9, the first discount. $45 — $9 = $36, the price after the first discount 10% or j\ of $36 = $3.60, the second discount. $36 - $3.60 = $32.40, the net selling price. ORAL EXERCISE Find the net price :. List Trade List Trade List Trade Price Discount Price Discount Price Discounts 1. 14 25% 8. $Q 40% 15. $4 25% and 331% 2. fl5 20% 9. $4 12|% 16. 130 331% and 25% 3. 190 331% 10. $24 81% 17. $35 20% and 25% 4. 120 10% 11. 142 16|% 18. $45 20% and 16| 7o 5. $50 50% 12. $35 20% 19. $50 20% and 25% 6. $2.50 20% 13. $100 25% 20. $100 20% and 10% 7. $4.50 16f% 14. $720 331% 21. $600 16§% and 20% 22. A piano listed at $750 is sold less 331 %, 20 %, and 10 %. What is the net cost to the purchaser ? 23. A dealer offers cloth at $3.50 per yard subject to a dis- count of 20 %. How many yards can be bought for $5Q ? 248 PRACTICAL BUSINESS AKITHMETIC WRITTEN EXERCISE Find the net price : Gross Selling Price Trade Discounts 1. 13360 25% and 10% 2. $3510 331% and 20% 3. 14500 20% andl6f% Gross Selling Price Trade Discounts 4. 12500 20%, 10%, and 5% 5. 15400 25 %, 20 %, and 10 % 6. 13960 331%, 20%,andl6|% 7. The list price of cloth is 14.80 per yard, but this price is subject to discounts of 25% and 20%. How many yards can bebought for 1288? 8. A hardware dealer sold 25 doz. 5-in. files at 12.50 and 25 doz. 12-in. files at 17.50, less 50% and 10%; 150 machine bolts at $21.50 per C, less 20% and 10%. What was the net amount of the bill ? 9. Study the following model. Copy and find the net amount of the bill, using the discounts named in the bill, and the following prices : 5-in. pipe, f 1.45 ; 1-in. pipe, 17^ ; valves, $2.67. M.^^-L ^^^^.^?^ .<^^. Chicago, 111.. yU^^^ / ^ tg Z2^f:^^ -^^^^^ CQ. Bought of GEORGE W. MUNSON & CO. Terms. ^^77, ^ ^j:^^>7^^^^^^?-7^'^:^^ 6£A^. L2JL JC /^r-7^^. /A^^IA^ r?^< ^£J2- ^^ j-< p V . 2^ Z2J.. c^^^ '^< i^ / c^ y^ zz j^ z^^^^. (/^-^. t^a 2^.^ J^ ^XV'^ J^ ^^ .<£^ Z-^ ' /. JC ^ ^^^/4^4Y ^ j^ 2JJ.^^ COMMERCIAL DISCOUNTS 249 10. One firm offers a piano for $400, subject to discounts of 20% and 20% ; another offers the same piano for $400 less discounts of 25 % and 15%. Which is the better offer? How much better? 11. A jobber bought a quantity of goods listed at 1 3600, sub- ject to discounts of 25% and 20 %. He sold the goods at the same list price, subject to discounts of 20 % and 10 %. Did he gain or lose, and how much? 12. Make out bills for the following, using the current date and the name and address, of some dealer whom you know. Terms in each case, 60 da. net. a. You bought 12 doz. hand saws, #27, at $18.50; "l\ doz. mortise locks, #271, at $4.25; 25 doz. pocket knives, #27, at $7.50; and If doz. cheese knives at $8.25. Discount: 25^,10^. h. You bought 41 J' of 2^' extra strong iron pipe at 70^; 94i' of 11" extra strong iron pipe at 31 J^; 153J^ of \^ iron pipe at 6|^; 88^' of f ' iron pipe at 7|^. Discount: 25^, 10^. c. You bought 25 kitchen tables at $3.25; 25 dining-room tables at $8.75; 15 doz. dining-room chairs at $12.50; 12 antique rockers at $12.25; and 15 oak bedroom sets at $32.50. Discount: 16|%, 5%. FINDING A SINGLE KATE OE DISCOUNT EQUIVALENT TO A DISCOUNT SERIES 306. Example. What single rate of discount is equivalent to a discount series of 25 %, 33^%, and 10% ? Solution. Represent the list price by 1.00 100%. Then, 75% equals the price after the .25 (25% of 100 %) first discount, 60% the price after the second „r discount, and 45% equals the net selling price. * . 100 %, the list price, minus 45 %, the net selling _^ (331 % of 75 % ) price, equals 55%, the single rate of discount .50 equivalent to the given discount series. 05 TIO ^7 of 50 ^ ^ A single discount equivalent to a discount — rp series may often be determined mentally (see §§ 307-308). 100 % - 45 % = bb % 250 PEACTICAL BUSINESS ARITHMETIC WRITTEN EXERCISE • 7u. Find a single rate of discount equivalent to a discount series of 50%, 25%, 20%, and 10%. 2. Which is the better for the buyer and how much, a single discount of 6b % or a discount series of 25 %, 20 %, and 20 %? 3. The net amount of a bill of goods was 1 450 and the dis- counts allowed were 25%, 33 J%, and 10 %. Find the total discount allowed. 4. I allowed a customer discounts of 50%, 10 %, and 10 % from a list price. What per cent better would a single dis- count of 65 % have been ? 5. Goods were sold subject to trade discounts of 25 %, 20 %, and 10 %. If the total discount allowed was 1 460, what was the net selling price of the goods ? 6. A quantity of goods was sold subject to trade discounts of 20 % and 20 % . The terms were 60 da. net or 5 % off for payment within 10 da. If a cash payment of 11026 was re- quired 3 da. after the date of the bill, what was the list price of the goods sold ? 307. Since the first of a series of discounts is computed on 100 % of the list price, and the second on 100 % minus the first discount, it follows that the sum of any two separate discounts exceeds the equivalent single discount hy the product of the two rates per cent. Thus, in a discount series of 20 % and 20 % the apparent single discount is the sum of the two separate discounts or 40%; but shice the second discount is not computed on 100%, but on 80%, 40% exceeds the true single discount by 20 % of 20 %, or 4% ; and the equivalent single discount is 40 % minus 4 %, or 36 %. Hence, 308. To find the single discount equivalent to a series of two discounts : From the sum of the separate discounts subtract their product^ and the remainder will he the equivalent single discount. When two separate discounts cannot be reduced to a single discount mentally, proceed as in § 306 ; when they can, proceed as in § 308. COMMERCIAL DISCOUNTS 251 ORAL EXERCISE State a single rate of discount equivalent to a discount series of : 1. 10% and 10%. 17. 50% and 5%. 33. 25% and 8%. 2. 20% and 20%. 18. 10% and 5%. 34. 8^% and 24%. 3. 30% and 30%. 19. 20% and 5%. 35. 8|%and36%. 4. 40% and 40%. 20. 40% and 5%. 36. 35% and 10%. 5. 50% and 50%. 21. 25% and 30%. 37. 20%andl2|%. 6. 20% and 10%. 22. 25% and 40%. 38. 40%andl2i%. 7. 30% and 10%. 23. 20% and 15%. 39. 60%andl2i%. 8. 40% and 10%. 24. 40% and 15%. 40. 12% and 121%. 9. 50% and 10%. 25. 35% and 20%. 41. 24%andl6|%. 10. 60% and 10%. 26. 45% and 20%. 42. 16|%and20%. 11. 30% and 20%. 27. 55% and 20%. 43. 14|%and35%. 12. 40% and 20%. 28. 60% and 25%. 44. 16|%and25%. 13. 50% and 20%. 29. 40% and 25%. 45. 331% and 15%. 14. 60% and 20%. 30. 60% and 15%. 46. 66|%andl5%. 15. 25% and 10%. 31. 25% and 331%. 47. 111% and 18%. 16. 35% and 40%. 32. 45%and33J%. 48. 36% and 111%. 309. When a discount series consists of three separate rates, the first two may be combined as in § 318 and then the result and the third may be combined in the same manner. 310. Example. Find a single rate of discount equivalent to a discount series of 25%,, 20%?, and 20%. Solution. — Combine the first two by thinking 25% + 20%- 5% = 40%, the single discount equivalent to the series 25 % and 20 %. 20 % + 40 % -8 % = 52 %, or the single rate equivalent to the discount series 25%, 20%, and 20%. ORAL EXERCISE State a single rate of discount equivalent to a discount series of: 1. 20%, 25%, and 20%. 7. 20 %, 10%, and 10%. 2. 20%, 15%, and 10%. 8. 40%, 10%, and 10%. 3. 20%, 20%, and 20%. 9. 50%, 10%, and 10%. 4. 10%, 10%, and 10%. 10. 30%, 10%, and 10%. 5. 20%, 20%, and 10%. 11. 20 %, 25%, and 10 %. 6. 25%, 331%, and 10%. 12. 20%, 20 %, and 25%. 252 PRACTICAL BUSINESS AEITHMETIC 311. When it is not desirable to show the separate discounts, the net selling price may be found as shown in the following example. 312. Example. A mahogany sideboard listed at $175 is sold subject to trade discounts of 20% and 25%. Find the net cost to the purchaser. Solution. By inspection determine that a 100 % — 40 % = 60 % discount of 40% is equivalent to a series of 25% aQcf of ^175 = S105 and 20%. Represent the gross cost by 100%. Then 100% — 40% = 60%, the net cost to the purchaser; that is, the net cost of the sideboard is 60% of the list price. 60% of ^ 175 = $ 105, the net cost to the purchaser. ORAL EXERCISE Bt/ inspection find the net cost of articles listed at: 1. 8400, less 20% and 25%. 5. $1000, less 50% and 50%. 2. 1300, less 20% and 20%. 6. $1000, less 30% and 10%. 3. f 600, less 10% and 10%. 7. |200, less 60% and 25%. 4. 1200, less 30% and 30%. 8. $400, less 20% and 40%. WRITTEN EXERCISE -^ 1. Find the net selling price of a piano listed at $450, less 20% and 20%. 2. Find the net selling price of an oak sideboard listed at $125, less 25%, 3-31%, and 10%. 3. I bought 125 cultivators listed at $8.50, each subject to trade discounts of 20% and 25%. If I paid freight $30.50 and drayage $7.90, how much did the cultivators cost me? 4. The net cost of an article was increased $ 30 by freight, making the actual cost of it $ 630. What was the list price of the article, the rates of discount being 25 % and 33^ % ? \ 5. You desire to buy 24,000 ft. choice cypress : one firm quotes you $60 per thousand feet, less trade discounts of 20 % and 5% ; another firm offers you the same lumber at $75 per thousand feet, less 331% and 8%. The terms offered by both firms are Yio, Vso* ^^^ accept the better offer and. pay cash. How much does the lumber cost you? COMMERCIAL DISCOUNTS 253 WRITTEN REVIEW EXERCISE 1. Find the cost of 125 1^" brass ells at $1.25 each, less 25% 20 % and 10 f. 2. An agent bought 10 pianos listed at 8450 each, less 33i% and 10 %, and sold them for |400 each, less 10 % and 5 %. Did he gain or lose and how much? 3. Apr. 15, E. L. Gano bought of W. L. Cunningham & Co. 5 phaetons listed at 1450 each, less 25% and 20%. Terms: Ygo, ^/eo- How much ready money would settle the bill? 4. Study the following bill. Copy and find the net amount of it, using the discounts indicated in the bill, and the follow- ing prices: windmills, $675; pumps, S610; 1-in. iron pipe, Vl\j\ 4-in. iron pipe, 73^; hose, 97)^; elbows, 21|j^; valves, $1.49. Boston, Ma55., a y>r^^//^, Terms. //a. Yj/}^ /6o Bought of E. M. McGregor & co. ^?^ U^ ^^"/o v ^^ y. ^ ^ ^U/^^^7^ V^v^^ ZS2 Aroo_. ziT^. /■'Tn^ mm ^;2^ WVlT^^-'T^C;^-,^-^ /^^^ 2jni l-^o ^ ^ .- ^ ^ ^~7 jL^ j^da ^^ z.o'/> "^z^y: 2^Z\ liUl ^^f^fo zAj.-. all: Ij2^ _2^ jm. 0^^y^y^^^ //^r^^^^ JZ^'- -^1 .^?^^^ ^^ yl y/^ y^ j^Al TJl .JIL 1^ ll/^ JJL 254 PEACTICAL BUSINESS AKITHMETIC . 5. How much cash would settle the model bill (page 253) Oct. 30 ? Nov. 8 ? How much cash would settle the bill called for in problem 4, if it is paid for on the day it is written? If it is paid Nov. 15 ? Copy the model bill in the form that it would be written if cash accompanied the order ; that is, copy it deducting the 3 % allowed for immediate payment. 6. Copy and find the net amount of the following bill : NLeith, Scotland, May lo. 19 Invoice of Wire Cloth Shipped by the J. M. ROBERTS COMPANY In the Steamship Winifredian To Edward M. Davidson & Co. Philadelphia, Pa. 6 PC. each 34' x 5' 6" 1122 sq. ft. 1/3 70 2 5 6 " " 40' X 6' 6" **** 1/4 *** * * 5 " " 42 ' X 7 ' 4 " **** 1/5 *** ** * 3 » " 48' X 7" 2" **** 1/5 ** ** * ««* ** * Less 10% ** ** * 7. E. M. French & Co., Albany, N.Y., bought of Austin Bailey & Co., Boston, Mass., Apr. 12, 3 doz. pr. hinges, 8 in., at $4.20, and 3 doz. pr. hinges, 4 in., at $2.10, less 60%, 10%, and 10% ; 50 lb. brads, | in., at 90^, and 50 lb. brads, | in., at 80^, less 50%, 10%, and 5%. Terms: Vio, Vao- ^^^^^ the net amount of the bill Apr. 15. ^^8. D. M. DeLong, Portland, Me., sold S. H. Shapleigh & Co., Concord, N.H., on account 30 da., 2% 10 da.: 35 cul- tivators listed at $7.50 each, less 20% and 10 % ; 15 doz. table knives listed at $9.75, less 10% ; 15 doz. hair curlers at 90^, less 5% ; 15 doz. locks. No. 534, at $3.75, less 10% and 5% ; I doz. steel squares. No. 8, at $36, less 25% and 10% ; 1 gro. knives and ^rks. No. 760, at $12, less 20% and 10% ; | doz. cheese knives at $9.75, less 16|%. Find the net amount of the bill 5 da. after date. COMMERCIAL DISCOUNTS 255 WRITTEN REVIEW TEST (Time, approximately, forty minutes) 1. If goods are bought 25% below the list price and sold at the list price, what is the advance per cent over the cost ? 2. If goods are bought 20% below the list price and sold at the list price, what is the advance per cent over the cost ? 3. If goods are bought 10 % below the list price and sold at 10 % above the list price, what is the advance per cent over the cost ? 4. If goods are bought at 20% and 12|% below the list price, and sold at 10% below the list price, what is the advance per cent over the cost ? 5. A hardware dealer bought a machine listed at S24, less 16|% and 10%, and sold it at the list price. At what per cent above cost did he mark the selling price ? 6. A jobber wished to buy at such a discount from the manu- facturer's list price that he could make an advance of 25% over cost, and stiU sell at the manufacturer's list price. What would the jobber pay for SIOOO worth of goods ? 7. A gentleman wished to buy a carriage. One dealer offered him a discount of 33^% and 10% from the list price, and an- other dealer offered him 20%,' 10%, and 10% from the list price. If the list price is S450, what will be the cost of the carriage if it is bought at the better discount ? 8. Aug. 5, you buy of Gray, Salisbury & Son, New York City, 4000 lb. raisins at 16/, less trade discounts of 25%, 20%, and 10%. Terms: Vio, ^Vso- You pay cash for freight $3.20. If you pay the bill Aug. 7, what will the raisins cost you ? 9. You desire to buy 200 lb. nutmeg. You find that S. S- Pierce Co., of your city, offer this article at 75/ per lb., less a discount of 25%, and that Smith, Perkins & Co., New York City, offer it at 70/ per lb., less discounts of 15% and 10%. The freight from New York to your city on a package of this kind is S1.50. The terms offered by both firms are: Vio» ^/so- You accept the better offer and pay cash. How much does the nutmeg cost you ? CHAPTER XIX GAIN AND LOSS ORAL EXERCISE ^1. What is 33^% of 8660? How much is gained on goods bought for 1900 and sold at a profit of 331% ? •L2. What per cent greater is 175 than $60? what per cent less is 160 than f 75? Goods bought for $100 are sold for $150. What is the gain per cent? 3. What per cent less is $80 than $100? what per cent more is $100 than $80? Goods bought for $100 are sold for $90. What is the loss per cent ? 4. If $800 is increased by 25% of itself, what is the result? Goods bought for $1400 are sold at a profit of 25%. What is the selling price ? ,5. If $1500 is decreased by 331% of itself, what is the result? Goods bought for $2700 are sold at a loss of 331%. What is the selling price ? 6. State a brief method for finding a gain of 6|%; a gain of 6|%; a gain of 81%; a gain of 10%; a gain of l-|-%; a gain of 1|%; a gain of 21%; a gain of 31%. 7. State a brief method for finding a loss of 11^%; a loss of 121% ; a loss of 14f % ; a loss of 16f % ; a loss of 20% ; a loss of 25% ; a loss of 9^^ % ; a loss of 37^%. 8. State a brief method for finding a gain of 33^%; a gain of 22|%;; a gain of 50% ; a gain of 66f %; a gain of 75 %. 313. The gains and losses resulting from business transac- tions are frequently estimated at some rate per cent of the cost, or of the money or capital invested. Since no new principles are involved in this subject, illustrative examples are unnecessary. 256 GAIN AND LOSS 257 FINDING THE GAIN OR LOSS ( ORAL EXERCISE By inspection find the gain or loss : Per Cent Per Cent Per Cent Cost of Gain Cost of Loss Cost OF Gain 1. 12900 50% 9. $1500 10% 17. $7500 20% 2. $1600 75% 10. $1600 1|% 18. $1400 25% 3. 15600 28f% 11. $3000 1|% 19. $2200 h\% 4. $2700 331% 12. $4800 2J% 20. $8100 lli% 5. 12400 37i% 13. $3600 31% 21. $6400 12|% 6. 11400 42f% 14. $3200 61% 22. $2800 Wf% 7. $3200 621% 15. $4500 6f% 23. $9600 161% 8. $2100 66|% 16. $8400 81% 24. $3600 22|% 25-48. Find the selling price in eacli ( 3f the above problems. WRITTEN EXERCISE 1. An importation of silks invoiced at £40 10s. was sold at a profit of 25 % . Find the amount (in United States money) of the gain. 2. An importation of German toys invoiced at 43,750 marks was sold at a gain of 33 J % . Find the amount (in United States money) of the gain. 3. An article that cost $1 was marked 10% above cost. In order to effect a sale, it was afterward sold for 10% below the marked price. Find the gain or loss on 250 of the articles. ' 4. A man bought a city lot for $1150 and built a house on it costing $2650. He then sold the house and lot at a gain of 5%. How much did he gain and what was his selling price? ^ 5. A man bought a quantity of silk for $450, a quantity of fancy plaids for $ 120, and a quantity of velvet for $ 90. He sold the silk at a gain of 25%, the plaids at a loss of 5 %, and the velvet at a gain of 331%. What was his gain, and how much did he realize from the sale of the three kinds of material ? 258 PRACTICAL BUSINESS ARITHMETIC EmDING THE PER CENT OF GAIN OK LOSS ORAL EXERCISE By inspection find the per cent of gain or loss : Cost Gain Cost Loss ^^„ Selling C^^:^ Price i- Selling Price Gain 1. flOO $10 7. $60 $15' 13. $80 $90 19. $300 $60^ 2. $150 $50 8. $40 $10 14. $90 $80 20. $115 $23 3. $140 $70 9. $90 $45 15. $60 $75 21. $102 $17 4. 1140 $140 10. $70 $14 16. $75 $60 22. $420 $60 5. $200 $400 11. $80 $16 17. $10 $50 23. $300 $200 6. $300 $750 12. $15 $10 18. $50 $10 24. $700 $100 WRITTEN EXERCISE 1. A milliner bought hats at $15 a dozen and retailed them at $3 each. What per cent was gained ? , 2. A stationer bought paper at $2 a ream and retailed the same at a cent a sheet. What was his per cent of gain ? 3. A dry-goods merchant bought gloves at $7.50 a dozen pair and retailed them at $1.25 a pair. What was his per cent of gain ? 4. A merchant imported 50 gro. of table knives at a cost of $1125. Two months later he found that the sales of table knives aggregated $920 and that the value of the stock unsold was $435. Did he gain or lose, and what per cent ? 5. An importer bought a quantity of silk goods for £ 400 5s. After disposing of a part of the goods for $1200 he took an account of the stock remaining unsold and found that at cost prices it was worth $1047.82. Did he gain or lose, and what per cent ? 6. Jan. 1, F. E. Smith & Co. had merchandise on hand valued at $2500. During the month they purchased goods costing $6000 and sold goods amounting to $7500. If the stock on hand at cost prices Feb. 5 was worth $2500, what was the per cent of gain on the sales ? GAIN AND LOSS 259 FINDING THE COST ORAL EXERCISE By inspection find the cost: Loss ] Rate of Loss Gain Rate of Gain 1. 1150 10% 7. $35 20% 2. $100 H% 8. $79 25% 3. 8200 H% . 9- $12 iH% 4. 1450 mo 10. $19 16|% 5. $220 6-1% 11. $44 22|% 6. 1115 81% 12. $15 331% Selling Rate Selling Rate Price OF Gain Price OF Loss 13. 11050 5% 19. $950 5% 14. $2040 2% 20. $900 50% 15. $3600 20% 21. $150 ■6i % 16. $1400 16f% 22. $550 16f% 17. $1800 12i% 23. $240 331% 18. $2400 331% 24. $490 22|% 25. A man bought a machine for S 240.48. For how much must he sell it to gain 121% ? 26. B sold a farm for S2400, thereby losing 25%. For how much should he have sold it to have gained 10% ? 27. By selling a piano at $400 a dealer realizes a gain of 33i%. What would be the selling price of the piano if sold at a gain of 25 % ? WRITTEN EXERCISE 1. A sleigh was sold for $64.80, which was 10 % below cost. What was the cost ? 2. An office safe was sold at $102, which was 20% above cost. What was the cost ? 3. A merchant marks goods 16|% above cost. What is the cost of an article that he has marked $21.70? 260 PRACTICAL BUSINESS ARITHMETIC 4. An owner of real estate sold 2 city lots for §12,000 each. On one he gained 25% and on the other he lost 25%. What was his net gain or loss from the two transactions ? 5. A merchant sold a quantity of goods to a customer at a gain of 25%, but owing to the failure of the customer he re- ceived in settlement but 88^ on the dollar. If the merchant gained $645.15, what did the goods cost him ? 6. A manufacturer sold an article to a jobber at a gain of 25%, the jobber sold it to a wholesaler at a gain of 20%, and the wholesaler sold it to a retailer at a gain of 33J%. If the retailer paid $28 for the article, what was the cost to manufac- ture it ? 7. A manufacturer sold an article to a wholesaler at a gain of 20%, the wholesaler sold the same article to a retailer at a gain of 33J%, and the retailer to the consumer at a gain of 25%. If .the average gain was §40, what was the cost to manufacture the article ? WRITTEN REVIEW EXERCISE 1. A merchant bought goods at 40 % off from the list price and sold the same at 20 % and 10 % off the list price. What was his gain per cent ? 2. I bought goods at 50% off from the list price and sold them at 25 % and 25 % off frongi the list price. Did I gain or lose, and what per cent ? 3. Apr. 15 you bought of Baker, Taylor & Co., Rochester, N. Y.,'4000 bbl. Roller Process flour listed at 14.50 a barrel, and 2000 bbl. of Searchlight pastry flour listed at $4.75 a barrel. Each list price was subject to trade discounts of 20% and 10%. You paid cash $16,000 and gave your note at 30 da. for the balance. What was the amount of the note ? 4. May 18 you sold to F. H. Clark & Co., New York City, 2000 bbl. of the Roller Process flour, bought in problem 3, at 331% above cost. Terms: Vio, Vao- ^'' H. Clark & Co. paid cash. Find the cash payment. GAIN AND LOSS 261 5. May 30 you sold Smith, Perkins & Co., Albany, N.Y., the balance of the :^ur bought in problem 3, at an advance of 33 J % on the costT^.Terms : Vioi Vao- The flour was paid for June 8. Find the cash payment. 6. What is the net gain on the transactions in problems 3, 4, and 5 ? the net gain per cent ? 7. Pec. 15 you bought of E. B. Johnson & Co. 400 bbl. of apples at ^2.50 per barrel. Terms : Vio^ Vso- You paid cash. Find the amount of your payment. 8. May 15 you sold F. E. Redmond the apples bought in problem 7, at $4 a barrel. Terms: Vio^ Vso- At the maturity of the bill Redmond refused payment and you placed the account in the hands of a lawyer who succeeded in collecting 75 % of the amount due. If the lawyer's fee for col- lecting was 4 ^, what was your net gain or loss ? 9. A tailor made 25 doz. overcoats with cloth worth $2 a yard. 4 yd. were required for each coat and the cost of making was $48 per dozen. He sold the overcoats so as to gain 33J^%. • How much did he receive for each? 10. Apr. 12 J. D. Farley & Son, Trenton, N. J., bought of Cobb, Bates & Co., Boston, Mass., a quantity of green Java coffee sufficient to yield 2400 lb. when roasted. If the loss of weight in roasting averages 4%, what will the green coffee cost at 30^ a pound, less a trade discount of 10%? Arrange the problem in bill form. 11. If the coffee in problem 10 is retailed SS^% above cost, and there is a loss of 1% from bad debts, what is the gain on the transactions in coffee ? the gain per cent ? 12. The Metropolitan Coal Co., of Boston, Mass., decides to bid on a contract for supplying 2240 T. of coal for the pub- lic schools of the city. It can buy the coal at $4.50 per long ton delivered on board track, Boston. It costs on an average 75^ per short ton to deliver the coal, and there is a waste of ^ % from handling. Name a bid covering a profit of 20%. Terms: cash. 262 PRACTICAL BUSINESS ARITHMETIC riNDING THE PER CENT OF GAIK OR LOSS ON THE SELLING PRICE ORAL EXERCISE 1. An article cost $80 and it is sold for SIOO. What is the sum gained ? The gain is what per cent of the cost ? of the selling price ? 2. An article costs $60 and it is sold for $75. What is the sum gained ? The gain is what per cent of the cost ? of the selling price ? 3. An article is sold for $90. If the gain on the selling price is 33i%, what was the cost, and what is the gain per cent on the cost price ? 314. Find by inspection the gain per cent on the selling price : Cost Selling Price Cost Selling Price a, $20 $30 /. $120 $150 h. $30 $40 g. $125 $150 c. $45 $60 h. $140 $160 d. $60 $75 ^. $150 • $175 e. $50 $60 j. $160 $180 This principle may be applied effectively when goods have been marked by a merchant at a certain per cent on the advance of the cost, and then marked down to sell at cost. 315. If an article that costs $1 is marked to sell at $1.10, what per cent of reduction will restore the original cost price ? Suggestion. It is evident that a reduction of 10% on the selling price will not restore the original marking of $1. 316. Find by inspection the per cent of reduction that must be made to reduce the marked price to the cost price. Cost Marked Price Cost Marked Price a. $1.00 $1.25 d. $1.50 $1.80 h. $1.25 $1.50 e. $2.00 $2.50 c. $1.60 $2.00 /. $3.00 $4.00 317. Business men are continually dealing with the problem of overhead charges; that is, the cost of doing business. Overhead GAIN AND LOSS 263 charges include such expenses as employees' salaries, rent, insur- ance, taxes, light and heat, postage, advertising, depreciation, telephone, and many others. To the invoice charges there must be added a certain per cent to cover the cost of doing business. 318. The following principle applies to subsequent problems: Divide the invoice cost plus the freight by 100 % minus the over- head charges plus the per cent of profit (100 % — charges + profits) ; the result will be the selling price. (This statement is based on reckoning the overhead expenses and the gain as a per cent of the selling price.) WRITTEN EXERCISE 1. An article was invoiced at $33.50; freight charges, S1.50. If the overhead charges amounted to 15 % and the gain to 10 %, what was the selling price ? Solution. 15% + 10% = 25%. 100% -25% = 75%. ^33.50 4- '^l.SO = $35, the cost. .$35 -^ .75 = $46.67, the selling price. Proof. 25% of $46.67 = $11.67, overhead charges and gain. $46.67- $11.67 = $35, the cost. 2. A merchant sold goods amounting to S 22,500. If the over- head charges amounted to 18 % and the profits to 8 %, what was the invoice price of the goods if the freight amounted to S 350 ? 3. A merchant marked a lot of goods 33i % above cost, but as he was unable to sell them at the marked price, he decided to reduce the marking to cost. What per cent reduction must be made ? 4. A machine was invoiced at S 53.50; freight charges, S3.50. If the overhead charges of the business amounted to 20%, and the gain to 10 %, what must be the selling price of the goods ? 5. An invoice of merchandise amounted to $1204.50; freight charges, $ 10.50. If the overhead charges amounted to 17| % and the gain to 7^ %, what must be the selling price ? 6. A merchant marked a lot of goods at 25 % above cost, but as the goods did not sell at the marked price, he reduced it 25 %, and announced that he was selling at cost. What per cent rep- resents the amount of his error? If the goods thus marked cost $1760.48, what did the merchant lose by his blunder? CHAPTER XX MARKING GOODS 319. Merchants frequently use some private mark to denote the cost and the selling price of goods. The word, phrase, or series of arbitrary characters employed for private marks is called a key. Many houses use two different keys in marking goods, one to represent the cost and the other the selling price. In this way the cost of an article may not be known to the salesmen, and the selling price may not be known to any except those in some way connected with the business. In large houses, when but one key is used, only the selling price is indicated on the article, it being deemed best to keep the actual cost of the article a secret with the buyers. In small houses, when but one key is used, both the cost and the selling price are frequently written on the article. 320. If letters are used to mark goods, any word or phrase containing ten different letters may be selected for a key. If arbitrary characters are used, any ten different characters may be selected for a key. Some methods of marking are so complicated that it is necessary to always have a key of the system at hand for reference. Goods are so marked in order that important facts, such as the cost of goods, may be kept strictly private. 321. When a figure is repeated one or more times, one or two extra letters called repeaters are used to make the key word more secure as a private mark. 322. The following illustrates the method of marking goods by letters : Cost Key Selling-price Key REPUBLICAN PERTHAMBOY 1234567890 1234567890 Repeaters: S and Z Repeaters: W and D 264 MARKING GOODS 265 *^T '^ n.u-u L A.p rt- -i The cost is generally written above and the selling price below a hori zontal line on a tag, or on a paster or box. Gloves No. 271, costing $5 a dozen and selling for $6.25 a dozen, might be marked as shown in the margin. Fractions may be desig- nated by additional letters or characters. Thus, W may be made to represent |, K ^, etc. in the above key. In marking goods for the retail trade, all fractions of a cent are called another whole cent. WRITTEN EXERCISE 323. Using the keys given in § 322, write the cost and the selling price in each of the following problems : First Cost OF Article Freight Gain 1. $2,50 10% 2. 11.00 10% 3. .50 f4.80 20% 20% 331% 4. 20% Loss 25% First Cost OF Article Freight 2i% 5. $16.00 6. $40.00 7. I 3.60 8. |'24.00 Gain 1 2 'I 37-i% 161% 2|% Loss 10% 324. Using the following hey, write the cost and the selling price in each of the following problems : Cost Key Selling-price Key r 1 L.1JhHCDJ- + 234567890 T 1 xunE3fnuJi# 234567890 Repeaters : □ C^s^ Repeaters : X — First Cost of Article Charges Gain Loss First Cost of Article Charges Gain Loss 9. 10. 11. 110.00 5% 20% 120.00 10% 50% 130.00 6|% 25% 12. 13. 14. $15.00 6|% 25% $18.00 10% 25% $12.00 5% 331% 325. Wholesalers and jobbers buy and sell a great many articles by the dozen. Retailers buy a great many articles by the dozen, but generally sell them by the piece. In marking goods, therefore, it is highly important that the student be able to divide by 12 with great rapidity. To divide by 12 with rapidity, the decimal equivalents of the 12ths, from rz ^^\\ inclusive, should be memorized. 266 PRACTICAL BUSINESS ARITHMETIC Table of Twelfths Twelfths Simplest Form Decimal Value Twelfths Simplest Form Decimal Value 1^^ $.081 A $.581 A h .16f 1% 1 .6()| A i .25 A f .75 T^^ i .33^ it 1 .83^ t\ An ii .91| A h .50 11 1 1.00 326. Example. What is the cost of one shirt when a dozen shirts cost 119 ? Solution. Divide by 12 the same as by any number of one digit and men- tally reduce the twelfths in the remainder to their decimal equivalent. Thus, say or think l/^* $1'58^5 practically $1.58. ORAL EXERCISE State the cost per i xrticle when the cost per dozen articles is : 1. 125.00. 7. •ifT.OO. 13. 123.20. 19. $9.00. 2. 137.00. 8. 13.60. 14. 119.20. 20. $7.00. 3. !|42.00. 9. 12.40. 15. $66.60. 21. $5.00. 4. 164.00. 10. $5.60. 16. 138.00. 22. $7.50. 5. 180.00. 11. 13.40. 17. IIT.OO. 23. $8.40. 6. $13.00. 12. 113.20. ORAL 18. 111.00. EXERCISE 24. $17.50 1. Hats costing $48 a dozen must be sold for what price each to gain 25 % ? 2. Rulers bought at $2 a dozen must be retailed at how much each to gain 50 % ? 3. Note books costing $1.60 per dozen must be retailed at what price each to gain 12|% ? 4. Erasers bought at $3.24 per gross must be retailed at how much each to gain 1H\% ? 5. Matches costing $3.60 per gross boxes must be retailed at what price per box to gain 100% ? MARKING GOODS 267 6. Envelopes bought at 1 2 per M must be sold at what price per package of 25 to gain 100%? 7. Pickles bought at il.80 per dozen bottles must be sold at what price per bottle to gain 33 J % ? 8. Mustard costing $14.40 per gross packages must be re- tailed at what price per package to gain 20% ? to gain 50% ? LISTING GOODS FOR CATALOGUES 327. In listing goods for catalogues dealers generally mark them so that they may allow a discount on the goods and still realize a profit. 328. Example. What should be the catalogue price of an article costing $24 in order to insure a gain of 25 % and allow the purchaser a discount of 20 % ? Solution. ^ of ^24 = .$6, the gain. ^30 = the selling price, which is 20% below the catalogue price. .80 of the catalogue price = $30, .-. the catalogue price = $30 -=- .80 = $37.50. WRITTEN EXERCISE 1. At what price must you mark an article costing $400 to gain 25 % and provide for a 20 % loss through bad debts ? 2. What should be the catalogue price of a library table costing $25 in order to insure a gain of 20% and allow the purchaser a discount of 25 % ? 3. You list tea costing 30^ a pound in such a way that you gain 33i % after allowing the purchaser a trade discount of 20 %. What is your list price? 4. You buy broadcloth at $3.80 per yard. At what price must you mark it in order that you may allow your cash customers 5 % discount and still realize a gain of 20 % ? 5. Having bought a quantity of oranges for $3.00 per C you mark them so as to gain 33^ % and allow for a 20 % loss through bad debts. What will be your asking price per dozen? 268 PEACTICAL BUSINESS ARITHMETIC 6. At what price must the articles in the following invoice be listed to gain 20 % and allow discounts of 25 % and 20 % ? Boston, Mass., Nov. 24, 19 Mr, Edgar C. Townsend Rochester, N.Y. Bought of WELLS, FOWLER & CO. Terms Net 50 da. " 400 300 630 700 70 #721500ak Bookcases |8.00 #924 25 Gentlemen's Chiffoniers 12.00 Less 10^ WRITTEN REVIEW EXERCISE 1. Using the word importance^ with repeaters s and w^ for the buying key, and the words huy for cash, with repeaters t and m,^ for the selling key, write the cost and selling price of the articles in the following bill. It is desired to gain 25 % on the pens and pencils, 20 % on the cards, and to provide for a loss of 12| % through bad debts. Boston, Mass., Oct. 18, 19 Messrs. WHITE & WYCKOFP Holyoke, Mass. Bought of C. E. Stevens & Co. Terms Net 30 da. 100 25 50 gro. Pens " Lead Pencils pkg. Record Cards Less 12 1/25^ $0.80 80 3.20 80 .40 20 180 22 50 157 50 MARKING GOODS 269 2. At what price must I mark the following shoes to gain 20%? M- ^. . "7^^^?:; J. 'Detroit^ Mich..,. ^^.^^1^7^/r 7, / ^ ' " /^ ■'9 -^^./j^y^^a^ Terms. //a^ /ie Bought of ATWOOD & RANDALL 3^^ ^ y^ y U^ J^^^^^^^-^:^^. ^^^-^ ^V. ^^:r/^^J^7„ /f ^^ 72=Z^ >^. -^^ -^A&A/MramA (fCniA/^cA^tJiM ^ 3. You list tea bought for 30^ at an advance of 33^% on the cost. Finding small sale for the article you determine to sell so as to gain but 16| % . What trade discount should you allow ? 4. What price per pound must be obtained for the follow- ing invoice of coifee to gain 25 % and allow 10 % for loss in roasting and 16| % for loss through bad debts ? ^Boston, ^Jtass., NoV. 25, /9 .-//Messrs. Merchant & Co. 120 Main St., City thought of (^066, fJjates cP* Go. !Terms 50 da. 2000 lb. Green Java Coffee 24^ Cartage 480 2 00 50 482 50 CHAPTER XXI COMMISSION AND BROKERAGE ORAL EXERCISE 1. A collected a bill of $350 and received 6% for his services. How much did he make ? 2. B bought $80 worth of eggs for a dealer who paid him 7J% for his services. How much did B make? 3. C receives $12 a week, and 5 % of his weekly sales. If he sold $350 worth of goods in a week, what was his income for the week ? 329. An agent is a person who undertakes to transact busi- ness for another called the principal. 330. A great deal of the produce of the country and a large variety of manufactured articles are bought and sold through agents called commission merchants and brokers. 331. A commission merchant (sometimes called a factor) is an agent who has actual possession and control of the goods of his principal ; a broker is an agent who arranges for purchases or sales of goods without having actual possession of them. 332. The sum charged by an agent for transacting business for his principal is called commission or brokerage. Commission and brokerage are frequently computed at a certain per cent of the amount of property bought or sold, or of the amount of business transacted. Brokerage is also often a fixed rate per bushel, barrel, tierce, or other standard measure. 333. Agents frequently charge an additional commission, called guaranty, for assuming any risk or guaranteeing the quality of goods bought or sold. The person who ships goods is sometimes called the consignor; the person to whom the goods are shipped, the consignee. 270 COMMISSIOK AND BROKERAGE 271 A quantity of goods sent away to be sold on commission is called a ship- ment ; a quantity of goods received to be sold on commission, a consignment. 334. All account sales is an itemized statement rendered by a commission merchant to his principal. It shows in detail the sales of the goods, the charges thereon, and the net proceeds remitted or credited. SBuffalo, J^.y., Zmt^q 18. 79 ^a/e of ^^^erchanctise for >^ccount of E. H. Barker & Co.. Poughkeepsie. .Y. «^y Zrlogg, %/aylon cF" >^ogg ' June 5 200 bbl. Roller Process Flour $6.00 1200 00 12 300 " Old Grist Mill Flour CAarges 6.10 1830 00 June 2 Freight and Drayage 40 75 12 Commission 5% 151 50 18 Net proceeds remitted 2837 75 3030 00 3030 00 335. An account purchase is a detailed statement rendered by a purchasing agent to his principal. It shows in detail the quantity, grade, and price of goods purchased, the expenses incurred, and the gross (total) cost of the transaction. Chicag< Purchase of Merchandise for Account .19- -y^^^^^^^^T^^-^^T^. By GRAY. DUNKLE & CO. ^^^^r9- T ^r } -X^>.&^^^^^^.^/^.,y^^ ■/ C(P(? — ^^2^__« ^ ^.d^ J ^ C^^^^f ^/z ^ ^^ AJr: Adji 2-/?^ Charges n S^^ ^ ■2^:tZ. -.-rg-i^^ JJL JJI "(o.-r>-^^^3''j<;^^^L^20.50 on the merchandise enumerated in the following shipping invoice. This sum is 5 % of the cost of the goods. Find the gross cost of the goods. New Torky. ^ ^^-^. f^. TQ Invoice of Merchandise shipped to- (STUDENTS NAME) (STUDENT'S ADDRESS) To be sold for account of C, L, BROWN ^ CO. ^JL ^ v-rz^. ^^^T^T^^f:^^^^ ^i!^ '.^^ . >^Z ^ . ^ 7. Dec. 15 you sell Morgan & Co., Albany, N.Y., 60 bx. lemons at $4. Terms: Viq, Vso- Morgan & Co. pay cash. What is the amount of the cash payment ? 274 PRACTICAL BUSINESS ARITHMETIC 8. Dec. 18 you sell Meachum & Co., Troy, N.Y., 50 bx. oranges at $4.50. Terms: Vio^ Vso- Meachum & Co. pay for the goods Jan. 12. What is the amount of their payment? 9. Render C. L. Brown & Co. an account sales for the goods received Dec. 8, commission, 5^. Assume that on Dec. 5 you advanced them $50 on the consignment. Find C. L. Brown & Co's net gain or loss on the shipment in problem 6. 10. Prepare an account sales, under the current date, for the following, sold by you, for the account of Lewis, Grayson & Co., Rochester, N.Y. : 60 bbl. Pillsbury's flour at $6.25; 75 bbl. XXXX flour at $5.75 ; 45 bbl. star brand flour at $5 ; 100 bbl. XXX flour at $4.90 ; 50 bbl. peerless flour at $5.15. Charges : freight, $38.95; cartage, $12.60; cooperage, $6.25; commis- sion, 31 % ; guaranty, l%. BUYING OX COMMISSIOX WRITTEN EXERCISE 1. B, a broker, bought for C, a speculator, 3000 bu. wheat at 90 J ^, on a commission of ^f^ per bushel. What was the broker's commission, and what did the wheat cost C? 2. I bought through a broker 5000 bags coffee, each con- taining 130 lb., at 121^. If the broker charged $10 for each 250 bags, how much did he earn on the transaction, and what did the coffee cost me? 3. I bought through a broker 20,000 bu. of wheat at Sl^-^f^, and three weeks later sold it through the same broker at 92|^. If the broker charged me ^^ per bu. for buying and the same for selling, what was my gain ? 4. A firm of produce dealers bought through a broker 1500 bbl. pork at $12.50, and immediately sold it through another broker at $12.12^. If each broker charged a commission of 2J^ per barrel, what was gained by the produce dealers? 5. You buy for your principal 1500 bbl. flour at $4.50, on a commission of 3%, and pay drayage $18.50. What is the cost of the purchase to your principal? COMMISSION AND BROKERAGE 275 6. By your principars instructions you put the flour (prob- lem 5) in storage and later sold it at 15.25 a barrel, on a com- mission of 3%. The storage charges were 5^ per barrel. What amount should you remit to your principal ? 7. A broker bought cotton for a manufacturer as follows : 750 bales, 375,000 lb. at lO-i ; 1500 bales, 750,000 lb. at ^Of ^; and 1000 bales, 500,000 lb. at lOf^. The broker's charges were $7.50 for each 100 bales. How much did he earn on the trans- action, and what did the cotton cost the manufacturers ? 8. Find the amount to be charged to Roe & Co. : New York, N.Y., Mar. 15, 19 Purchased by Arault & Co. For the account and risk of Roe & Co. Telephone, 690 Main Poughkeepsie, N.Y. hf. ch. Japan Tea 1200 # hf. ch. Oolong Tea 1000# Charges Drayage Commission, 2%, $ ; guaranty, ^%, $ Amount charged to your account 30^ 45^ 50 9. Find the rate of commission and the amount due Brown Bros. Co. in the following account purchase. Rochester, N.Y., Apr. 20, 19 Purchased by Brown Bros. Co. For the account and risk of W. D. Snow Telephone, 1291 Main Springfield, Mass. 600 bbl. Pillsbury's Best Flour 100 bbl. xxxx Flour 200 bbl. Peerless Flour Charges Cartage Commission ? % Amount due us 6.00 5.50 5.25 15 00 104 00 276 PRACTICAL BUSINESS ARITHMETIC A WRITTEN REVIEW TEST (Time, approximately, forty minutes) Qofy problems 1—12 and complete the work in each one : Face of THE Debt Rate of Commission Amount received BY THE Agent Amount received BY THE Principal 1. S457.75 2% ? ? 2. ? 1% $2.59 ? 3. ? ? $5.27 $170.23 4. S 325.45 ? ? $318.94 5. S182.40 5% ? ? 6. S 255.50 ? $10.22 ? 7. $112.75 ? ? $108.24 8. $282.00 ? $4.23 ? 9. ? %% ? $251.55 10. ? ? $14.84 $409.16 11. $455.95 2% ? ? 12. ? ? $6.60 $125.40 13. A commission merchant sold 5000 bu. grain and charged IJ/ per bushel for selling. If the grain was sold at 49/ per bushel, what sum did he remit to his principal ? 14. The net proceeds of a consignment were $593.75. The following were the different charges : commission, $ 26 ; freight, $8.55; drayage, $ 3.40 ; storage, $9.20 ; advertising, $ 3 ; insur- ance, $6.10. What was the rate of commission ? 15. A firm of contractors employed an agent to collect their overdue accounts. As a special inducement for closing the accounts, they were to give him 6 % on all collections made the first month, and 3i % on all collections made the second month. The first month he returned to the firm $4013.80; the second month he returned $2798.50. The returns were made after taking out his commission. What was the agent's commission ? CHAPTER XXII PROPERTY INSURANCE FIRE INSURANCE ORAL EXERCISE 1. One hundred persons have property valued at $500,000. They pay into a common fund 60/ per S 100 of this sum. What is the amount of the fund ? 2. These one hundred persons live in widely separated parts of the country. Is it likely that many of them will suffer losses by fire in the same year ? 3. Suppose the losses to this property by fire for a year amount to S2500. What portion of the common fund will remain on hand as a surplus ? (No interest.) 4. If this surplus is divided among the hundred persons at the end of the year, how much should A, who paid in S 30, receive ? 5. What are the companies organized to receive and distribute the fund in problem 1 called ? 336. Insurance is a contract whereby for a stipulated con- sideration one party agrees to indemnify another for the loss or damage on a specified subject by specified perils, according to certain prescribed terms and conditions. The best-known forms of property insurance are jire insurance and marine insurance. There are also property-insurance companies which insure against loss due to steam-boiler explosions, failure of crops, death of live stock, burglary, injury to business by strikes among employees, and numerous other hazards. 337. Fire insurance is insurance against loss of property or damage to it by fire. A contract of fire insurance frequently covers loss by lightning or tornado. It also covers damage resulting from or consequent on a fire, such as the loss 277 278 PEACTICAL BUSINESS ARITHMETIC resulting from water applied for the purpose of extinguishing flames, also, for the loss when such destruction has been ordered by the proper authorities. 338. The insurer, also called the underwriter, is the one who agrees to indemnify. The insured is the one to whom the promise of indemnity is made. The premium is the considera- tion agreed upon to be paid by the insured. The policy is the written contract between the insurer and the insured. 339. Fire insurance' is usually conducted under the joint stock or the mutual plan. In a joint stock company capital is subscribed, paid for, and owned by- persons called stockholders, who share in the gains and are liable, to the extent of their subscriptions, for all the losses, A mutual insurance company is one in which all the f)olicy holders share the gains and bear the losses in proportion to the amount of the premiums they pay to that particular company, and their fire funds consist of the reserve earnings and the results of investments. 340. Policies of insurance are of various kinds. The ordinary policy is a contract of indemnity, that is, a contract in which the amount paid in case of loss does not exceed a certain specified sum; this sum is determined by evidence after the loss occurs. A valued policy is one that states in advance the amount to be paid in case of loss. Further subdivisions of policies are as follows : specific, one that covers a particular kind of property, as a single building ; blanket, one that covers several items of property, as a group of buildings and the contents ; fixed, one that covers property at some particular defined location ; floating, one that covers specified property while in transit or in various defined locali- ties ; open, one which, while it affixes the extreme limit of the amount and duration of the risk, is yet open to secure endorsements granting insurance in various amounts and places at any time and for any period that may be agreed uj)on at the time of the endorsement ; this policy is used largely to protect such stocks as grain in elevators or as the contents of warehouses, and the records are usually kept in a book known as an open policy hook. 341. The standard forms of contract used in fire insurance policies are prescribed by the state. These forms not only define the maximum amount and the term for which the company is liable but also the consideration paid by the insured, PROPERTY INSURANCE 279 the conditions under which the contract will become void, the methods to be followed in the settlement of a loss, and the procedure to effect the cancellation of the contract. If a loss either total or partial occurs under such a policy, the company- is bound to pay only so much of the sum stated in the policy as will in- demnify the insured; e.g. if a building insured for $3000 is damaged by fire $400, only the actual loss, $400, can be recovered; but if the same building were damaged by fire $3500, the company could not be held for more than $3000, the sum stated in the policy. 342. Average and co-insurance clauses. Where a number of detached properties are msured under one poHcy, it is customary to attach what is known as an average clause which specifies that the amount of insurance covering any one particular piece of property shall bear such proportion to the total amount of insur- ance on the whole as the value of that special piece of property bears to the value of all of the properties so covered. 343. Many fire-insurance policies contain what is known as a co-insurance, or a reduced-rate, clause. Under this clause the insured party agrees to keep his property insured for a certain percentage of its value ; failing to do this, the company or com- panies insuring him are liable only for that proportion of a loss which the amount they insure bears to the specified percentage of the sound value of the property covered. Thus, the value of a piece of property is $10,000, and the insured agrees to keep it insured for 80% of its value, or $8000, but fails to do so and carries only $6000 insurance. Should a loss occur, the company will pay only three fourths (f ^^f ) of the amount of such loss. 344. The rate in fire insurance is the amount to be paid to secure SlOO of indemnity for one year. The rate is based on the character of the risk; the greater the likeli- hood of fire the higher the rate. When policies are written for a period of more than one year, a reduc- tion is usually made in figuring the premium. Illustrations : on city dwell- ings the jiremium for five years is charged for four times the annual rate ; if written for three years, for two and one-half times the annual rate. Rates are expressed by the number of cents charged for $ 100 of insurance. When over $1 per hundred, the rate is often stated in dollars and cents. Short rates are those used for a term of less than one year; they are proportionately higher than the annual rates. 280 PRACTICAL BUSINESS ARITHMETIC ORAL EXERCISE 1. What is the cost of $6500 insurance at 80/ per SlOO? 2. What is the premium on a $ 4000 policy at S 1.50 per S 100 ? 3. What is the cost of $6000 insurance at 75/ per $100 ? 4. B insures a $6000 barn for | value at 50/ per $100. What quarterly premium should he pay ? 5. A insures a $6000 house for | value, at 50/ per $100. What is the semiannual premium ? 6. Goods worth $3000 are insured for |- value. If the annual premium is $ 30, what is the rate ? 7. I insure $ 2400 worth of merchandise for | of its value at 60/ per $100. What premium must I pay? 8. I insure a stock of goods worth $8000 for $6000 at 2%. The goods become damaged by fire to the extent of $3000. Under an ordinary policy how much can I recover ? What will be my net loss, premium included ? 9. A brick schoolhouse is insured at 50/ per $100, the annual premium is $50, and the face of the policy | of the value of the building. What is the value of the building ? ORAL EXERCISE State the premium in i meh of the following problems : Face Face OF Policy Rate OF Policy Rate 1. $1600 4% 3. $3500 $1.10 per $100 2. $1000 n% 4. $5000 $1.20 per $100 State the face of the policy in each of the following problems : Premium Rate Premium Rate 5. $9 2% 7. $13.50 $1.35 per $100 6. $15 11% 8. $24.00 $1.60 per $100 State the rate of insurance in each of the following problems : Face Face of Policy Premium of Policy Premium 9. $1700 $25.50 11. $3200 $130.00 10. $1850 $37.00 12. $6500 $40.00 PROPERTY INSURANCE 281 345. The following is an extract from a tariff, or rate, book for the properties shown on the map which follows this schedule. MAIN STREET, SOUTH No. 189 193 197 199 John Smith & Co. Frame carriage factory Contents John Smith Frame dwelling Frame stable (private) William Brown Frame store and dwelling Contents of grocery store Contents of dwelling 203-205 James Robinson Brick mercantile building Robinson & Co. Department store Offices second and third floors SIDE Flat Rate $1.75 c 1.76 c $0.25 a 1.00 a $0.40 c 0.40 c 0.40 a $0.70 a $0.70 c 0.70 c STATE STREET, NORTH SIDE 244 James Green Brick store and dwelling National Butter Co. Dwelling 248 Thomas White Frame stable White's Livery 252 Thomas White Frame dwelling and contents 256 Town of Jonesville Brick high school Contents 258 Samuel Parker Brick dwelling 260 State Street Baptist Society Brick church building Organ and other contents $0.25 a 0.25 c 0.25 c $1.00 c 1.00 c $0.25 a $0.50 a 0.50 a $0.17 a $0.50 a 0.50 a 80% Rate $1.23 c 1.23 c $0.28 c 0.28 c 0.28 c $0.50 a $0.50 c 0.50 c $0.17^ a 0.17i c $0.70 c 0.70 c $0.17^ a $0.35 a 0.35 a $0.12 a $0.35 a 0.35 a The letter a after the rate indicates that the insurance on this property can be written for more than one year ; that is, at two and one-half times the rate, for a three-year policy, and at four times the rate, for a five-year policy. The letter c after the rate indicates that the insurance on this property can be written for one year, or for a number of years, at yearly rates. The city block, page 282, contains properties insured under the above schedule of rates. 282 PRACTICAL BUSINESS ARITHMETIC J Diagram of a City Block INIain 193 197 Street 199 n 244 248 262 256 258 2C0 State Street WRITTEN EXERCISE r These problems apply to the properties shown on the above diagram ; also to the tariff of rates in the preceding schednle. The flat rate is used unless the co-insurance clause is mentioned. 1. The frame carriage factory at 189 Main Street is worth $7000. The contents are worth S8000; both are insured at | of their value. What is the amount of the annual premium ? 2. The frame dwelling at 193 Main Street is worth $ 3400, and the contents, S1200. The frame stable owned by the same party at 197 Main Street is worth $1500, and the contents, $1100. All of this property is insured for 1 yr. at a | valuation. What is the annual premium ? What will it cost to insure it for 3 yr. ? 3. The store and dwelling at 199 Main Street are worth $4800. The contents of the store are worth $2400, and of the dwelling, $800. What will it cost to insure the property for 1 yr. ? 4. The brick mercantile building at 203-205 Main Street is worth $20,000. The contents of the first floor are worth $4500, and of the second and third floors, $7500. All are insured at a 75% valuation for 1 yr. What is the amount of the premium? A fire occurs, and the building and the contents are damaged to the extent of $4500. If the policies contained an 80% co-insurance clause, how much will the insuring company have to pay ? PEOPERTY INSURANCE 283 5. Suppose that the building described in problem 4 was insured in Company A for S 18,000 at the tariff rate, and the con- tents in Company B for S 10,000 at a rate of 75/; that each company had an 80 % co-insurance clause attached to its policy ; that the building was damaged to the extent of S 3000, and the contents, $ 2500. How much would each company have to pay ? What would be the net loss to the owner of the building ? to the owner of the contents? (Premium included in each case, but no interest.) 6. The brick church at 260 State Street is worth S 10,000, and the contents, S3500. The property is insured for 1 yr. for $8100. If the policy contains an 80 % co-insurance clause, what is the net loss to the insurance company (premium included) if the property is wholly destroyed by fire ? 7. If the brick school building at 256 Main Street is worth $15,000 and the contents are worth $7500, what will it cost under the term rule to insure it for 5 yr. for 80 % of its value ? 8. For insuring the frame buildings at 252 and 248 State Street, and the contents of each for | of their value, the owner pays an annual premium of $22.50. If the frame stable and the contents are worth ^ of the frame dwelling and the contents, what is the value of each building, including the contents ? 9. The brick store and the dwellmg at 244 State Street are worth $15,000 ; the property is insured in three companies for ^ of its value. Company A carries i of the line at the tariff rate ; Company B, | of the line at a 50 / rate ; Company C, the re- mainder of the line at a 66|/ rate. What is the total premium paid ? The building is damaged by fire to the amount of $6000. What amount will each company pay ? 10. I insured a block of buildings in the JEtna Insurance Company for $75,000 at an annual rate of 75/. The jEtna afterwards reinsured $15,000 of its liability under my policy in t^e Continental Insurance Company at 75/, and $20,000 in the German American Insurance Company at the same rate. The building was damaged by fire $ 20,000. What was the net loss of each of the three companies ? 284 PRACTICAL BUSINESS ARITHMETIC 11. All of the Main Street buildings shown on the preceding diagram were purchased by one party for the following sums : Frame carriage factory No. 189 Frame dwelling at No. 193 Frame stable at No. 197 Frame store and dwelling at No. 199 Brick mercantile building at 203-205 $7,000 3,400 1,500 4,500 20,000 $36,400 It is proposed to insure them under a blanket form of policy at a 60/ rate for |^ of the cost. The policies have an average clause attached. Formerly these properties were insured sepa- rately at the tariff rates for I of the above values. Will the proposed plan of insurance cost more or less, and how much for lyr.? Information regarding the different kinds of policies is given on page 278 ; the student is referred to this page for a suggestion regarding the blanket form of policy, the form used in problem 12. 12. A certain man owns four grain warehouses, and carries an insurance of $20,000 on the contents of them all, with an average clause attached. At the time of a fire which damaged the contents of warehouse B $1500, and the contents of ware- house D $ 7000, it was found that the grain in each warehouse was of the following values : warehouse A, $ 3000 ; warehouse B, $6000; warehouse C, $8000; warehouse D, $10,000. What must the insuring company pay on the damaged stock in ware- house B ? in warehouse D ? MARINE INSURANCE 346. Marine insurance is insurance against loss to ships and cargoes by perils of navigation. 347. In marine insurance, the policies usually contain a clause to the effect that if a vessel or cargo, or both, are valued at more than the amount insured, the insurers will pay only such part of the loss, either partial or total, as the amount insured bears to the full valuation. This clause is called an average clause. PROPERTY INSURANCE 285 Thus, should a vessel valued at $20,000, and insured for $15,000, become damaged by fire to the extent of $8000, under an average clause policy the company will pay three fourths (iooo§) of the loss, or $6000. Should the same vessel and cargo be wholly destroyed, the company will pay the full $15,000, which is three fourths of the entire valuation. In order to be fully protected in a marine risk, the insured must insure his property for full value. Some fire insurance policies contain a clause similar to the average clause of marine insurance policies. WRITTEN EXERCISE 1. A vessel valued at $50,000 is insured (average clause policy) for $18,000 in Company A, and for $17,000 in Company B. A fire occurs by which the vessel is damaged $15,000. What is the amount to be paid by each company ? 2. I paid $25.40 for insuring a shipment of goods by steamer from Boston to Manila. If the rate was 1| %, less 20 %, what was the face of the policy ? If the face of the policy was equal to the value of the goods, what would it cost to make the shipment by sailing vessel at 1| %, less 20%? 3. You take out a $7500 average clause policy on your stock of merchandise worth $9000. The premium is 75^ per $100, which you pay in advance. A fire occurs by which the stock is damaged $3000. Estimate your total loss and the net loss to the company. (Premium included in each case.) 4. A of Boston instructed B of Sidney, Australia, to purchase $25,000 worth of hides. B made the investment as instructed and charged 1J% commission. The hides were then shipped by steamer and insured at 1| % for enough to cover the value of the hides and all charges. What was the amount of the policy and what was the premium ? 5. A of New York ordered B of Duluth to buy on commission 6000 bu. of wheat and 6000 bu. of corn. B bought the wheat at 92^ and the corn at 57^ per bushel, and charged IJ^per bushel commission. Before shipping the grain to A by boat, B took out a policy of insurance at 1| % to cover the cost of the goods and all charges. What was the agent's commission ? the insurance premium ? What did the grain cost A ? CHAPTER XXIII STATE AND LOCAL TAXES ORAL EXERCISE 1. How are the expenses of towns, cities, counties, and states met ? 2. A has property worth $5000 and B property worth $10,000. How should the taxes of these two men compare? 3. Mention several purposes for which taxes are raised in your city or town. 348. A tax is a sum levied for the support of government, or for other public purposes. Taxes are of two kinds : direct taxes, which are taxes levied on a person, his property, or his business ; indirect taxes, which are taxes levied on imported goods, and on tobacco, liquors, etc., produced and consumed in the United States. The expenses of town, county, city, and state governments are met by capitation or poll taxes, property taxes, and license fees. The expenses of the National Government are met chiefly by import duties, or customs, and excise duties. 349. A capitation, or poll tax, is a tax sometimes levied on each male inhabitant who has attained his majority. A property tax is a tax levied on real estate or on personal property. A license fee is a tax paid for permission to engage in certain kinds of business. Real estate and personal property belonging to religious or charitable organizations are frequently exempt from taxation. 350. Property taxes are imposed in nearly all the states by practically the same method, namely : 1. Officers called assessors are elected in every city and town, whose business it is to set a valuation upon all property subject to taxation. 286 STATE AND LOCAL TAXES 287 2. In most of the states a County Board of Equalization reviews the original assessments, and the judgment of this body is subsequently passed upon by the State Board of Equalization. 3. All the taxes for state purposes are then equitably appor- tioned among the different counties, cities, and towns. Each county, city, town, and school district also levies taxes for its own local expenses. 351. The tax rate is expressed as so many mills on the dollar or so many dollars on a hundred or a thousand dollars. The Federal Income Tax law was approved Oct. 13, 1913. It is a new provision for raising revenue to support the National Government. Only a few leading provisions are noted here. Every citizen of the United States, whether residing at home or abroad, and every person residing in the United States, though not a citizen thereof, who has an annual net income from all sources in excess of $ 3000 will be required to pay a normal tax of 1 % on such entire net income in excess of $3000 or in excess of ^4000 if a person is married and living with a wife or a husband. The normal tax of 1% is also imposed on corporations, joint- stock companies or associations, and insurance companies. For special information address any collector of internal revenue. ORAL EXERCISE 1. If the rate of taxation is 12 mills on a dollar, how much tax must I pay on property assessed at $ 5000 ? 2. The tax rate is 13 mills on a dollar. B has property valued at 1 8000 and assessed at | value. What is his tax ? 3. C pays 1^% tax on a city lot 100 ft. by 150 ft., valued at 11 per square foot, and assessed at | value. What is the amount of his tax ? 4. What tax must I pay on $80,000, at 5 mills on $1, the collector's commission being 1 % ? Solution. .005 of $80,000 = $400, the property tax. 1 % of the tax = 4, the collector's commission. $404, my total tax. 5. What tax must I pay on $10,000 at 4^ mills on $1, the collector's commission being 1 % ? 288 PKACTICAL BUSINESS AEITHMETIC 6. An unmarried man has a net annual income of $4568. If exemptions are allowed amounting to $215, what income tax will he have to pay ? 7. A married man living with his wife has a net annual income of $5432.50. If exemptions are allowed amounting to $384.25, what income tax v/ill he pay ? 8. A collector turns over to the county treasurer f 8000. If his commission was 1^ % what amount did he collect? If the property taxed was worth f 800,000, what was the rate of taxa- tion? Express this rate in three ways. 9. The assessed valuation of real and personal property in a certain city is 1400,000,000. The city has a bonded indebt- edness of i 2,000,000, on which it pays 4 % interest. Find the tax rate necessary to pay the interest. WRITTEN EXERCISE Find the total tax: 1. Valuation, $3600; rate, 10.016; 3 polls at $2. 2. Valuation, 14550; rate, 9^ mills; 1 poll at |1.50. 3. Valuation, $2875; rate, 10.0175; 1 poll at 11.75. 4. Valuation, $5600; rate, $1,121 per $100; 1 poll at $2. 5. Valuation, $6000; rate, $13.40 per $1000; 2 polls at $1.00. Find the valuation : 6. Total tax, $3800; rate, $0,015; 100 polls at $2.00. 7. Total tax, $11,295; rate $1.40 per $100; 250 polls at $1.50. 8. Total tax, $8850; rate, $15.00 per $1000; 225 polls at $1.00. 9. In a town 1040 persons were subject to a poll tax; the assessed valuation of real estate was $3,209,400, and of personal property $265,100. The polls were taxed $1.25 each. The tax levy was $42,994. What was the tax rate ? What was the total tax of Charles B. Lester, who owned real estate valued at $6450, and personal property valued at $1250, and who paid for 2 polls? STATE AND LOCAL TAXES 289 10. In a town taxes were levied as follows : state tax, $4287 ; county tax, 19312.50 ; town tax, 193,156.20. There were 1850 polls assessed at ^2 each. If the total property valuation was $6,245,800, what was the tax rate per thousand ? 11. A town made provision by taxation for the following expenses: public schools $18,180; interest on borrowed money $2106; public highways $4720; officials' salaries $4620; general expenses $11,746; sinking fund $8000. The value of real and personal property was $ 2,450,600, and 2120 polls were assessed $1.50 each; $4531.80 was collected from license fees. What was the tax rate ? 12. A died leaving property valued at $47,950 to B, his son, and property valued at $ 17,500 to C, a friend. The statutes of the state in which these three live provide that B, a lineal heir, and C, a collateral heir, shall pay to the state an inheritance tax. The rate for lineal heirs is 1%, and for collateral heirs 5%. What inheritance tax must B and C, respectively, pay when they come into possession of the property? 13. A city made the following appropriation for its public schools: teaching and supervision, $36,000; care and cleaning, $3360; fuel, $3000; repairs, $2000; text-books, $1700; supplies, $1700; printing, $300; contingent fund, $775; truant officer, $500; evening schools, $1305; transportation of pupils, $600; kindergarten, $1100; manual training, $700. The assessed value of real estate was $6,709,998 and of personal property $2,130,002. What was the tax rate for school purposes ? 14. An agent made the following report of his income as a basis for computing his income tax : Salary per year $3500 Interest on money loaned . . $415 Commissions 985 Dividends on bank stock . . 50 Dividends on preferred stock in a corporation $250 If the dividends received were exempt, the tax having been paid by the corporations, what would be his income tax if he were a married man living with his wife ? What would be the mcome tax of an unmarried man havmg the same income ? 290 PRACTICAL BUSINESS ARITHMETIC 352. In order to facilitate clerical work a table may be used for computing taxes. The following table was made from the published tax lists of a city in Massachusetts: Tax Table. Rate $18.60 PER $1000 1 2 3 4 5 6 7 8 9 .0000 .0186 .0372 .0558 .0744 .0930 .1110 .1302 .1488 .1674 1 .1860 .2046 .2232 .2418 .2604 .2790 .2976 .3162 .3348 .3534 2 .3720 .3906 .4092 .4278 .4404 .4650 .4836 .5022 .5208 .5394 3 .5580 .5766 .5952 .6138 .6324 .6510 .6696 .6882 .7068 .7254 4 .7440 .7626 .7812 .7998 .8184 .8370 .8556 .8742 .8928 .9114 5 .9300 .9486 .9672 .9858 1.0044 1.0230 1.0416 1.0602 1.0788 1.0974 6 1.1160 1.1346 1.1532 1.1718 1.1904 1.2090 1.2276 1.2462 1.2648 1.2834 7 1.3020 1.3206 1.3392 1.3578 1.3764 1.3950 1.4136 1.4322 1.4508 1.4694 8 1.4880 1.5066 1.5252 1.5438 1..5624 1.5810 1..5996 1.6182 1.6368 1.65.54 9 1.6740 1.6926 1.7112 1.7298 1.7484 1.7670 1.78.56 1.8042 1.8228 1.8414 In the table the rate on each $1000 was made up as follows : state tax $.0807 ; county tax, $.5643 ; state highways, $.003 ; city tax, $17,952. The first figure of the number of dollars assessed is given at the left, and the second one at the top. 353. Example. What is the tax on a valuation of $16,400? Solution. Tax on $16,000 = $297.00 (1000 times .2976) Tax on 400 = 7.44 (100 times .0744) tax on $ 16,400 = $305.04 WRITTEN EXERCISE Using the tahle^ find the tax on the following valuations : 1. 12485. 5. 18,478. 9. $34,500. 13. 120,000. 2. $1200. 6. 113,200. 10. $82,500. 14. $27,800. 3. $1050. 7. $14,700. 11. $98,250. 15. $71,690. 4. $4630. 8. $18,400. 12. $21,850. 16. $89,800. Find the tax on the following valuations when the collector's commission is 1% : 17. $5500. 21. $9500. 25. $19,000. 29. $21,000 18. $7500. 22. $8700. 26. $26,000. 30. $89,000 19. $2900. 23. $6500. 27. $85,000. 31. $-10,000. 20. $4700. 24. $7250. 28. $78,000. 32. $21,000 CHAPTER XXIV CUSTOMS DUTIES ORAL EXERCISE 1. The expenses of tlie National Government average about $ 2,250,000 per clay. What is this per year ? Suggestion. To multiply by 16, multiply by 10 and add | of the result. 2. Name five sources of income to the National Government. 3. Name ten expense items of the National Government. 354. Duties, or customs, are taxes levied by the National Gov- ernment on imported goods. They are imposed in two forms : ad valorem and specific. An ad valorem duty is a certain per cent levied on the net cost of the importation. A specific duty is a fixed sum levied on each article, or on each pound, ton, yard, or other standard measure, without regard to the cost. Ad valorem duties are not computed on fractions of a dollar. If the cents of the net cost are less than fifty, they are rejected; if fifty or more than fifty, one dollar is added before computing the duty. Some articles are subjected to both ad valorem and specific duties. Be- fore specific duties are estimated allowance is usually made^for tare and breakage. Specific duties are not computed on fractions of a unit. Frac- tions less than ^ of a unit are rejected ; fractions ^ or more are counted a whole unit. The long ton of 2240 lb. is used in computing specific duties. 355. A tariff is a schedule exhibiting the different rates of duties imposed by Congress on imported articles. A free list is a schedule of imported articles exempt from duty. 356. A customhouse is an office established by the National Government for the collection of duties and the entry and clearance of vessels. A port at which a customhouse is estab- lished is called a port of entry; ports of entry and other ports are called ports of delivery. 291 292 PEACTICAL BUSINESS ARITHMETIC The United States is divided into customs districts, each with a head- quarters port. Goods arriving must be entered at the original port of entry ; if consigned to an interior port, this entry is a transportation entry, but at the other port it may be entered either for consumption or the warehouse. 357. In the most important ports of the United States the customhouse business is distributed among three departments : 1. The collector's office, which takes charge of the entries and papers, issues the permits, and collects the duties. 2. The surveyor's office, which takes charge of the vessel and cargo, receives the permits, ascertains the quantities, and delivers the merchandise to the importer. 3. The appraiser's office, which examines imported merchan- dise and determines the dutiable value and the rate of duty on same. One package of every invoice and one package, at least, out of every ten similar packages is sent to the appraiser's store for examination. Merchan- dise in bulk and all heavy and bulky packages uniform in size and quantity of contents are generally examined on the wharf. 358. A manifest is a memorandum, signed by the master of the vessel, showing the name of the vessel, its cargo, and the names and addresses of the consignors and consignees. An invoice is a detailed statement showing the particulars of the goods imported. All invoices should be made out in the weights and measures of the coun- try in which the goods are purchased ; and if the goods are subject to an ad valorem duty, they must be invoiced in the currency of the country into which they are imported. Invoices over $100 must be certified before a United States consul, who causes three copies of the invoice to be made. One is sent to the collector of the port at which the goods are to be entered, one is kept on file in the consul's office, and one is sent to the importer. When the merchandise is loaded on board the vessel the shippers are given a bill of lading which acknowledges the receipt of the several pack- ages and agrees to deliver the same at destination. The vessel's commander keeps a copy of the bill of lading and from the several that have been issued makes out his manifest of cargo. The shippers mail the invoice and bill of lading to the purchaser, who fills out an entry therefrom and presents it and the invoice at the customhouse where the duties imposed by law on the several classes of merchandise are collected and a permit issued for the land- ing and delivery of the merchandise, subject to examination. CUSTOMS DUTIES 293 359. The values of foreign coins are periodically proclaimed by the Secretary of the Treasury, and these values must be taken in estimating duties unless a depreciation of the value of the foreign currency expressed in -an invoice shall be shown by the consular certificate thereto attached. The following esti- mate of the values of foreign coins was recently proclaimed. Values OF Foreign Coins Country Standard Monetary Unit Value in U. 8. Gold Brazil Denmark, Norway, Sweden . France, Belgium, Switzerland German Empire Great Britain Japan Mexico Netherlands Philippine Islands .... Russia Gold Gold Gold Gold Gold Gold Gold Gold Gold Gold Milreis Crown Franc Mark Pound sterling- Yen Peso Florin Peso Ruble $ .546 .268 .193 .238 4.866i .498 .498 .402 .500 .515 The lira of Italy, and the peseta of Spain, are of the same value as the franc. The dollar, of the same value as our own, is the standard of the British possessions of North America, except Newfoundland. 360. Depositing goods in a government or bonded ware- house is called warehousing. Many importers buy foreign goods in large quantities, withdraw a part of them, and store the remainder in the government warehouse. The goods so deposited may be taken out at any time in quantities not less than an entire package, or in bulk, if not less than one ton, by the payment of duties, stor- age, and labor charges. Foreign goods are sometimes bought three or four months earlier than they can be placed on the market and are stored in the government warehouse until they are seasonable. In this way importers are able to make better selections and they also get better terms and prices. 361. A bonded warehouse is a building provided for the storage of goods on which duties have not been paid. The importer must give bond for the payment of duties on all goods stored in a bonded warehouse. Goods left in the government warehouse 294 PRACTICAL BUSINESS ARITHMETIC beyond 3 yr. unclaimed are forfeited to the government and sold under the direction of the Secretary of the Treasury. Goods may })e withdrawn from a bonded warehouse for export, or for transfer to a warehouse in another district, without the payment of duty. 362. The two common forms of entry under which duties are collected are known as consumption entry and warehouse entry. The former is used for merchandise entered for consumption; the latter for merchandise that is placed in a bonded warehouse under charge of the government storekeeper. 363. Excise duties are taxes levied on certain goods produced and consumed in the United States. If goods, on which either excise or import duties have been paid, are exported, the amount so paid is refunded. The amount refunded is called a drawback. Table of Duties on Certain Imports Article and Description Axminster rugs Barley, 48 lb. to the bushel .... Barley malt, 34 lb. to the bushel . . Beans, 60 lb. to the bushel .... Brussels carpets Books , Butter Castile soap Cheese China and porcelain, undecorated . Clocks . Cotton tablecloths Hay Ingrain carpets Knit woolens Manufactures of leather Manufactures of marble Plate glass, 16" x 24" Pocket knives, value not over $1 per doz. Potatoes, 60 lb. to the bushel ... Saccharin Silk dress goods Toilet soap, unperfumed Wheat Window glass Duty Specific 15^ per bu. 25^ per bu. 25^ per bu. 2i f per lb. $2 per T. Qtf per sq. ft. (Shf per lb. \^f' per bu. If per lb. Ad Valorem 50% 25% 15% 10% 20% 50% 60% 35% 20% 35% 30% 45% 35% 10% 50% 10% CUSTOMS DUTIES 295 FINDING A SPECIFIC DUTY ORAL EXERCISE Using the table on page 294, find the duty on: 1. 67,200 lb. of hay. 2. 48,000 lb. of barley. 3. 100 pc. plate glass 16" x 24". 4. 2400 lb. of window glass 10^' x lb'\ 5. A quantity of butter weighing 1000 lb. 6. A shipment of wheat weighing 240,000 lb. 7. A quantity of saccharin weighing 2100 lb. ; tare 100 lb. WRITTEN EXERCISE 1. Using the table on page 204^ find the total duty on : 2500 bu. potatoes ; value, S1200. 96,000 lb. barley. 1275 lb. toilet soap ; value, $425. 24,000 lb. beans. 30,000 bu. potatoes ; value, $15,000. 136,000 lb. barley malt. 2. What is the duty on 175 bx. castile soap, each weighing 110 lb., if 5% is allowed for tare ? Invoiced at 20/ per pound. 3. Calculate the duty on 10 hogsheads of saccharin weighing 1060-105, 1040-105, 1160-112, 1240-120, 1180-116, 1100-102, 1090-101, 1100-100, 1005-100, 1210-118 lb., respectively. 4. Richard Roe & Co. imported from Canada 3750 bu. of potatoes invoiced at 20^ per bushel. If the transportation and other charges amounted to $187.50, how much must be re- ceived per bushel for the potatoes in order to gain 25 % ? FINDING AN AD VALOREM DUTY ORAL EXERCISE Find the total duty : 1. On 40 clocks invoiced at $4.50 each. 2. On 12 books invoiced at $1.50 each. 3. On 25 doz. pocket knives invoiced at 50^ per doz. 4. On 100 sq. yd. ingrain carpet invoiced at $1 per yard. 296 PRACTICAL BUSINESS ARITHMETIC WRITTEN EXERCISE Find the duty on : 1. An Axniinster rug, 12' x 18', invoiced at <£10. For the values of foreign coins, see page 293. 2. A 200 lb. box of knit woolen goods invoiced at £ 100. 3. An importation of cotton table cloths invoiced at ^100. 4. An importation of cotton table cloths invoiced at £ 255. 5. 300 bx. plate glass, each containing 25 plates 16" x 24". 6. 20 Axminster rugs, each 12' x 18', invoiced at X8 6s. per rug. 7. An importation of Dresden china, undecorated, invoiced at 100 fr. 8. An invoice of knit woolens weighing 600 lb. and valued at £315 12s. 9. 200 blocks of marble, each 10' x 4' x 2', invoiced at 328,000 lira. 10. An importation of leather from Sweden invoiced at 6750 crowns. 11. 400 yd. of Brussels carpeting, | yd. wide, invoiced at $2 per yard. 12. 4000 meters of Brussels carpeting, | yd. wide, invoiced at 5 francs per meter. A meter equals approximately 1.1 yd. 13. 4800 meters of silk dress goods, | yd. wide, invoiced at 3.75 marks per meter. 14. A case of silk dress goods containing 200 yd., 1 yd. wide, invoiced at 1000 marks. 15. An invoice of leather goods from the Netherlands in- voiced at 12,520 florins. 16. 5 cs. of silk dress goods, each containing 200 yd., J yd. wide, invoiced at 20 marks per yard. 17. I bought an invoice of Swiss clocks, paying 10,750 fr. for them in Geneva. What was the total cost of the clocks, including the duty ? CUSTOMS DUTIES 297 INVOICES AND ENTRIES WRITTEN EXERCISE 1. At what price per pair must the lace curtains in the fol- lowing invoice be sold in order to realize a gain of 33J % ? No. 427 Manchester y England, Dec. 15, zp Invoice of Lace Shipped by WILLIAM P, FIRTH & CO. In the Steamer Catalonia Ti? R. H. White Company Boston, Uass. Marks 317 Quantity 50 doz. pr, Articles and Description Lace Curtains Less 2% Insurance and Freight Packing and Carting 60% ad valorem duty 3/2/6 Extension *«*-**-«* #-»*-** 4-10-6 16-6 2. Find the total cost of the following invoice: Antwerpy Belgium, Apr. 2. /9 iV/essrs. A. T. Summers & Co. New York City Bought of SCHMIDT & WESTERFELDT Terms 30 da. PC Black Silk 39.00. 40.50. 39.00, 40.00. 41.00, 40.50 Insurance and freight Cartage 50% ad valorem duty 240 5 fr, Do not compute duty on insurance and freight, nor on cartage. 39.00, 40.50, etc, above, equal the number of meters in each piece. 298 PKACTICAL BUSINESS AEITHMETIC 3. Copy the following invoice, supplying the missing terms Bradford, England, Dec. 5, 19 Invoice of Woolen Goods Shipped by RADCLIFFE & SON In the Steamship Winifredian To R. H. Stearns & Co. Terms 30 da. Boston, Mass. R 317 25 PC Black Wool Crepon 68 69 69 68 69 60 55 60 56 54 60 60 60 68 68 60 45 65 65 55 60 65 65 60 60 Consul's fee 1544 1/9 *** * « 14 10 *** * 4. If the foregoing invoice of goods were entered for im- mediate consumption, the following is the entry that would be made out. Complete the computation in the entry. Manifest No. ^S'a Invoiced at 'A^H^WJ!?-'?^, (o-n^r^^ 19— INWARD FOREIGN ENTRY OF MERCHANDISE Impoiled b; . -^^^^^^^ y^^^^^^ :i£^^^2s^^-?^--/;^; * times the interest for 54 da. Dividing this result by 6 gives $4.05, the required interest. 9 By arranging the numbers as shown in the 54 x $0.45 margin and canceling the work is greatly short- Tj, =$4.05 ened. ^ WRITTEN EXERCISE At 6^0 find the interest on each of the following problems. Reduce the time expressed in months and days to days. Principal Time 13. $375.80 2 mo. 15 da. 14. $300.00 3 mo. 19 da. 15. $171.15 1 mo. 14 da. 16. $120.00 4 mo. 14 da. 17. $211.16 6 mo. 16 da. 18. W^b.^^ 1 mo. 10 da. ORAL EXERCISE 1. What is the interest on $800 for 6 da. at 3 % '^ Solution. 80^ is the interest for 6 da. at 6 %. 3% is | of 0%; therefore, ^ of 80 j?, or 40 (^, is the interest for 6 da. at 3%. 2. If the interest at 6% is $45, what is the interest for the same time at 3% ? at 12%? at 2% ? at 1% ? at 1^%? 3. Formulate a short method for changing 6% interest to 8% interest. Solution. 8% is \ more than 6%; hence, the interest at 6% increased by I of itself equals the interest at 8%. 4. State a short method for changing 6% interest to 7% interest; to 5% ; to 9% ; to 7|% ; to 41%. 5. If the interest at 6% is $120, what is the interest at 7%? at 5% ? at 8%? at 4% ? at 7^%? at ^% ? Principal Time Principal Time 1. $620 54 da. 7. $900.00 29 da. 2. $175 84 da. 8. $865.45 93 da. 3. $645 42 da. 9. $700.00 96 da. 4. $300 84 da. 10. $974.30 62 da. 5. $600 72 da. 11. $178.45 40 da. 6. $502 66 da. 12. $438.55 50 da. INTEREST 303 368. In the foregoing exercise it is clear that 6% interest in- creased hy \ of itself equals 9 % iyiterest; hy | of itself^ 8 % interest; by ^ of itself 7| % iyiterest; hy 1 of itself 7 fo interest; also that 6% interest decreased hy ^ of itself equals 4 % interest; hy \of itself^ 4\ /g^;^; S:i^Z= INTEREST 315 390. In the foregoing note Ellis B. Pitkin is the maker ; William B. Harris, the payee ; and 1243.50, the face. The note is negotiable ; that is, it may be transferred by the payee to any other person by indorsement. If the note were drawn payable to William B. Harris, or hearer, it would be transferable by delivery and would be negotiable. If the words to the order of were omitted, the note would not be transferable either by indorse- ment or by delivery ; it would be payable to William B. Harris only, and would be called a non-negotiable note. 391. If the payee should sell the foregoing note, he would have to indorse it; that is, make it payable to the buyer by a writing on the back of the instrument. This indorsement may be made in either of the three ways shown in the margin. William B. Harris sold the note to O. D. Merrill and effected the transfer by a blank indorsement. This is simply William B. Harris's signature. It makes the note payable to bearer. O. D. Merrill sold the note to Andrew J. Lloyd and effected the transfer by a full indorsement, an indorsement which specifies the one to whose order the note is made payable. By indorsing the note both William B. Harris and O. D. Merrill make themselves responsible for its payment in case the maker does not pay it. O. H. Briggs was willing to buy the note without Andrew J. Lloyd's guarantee to pay it. The transfer was effected by a qualified indorsement. By this indorsement Andrew J. Lloyd avoids the responsibility of an ordinary indorser. The note just considered is a time note; if the words On demand were substituted for the words Two months after date the form would be called a demand note. The note is interest-bearing because it contains a clause to that effect ; it would draw interest after it became due without any interest clause. A demand note, in which there is no interest clause, draws interest after payment has been demanded. Blank Indorisement Full Indorsement ':^^.^^t(7::^t:d.^^i;y'^p^^■■■d^c Qualified lndor$ement 316 PRACTICAL BUSINESS ARITHMETIC 392. A note in which two or more persons jointly and severally promise to pay is called a joint and several note; a note in which two or more persons jointly promise to pay, a joint note. %.:3j2J2:==r Rochester, N.Y.,_^ uC 19 .' " ^~r::^Z-i>iP:^^^r<^ '''•- -' —after date we jointly and severally promise to pay tojjhe^order of ^ ^ , //f . V?.^rP-^ ^^^-k'^^T?-^^ - — - — ■ ■ _ — - D nllars ^^^^^ yp/^^-^^^^^ "^/if- Payable a«- --r<^'^^^-'T^7S/^^^ yZ^^^€y-7 (^^4fy^ ^O^/r^J^^^^n^. lu a joint and several note, the holder may sue and collect of any one signer without proceeding against the others, or he may sue all of them together. In a joint note the signers must be sued jointly. The distinction between a joint and a joint and several note has been abolished by law in many of the states. The above form is a joint and several note. If the words and severally were omitted it would be a joint note. The words value received in a note are equivalent to an acknowledgment that there has been a consideration. Their insertion is usual and advisable, but not legally required in all the states WRITTEN EXERCISE Write interest-hearing notes as follows : 1. A demand note; amount, 11283.97 ; current date; payee, C. H. Good; maker (your name); interest at 5|^. 2. A time note ; amount,- 1 728.79 ; current date ; time, 90 da. ; payee. Snow & Co.; maker (your name); interest at 3| ^. 3. A joint note; amount, 11795.73; current date; time, 6 mo.; payee, Ellis & Co.; maker (your name), and Richard Roe ; interest at 4|/o. Write a joint note under the same con- ditions. 4. Find the amount (face plus interest) due 87 da. after date in note No. 1; at the end of the time in note No. 2; at the end of the time in note No. 3. INTEREST B17 EXACT INTEREST 393. Exact interest is simple interest for tlie exact number of days on the basis of 365 da. in a common year, or 366 da. in a leap year. The United States Government takes exact interest, and its use is growing among business men. In strict justice it is the only correct method of computing interest. 394. The difference between the common year of 365 da. and the commercial year of 360 da. is 5 da., or yig of the com- mon year. If any sum were divided into 360 parts, each part would be larger than it would be if the sum were divided into 36.5 parts. Thus, -^^^ and -^^\ are greater than gV^ and -^^^. It is therefore clear that exact interest is less than ordinary interest. 395. To find the exact interest, compute interest in the usual way for the commercial year, and from the interest thus obtained subtract y^^ of itself In many cases the work may be shortened by cancellation. 396. Example. Find the exact interest, on 13285 for 35 da. at 5%. 9 Solution. :2^^i-§^AlMf = .05x35 x $9 = $15.76. m WRITTEN EXERCISE Find the exact interest : 1. 1734.50 for 124 da. at 6 %. 7. $1240.35 for 50 da. at 6%. 2. 1420.60 for 99 da. at ^%. 8. 11630.25 for 67 da. at 4 %. 3. $965.50 for 82 da. at ^ %. 9. $150,000 for 28 da. at 6%. 4. $356.40 for 236 da. at 4%. 10. $100,000 for 135 da.. at 5%. 5. $672.50 for 53 da. at 5^ %. ii. $4653.28 for 182 da. at 4%. 6. $546.24 for 38 da. at 41 %. 12. $45,000 for 42 da. at 21%. 13. $3500 from July 17, 1916, to Nov. 26, 1916, at 3% ; at 4i%. 14. S2315.89fromMar. 11, 1916,toSept.l,1916,at6%; at 2%. 15. S872.54 from Oct. 18, 1915, to Jan. 16, 1916, at 5% ; at 71%. 16. X1006 68. from Apr. 1, 1916, to Yob. 19, 1917, at 3% ; at 2%. 318 PRACTICAL BUSINESS ARITHMETIC PROBLEMS IK INTEREST ORAL EXERCISE Principal Interest Time Rate Amount 1. $200 $24 2yr. ? ? 2. S250 $30 ? 3% ? 3. $240 $30 ? 5^^, ? 4. $320 ? 3 yr. 5% ? 5. ? $54 Syr. 6% ? 6. $450 $45 2yr. ? 9 7. $525 ? 4yr. 2% ? 8. ? $84 3-1 yr. 6% ? 9. ? ? 3yr. 4% $112 10. $225 $36 4 yr. ? ? 11. $625 ? ^ yr. 4% ? 12. ? $52.50 ? 3% $402.50 13. If the cash price of an article is $125, what will be the sixty-day credit price if money is worth 6 % ? Suggestion. The cash price plus the interest for the given time at the given rate equals the credit price. 14. If the thirty -day credit price of an article is $50.25, what will be the cash price if money is worth 6 % ? Suggestion. The credit price divided by the amount of one dollar for the given time at the given rate equals the cash price. 15. If the cash price of an article is $240.50, what will be the sixty-day credit price if money is worth 6 % ? 16. If the four months credit price of an article is $163.20, what will be the cash price if money is worth 6 % ? 17. If the cash price of an article is $265.50, what will be the sixty -day credit price if money is worth 6 % ? 18. If the cash price of an article is $210, what will be the sixty-day credit price if money is worth 4 % ? 19. One contractor offers to do a certain piece of work for $425.50 cash; another offers to do the same work for $441, payable in 1 yr. If money is worth 5 %, which is the better offer ? INTEREST 319 WRITTEN EXERCISE 1. Which is the better for a tailor, to sell a suit for $65 cash, or for $73.15 on 9 mo. time, money being worth 6% ? 2. Which is the better, to sell carpet at $1.50 per yard cash, or at $1.68 per yard on 1 yr. time, money being worth 5% ? 3. Which is the more advantageous, to buy an article for $58.50 cash or for $61.80 on 6 mo. time, money being worth 6%? 4. A merchant paid $160 cash for 4 sewing machines. After keeping them in stock 1 yr. 6 mo. he sold them for $190.80, on one year's time without interest. If money is worth 6% what was his gain or loss at the time of the sale ? 5. An invoice of merchandise listed at $2500, on which trade discounts of 20% and 10% were allowed, was purchased at 90 da. What was the actual cash value of the debt on the day of the purchase, money being worth 5% ? 6. A merchant bought 600 bbl. of flour at $7.50 per barrel. Terms: one half on account, 3 mo.; one half on account, 6 mo. At the end of 1 mo. he paid the cash value of the entire bill. How much did he gain, money being worth 6%? 7. Sept. 8 you purchased of Edward Sprague & Son, at trade discounts of 20% and 25%, an invoice of coffee listed at $2006. Terms : 30 da. Sept. 20 you sent Edward Sprague & Son a check for the actual cash value of the bill. What was the amount of the check, money being worth 6%? PERIODIC INTEREST 397. Periodic interest is simple interest on the principal increased by the simple interest on each installment of interest that was not paid when due. As periodic interest can be legally enforced in only a few states, special contracts should be made if it is to be collected. Where technically illegal, periodic interest is often collected ; as, when a series of notes is given for the interest on a note secured by a real-estate mortgage, such notes to draw interest if not paid when due. 320 PRACTICAL BUSINESS ARITHMETIC 398. Example. If payments of interest are due semiannually, what is the interest on flOOO for 3 yr. at 6% ? Solution $ 180 = interest on $ 1000 for 3 yr. at 6%. f 30 is the interest on $ 1000 for one semiannual period, 6 mo. 1st installment of interest, $30, was unpaid for 2 yr. 6 mo. 2d installment of interest, f 30, was unpaid for 2 yr. 3d installment of interest, $ 30, was unpaid for 1 yr. 6 mo. 4th installment of interest, $ 30, was unpaid for 1 yr. 5th installment of interest, f 30, was unpaid for 6 mo. The sum of the periods for which interest was unpaid is 7 yr. G mo. The interest on each $ 30 for the period it was unpaid is the same as the interest on $ 30 for the sum of the periods. 13.50 - interest on $30 for 7 yr. G mo., at 6%. $193.50 = the total interest due. WRITTEN EXERCISE 1. If payments of interest are due annually, what is the interest on f 850 for 5 yr., at 8 % ? 2. If payments of interest are due quarterly, what is the interest on 11380 for 2 yr. 6 mo., at 4%? 3. What is the difference between the simple interest and periodic interest (payable annually) on $1800 for 6 yr. at 4%? 4. If payments of interest are due semiannually, what amount should be paid in settlement of a debt of $1450 which, has run 5 yr. at 6%? 5. If payments of interest are due annually, what amount will settle a debt of $1500 for 5 yr., at 6 %, if the first install- ment of interest was paid when due ? COMPOUND INTEREST 399. Compound interest is interest computed, at certain inter- vals, on the sum of the principal and unpaid interest. Interest maybe compounded annually, semiannually, quarterly, or even monthly. In most states the law does not sanction the collection of com- pound interest, but if it is agreed upon by the parties, the taking of it does not constitute usury. It is a general custom of savings banks to allow compound interest. Compound interest is also used by life insurance companies. INTEKEST 321 400. Example. for 4 yr What is the compound interest on if the interest is compounded annually at 5 % ? Solution. $6000 300 6300 315 6615 330.75 6945.75 347.29 7293.04 $7293.04 = 1st principal. = interest 1st year. = amount, or the principal the 2d year. = interest 2d year. = amount, or the principal the 3d year. = interest 3d year. = amount, or the principal the 4th year. = interest 4th year. = amount due at the end of the 4th year. - $ 6000 = $ 1293.04, compound interest for 4 yr. WRITTEN EXERCISE 1. If interest is compounded annually, what will be the amount of ^600 for 5 yr. at G % ? 2. If interest is compounded semiannually, what will be the compound interest on $1500 for 2 yr. 6 mo. at 4 % ? 3. A placed $750 in a savings bank Jan. 1, 1915, and inter- est was added thereto every 6 mo. at the rate of 4%. No with- drawals having been made, what was the balance due Jan. 1,1917? Table Showing the Amounts of $1 at Compound Interest Compounded Annually Yii. 2% '4% 3% H% 4% 4h7o 'o% Yii. 1 1.02000 1.02500 1.03000 1.0.3500 1.04000 1.04500 1.05000 1 2 1.04040 1.05063 1.06090 1.07123 1.08160 1. "09203 1.10250 2 3 1.0(5121 1.07689 1.09273 1.10872 1.12486 1.14117 1.15763 3 4 1.08243 1.10381 1.12551 1.14752 1.16986 1.19252 1.21551 4 5 1.10408 1.13141 1.15;)27 1.18769 1.21665 1.24G18 1.27628 5 6 1.12616 1.15969 1.19405 1.22926 1.26532 1.30226 1.34010 6 7 1.1486:) 1.18869 1.22987 1.27228 1.. 31 593 1.36086 1.40710 7 8 1.17166 1.21840 1.26677 1.31681 1.36857 1.42210 1.47746 8 9 1.19509 1.21886 1.30477 1.36290 1.42331 1.48610 1.55133 9 10 1.21899 1.2S009 1.. 34392 1.41060 1.48024 1.55297 1.62889 10 11 1.24337 1.31209 1.. 38423 1.45997 1.53945 1.62285 1.71034 11 12 1.26824 1. .314 89 1.42576 1.51107 1.60103 1.69588 1.79586 12 13 1.29361 1.37851 1.46853 l.f;6396 1.66507 1.77220 1.88565 13 14 1.31948 1.41297 1.51259 1.61870 1.73168 1.85194 1.97993 14 15 1.34587 1.44830 1.55797 1.67535 1 .80094 1.9.3528 2.07893 15 10 1.37279 1.48451' 1.60171 1.73399 1.87298 2.02237 2.18287 16 17 1.40024 1.52162 1.65285 1.79468 1.94790 2.11338 2.29202 17 18 1.42825 1.559(J6 1.70243 1.85749 2.02582 2.20848 2.40662 18 19 1.45681 1.59865 1.753.51 1.92250 2.10685 2.30786 2. .52695 19 20 1.485% 1.63862 1.80611 1.98979 2.19112 2.41171 2.65330 20 322 PRACTICAL BUSINESS ARITHMETIC ORAL EXERCISE Refer to the tahle^ page 321, a7id give rapid ansivers to the following : 1. What is the amount of |1 for 12 yr. at 4% ? at 8% ? at 5% ? at 41% ? at 2^% ? 2. What is the amount of |1 for 18 yr. at 4i% ? at 8^% ? at 2% ? at 3% ? at 2|%? 3. What is the amount of $1 for 9 yr. at 5% ? at 4|% ? at 21% ? at 31% ? at 8% ? at 4% ? 4. What is the amount of il for 20 yr. at 2% ? at 5% ? at 41% ? at 31% ? at 21% ? at 3% ? 5. What is the amount of $10 for 10 yr. at 4 % ? for 20 yr. at 2 % ? for 5 yr. at 5 % ? 6. What is the amount of flOO for 5 yr. at 2% ? for 11 yr. at 81 % ? for 19 yr. at 5 % ? 401. Example. What is the compound interest on $8000 for 10 yr., if interest is compounded annually at 5% ? Solution. $1.62889 = amount of $1 for 10 yr. at 5%. 8000 X $ 1.62889 = $13031.12, amount due in 10 yr. at 5%. $13031.12 - $8000 = $5031.12, the compound interest. If interest is compounded semiannually, take one half the rate for twice the time ; if quarterly, take one fourth the rate for four times the time. The table may be used for periods longer than 20 yr. For 40 yr. multiply the amount of $1 for 20 yr. by itself, and the product will be the amount for 40 yr. ; for 35 yr. multiply the amount of $ 1 for 20 yr. by the amount of $1 for 15 yr. ; the result will be the amount for 35 yr. WRITTEN EXERCISE Find the compound interest : Principal Rate 1. $7500 4% 2. $2500 2% 3. $5600 31% 4. $3350 5% 5. ,$2875 3% 6. $4600 4% Time Interest Payable 5 yr. Annually 12 yr. Annually 20 yr. Annually 10 yr. Semiannually 17 yr. Annually 15 yr. Semiannually INTEREST 323 Sinking Funds 402. A sinking fund is a sum of money set aside at regular intervals for the purpose of paying off an existing or anticipated indebtedness, or of replacing a value which will disappear by depreciation, exhaustion, or termination. The payment of a public or a corporation debt and the replacing of certain public and corporate values are sometimes facilitated by regularly investing a certain sum in some form of security. The interest and prin- cipal from these investments from year to year constitute a sinking fund, which, it is planned, shall accumulate to an amount sufficient to redeem the debt when it falls due or replace the value when it disappears. ORAL EXERCISE 1. In what time will any sum of money double itself at 4 % simple interest ? at 3 % ? at 6 ^o ? at 4| % ? 2. How long (approximately) will it take 81 to double it- self at 3| % ? compound interest, compounded annually ? (See table, page 321.) 3. How long (approximately) will it take any sum to double itself at 4| % compound interest, compounded annually ? at 5 % compound interest, compounded annually ? 4. If you put 11 at compound interest to-day, $1 one year from to-day, and so on for 20 yr., how much would you have at the end of the twentieth year, interest being compounded annually at 4 = (See table below.) 403. In the following table is shown the sum to which f 1, paid at the beginning of each year, will increase at certain rates of com- pound interest in any number of years not exceeding twenty. Ye. 2% 4% 4^% Ye. 2% 4% 4i% 1 1.020000 1.040000 1.045000 11 12.412089 14.025805 14.464031 2 2.060400 2.121600 2.137025 12 13.680331 15.626837 16.159913 3 3.121608 3.246464 3.278191 13 14.973938 17.291911 17.932109 4 4.204040 4.416322 4.470709 14 16.293416 19.023587 19.784054 5 5.308120 5.632975 5.716891 15 17.639285 20.824531 21.719336 6 6.434283 6.898294 7.019151 16 19.012070 22.697512 23.741706 7 7.582969 8.214226 8.380013 17 20.412312 24.645412 25.855083 8 8.754628 9.582795 9.802114 18 21.840558 26.671229 28.063562 9 9.949721 11.006107 11.288209 19 23.297869 28.778078 30.371432 10 11.168715 12.486351 12.841178 20 24.783317 30.5)69201 32.783136 324 PEACTICAL BUSINESS AEITHMETIC WRITTEN EXERCISE 1. At the beginning of each year for 10 yr. a certain rail- road company put aside out of the profits of the previous year 150,000 as a sinking fund. If this sum was invested at 4% compound interest, compounded annually, what did it amount to at the end of the tenth year ? 2. Jan 1, 1915, a certain city borrowed 8500,000 and agreed to pay the same on Jan. 1, 1925. What sum must be invested on Jan. 1, 1915, and annually for 10 yr., in securities, paying 4 J % compound interest, compounded annually, in order to pay the loan when it becomes due? 3. On Dec. 31, 1915, a certain town borrowed 140,000 with which to build a new high school. It was agreed that this amount should be paid on Dec. 31, 1920. What sum must the town set aside and invest at 41^% compound interest, com- pounded annually, on Jan. 1, 1913, and each year thereafter for 5 yr., in order to pay the debt when it becomes due? 4. What sum must a town set aside and invest annually to rebuild a bridge costing $30,969.20, estimated to last 20 yr., allowing 4 % compound interest, compounded annually? WRITTEN REVIEW EXERCISE 1. What amount of interest (in United States money) at 6 % will accrue on a debt of X84 12s. in 5 mo. 24 da.? 2. The yearly taxes on a house and lot which cost 112,500 are $162. How much should the house rent for per month to clear 6 % on the investment ? 3. A bought 16,000 bu. of wheat at 85/, and paid for it in 10 da. 46 da. from the date of purchase he sold the wheat for 92/ per bushel, cash. If money was worth 4%, what did he gain? 4. A savings bank account was opened July 1, 1914, with a deposit of f 800. Interest was credited every 6 mo. at 4%. No withdrawals or subsequent deposits having been made, what was the balance of the account Jan. 1, 1920 ? INTEREST 325 5. The note on page 314 was not paid until May 27. How much was due the holder of the note on that date ? 6. Jan. 1, 1915, B invested $24,000 in a manufacturing busi- ness. July 1, 1917, he withdrew $33,000, which sum included the original investment and the net gains. What average yearly per cent of simple interest did the investment yield ? 7. Derby & Co. offer B the following terms: Yjq, Vso* '^^^' ^"^ B bought a bill of goods amounting to $4000 which he paid Jan. 31. What rate of interest did he practically pay on the net amount of the bill by not taking advantage of the cash offer ? 8. In a certain town the taxes are due Sept. 15 of each year, and all taxes unpaid by Oct. 15 are subject to interest from the date they are due, at 6%. The following taxes were paid on the dates named: Oct. 18, $68.40; Oct. 21, $22.50; Oct. 25, $132.75 ; Oct. 31, $98 ; Nov. 11, $176.80 ; Nov. 23, $326.30; Dec. 2, $45 ; Dec. 16, $13.25 ; Dec. 29, $21. How much in- terest was paid, the time being the exact number of days ? 9. Jan. 1, 1915, F bought a piece of city property for $20,000, paid cash $4000, and gave a note and mortgage for 5 yr. without interest, to secure the balance. To cover the in- terest, which it was agreed should be met quarterly, he gave twenty notes for $240 each, one maturing every three months. The first five installments of interest were paid when due, and the balance of the mortgage and the interest were paid Jan. 1, 1920. Find the final payment. CHAPTER XXVI BANK DISCOUNT ORAL EXERCISE 1. What is meant by a promissory note ? by the face of a note ? by the time ? by the maker ? by the payee ? 2. How would you word a promissory note for $600, dated at your place to-day, payable in 60 da. at a bank in your place, with interest at 5%, to C. B. Powell, signed by yourself? 3. What is meant by negotiable? by indorsing a note? Illustrate a blank indorsement ; an indorsement in full ; a qualified indorsement. 404. A commercial bank is an institution chartered by law to receive and loan money, to facilitate the transmission of money and the collection of negotiable paper, and, in some cases, to furnish a circulating medium. 405. If the holder (owner) of a promissory note wishes to use the money promised before it becomes due, a commercial bank will usually buy th« note, provided the holder can show that it will be paid at maturity, that is, when it becomes due. This is called discounting the note. NcwYorfv C^/^.^'?t^^^^.,^^.-^iif:r^y^^>^S*^^^ Nft /C 326 -"tZ^/ //^^ f J -pay to Doltora - ^^^f^^^J/ 7 ^^ . BANK DISCOUNT 327 406. A commercial draft is now frequently used, instead of tlie promissory note, as security for the payment of goods sold on credit. Such a draft may be defined as a written order in which one person directs another to pay a specified sum of money to the order of himself or to a third person. The circumstances under which the foregoing draft was drawn are as follows : Geo. H. Catchpole sold Frank G. Hill goods amounting to $460.80. Terms : 30-da. draft. The draft and an invoice were made out and sent to Frank G. Hill by mail. Frank G. Hill accepted the draft, that is, signi- fied his intention to pay it by writing the word accepted, the date, and his name across the face. The draft was then returned to Geo. H. Catchpole, who may discount it the same as he would an ordinary promissory note. The parties to a draft are the drawer, the drawee, and the payee. In the foregoing draft, George H. Catchpole is both the drawer and the payee, and Frank G. Hill is the drawee. A draft payable after sight begins to mature from the date on 'which it is accepted. An acceptance must, therefore, be dated in a draft payable after sight, but it may or may not be dated in a draft payable after date. j^o.^2^ ^^^^Hr.^l^.:k Some states allow three days of grace for the payment of notes and other negotiable paper. Days of grace are obsolete in so many of the states that they are not considered in the exercises in this book. Some states provide that when paper matures on Sunday or a legal holiday it must be paid the day preceding such Sunday or legal holiday ; others provide that it must be paid on the day following. To hold all interested parties, the laws of any given state should always be observed. When the time of negotiable paper is expressed in months, calendar months are used to determine the date of maturity ; but when the time is expressed in days, the exact number of days is used. Thus, a note payable 2 mo. after July 15 is due Sept. 15 ; but a note payable 60 da. after July 15 is due Sept. 13. Paper payable 1 mo. from May 31, Aug. 31, etc., is due June 30, Sept. 30, etc. 328 PEACTICAL BUSINESS ARITHMETIC Maturity Table 407. The time from the date of discount to the maturity of paper is called the term of discount ; the whole sum specified to be paid at maturity, the value, or amount, of the paper. The term of discount is usually the exact number of days from the date of discount to the date of maturity. Some banks, however, find the term of discount by compound subtraction, and then reduce the time to days ; e.g. the term of discount on a note due May 6 and discounted Mar. 1 is counted as 2 mo. 5 da., or 65 da. In this text the term of discount is the exact number of days from the date of discount to the maturity of the paper. 408. The reduction made by a bank for advancing money on negotiable paper not due is called bank discount. The value of negotiable paper at maturity, minus the bank discount, is called the proceeds. Bank discount is always the simple interest for the term of discount on the whole sum specified to be paid at maturity. 409. The accompanying maturity table is sometimes used by bankers in finding the maturity of notes and drafts. The following examples illustrate its use. 410. Examples, l. Find the maturity of a note payable (a) 6 mo. from Apr. 27, 1915; (6) 6 mo. from Sept. 25, 1915. Solutions, (a) Referring to the table, observe that April is the 4th month; adding 4 and 6, the result is 10, and the 10th month (see number on left) is October. The note is therefore due Oct. 27, 1915. (&) September is the 9th month. 9 + 6 = 15, and the 15th month (see number on right) is March of the next year. The note is therefore due Mar. 25, 1916. 2. Find the maturity of a note payable 90 da. from Jan. 18, 1916. Solution. 1 + 3 = 4, and the 4th month is April. If the note were pay- able in 3 mo., it would be due Apr. 18. Keferring to the table, note that 2 da. (1 da. + 1 da.) must be subtracted for January and March, and 2 da. added for February. The note is therefore due Apr. 18. After the student has become familiar with the principles of the table it will not be found necessary to consult it. 1 Jan. - 1 13 2 Feb. + 2 14 3 Mar. - 1 15 16 4 Apr. 5 6 May- 1 17 June 18 7 July - 1 19 8 Aug. - 1 20 21 9 Sept. 10 Oct. - 1 22 11 Nov. 23 24 12 Dec. - 1 BANK DISCOUNT 329 ORAL EXERCISE Find the maturity of each of the following notes : Date Time Date Time 1. Apr. 6, 1915 30 da. 6. Jan. 30, 1916 30 da. 2. Oct. 6, 1916 3 mo. 7. Jan. 31, 1915 30 da. 3. Nov. 9, 1915 60 da. 8. May 10, 1916 90 da. 4. Jan. 31, 1916 1 mo. 9. June 19, 1916 60 da. 5. Sept. 18, 1915 . 90 da. 10. Nov. 15, 1916 30 da. Fi7id the maturity of each of the follotving acceptances : J. Time after "^^^ Date Datk Time after Date 11. Apr. 3 30 da. 14. Dec. 31 2 mo. 12. May 5 60 da. 15. Jan. 12 1 mo. 13. Jan. 29 1 mo. 16. Feb. 18 3 mo. Find the maturity of each of the following acceptances : Date Time after Date riME after Accepted Sight Accepted Sight 17. Aug. 12 3 mo. 20. Apr. 25 60 da. 18. Sept. 18 2 mo. 21. May 17 3 mo. 19. Oct. 30 . 4 mo. 22. June 18 30 da. WRITTEN EXERCISE Find the maturity and the term of discount Date Time Discounted 1. Jan. 16, 1916 3 mo. Mar. 1 2. Jan. 31, 1916 1 mo. Feb. 3 3. Feb. 12, 1916 90 da. Mar. 2 4. • Feb. 24, 1916 60 da. Apr. 1 5. Mar. 31, 1916 90 da. May 13 Date of Draft Time after Date Date Accepted Date Discounted 6. Feb. 7 60 da. Feb. 8 Feb. 9 7. Mar. 12 30 da. Mar. 12 Mar. 15 Date of Draft Time after Sight Date Accepted Date Discounted 8. May 31 60 da. May 31 June 3 9. Mar. 17 90 da. Mar. 20 Mar. 21 330 PRACTICAL BUSINESS ARITHMETIC 411. The following time table is frequently used by bankers in finding the exact number of days between any two dates : Table of Time From Any Dai To THE Same Day of the Next OF Jan. Feb. Mar. 59 Apr. 90 May 120 June 151 July 181 Aug. 212 Sept. 243 Oct. 273 Nov. 304 Dec. January .... 365 31 334 February . 334 365 28 59 89 120 150 181 212 242 273 303 March 306 337 365 31 61 92 122 153 184 214 245 275 April . . 275 306 334 365 30 61 91 122 153 183 214 244 May . . - 245 276 304 335 365 31 61 92 123 153 184 214 June . . . 214 245 273 304 334 365 30 61 92 122 153 183 July . . 184 215 243 274 304 335 365 31 62 92 123 153 August .' 153 184 212 243 273 304 334 365 31 61 92 122 September 122 153 181 212 242 273 303 334 365 30 61 91 October . 92 123 151 182 212 243 273 304 335 365 31 61 November 61 92 120 151 181 212 242 273 304 334 365 30 December 31 62 90 121 151 182 212 243 274 304 335 365 The exact number of days from any day of any month to the correspond- ing day of any other month, within a year, is found in the column of the last month directly opposite the line of the first month. Thus, from June 6 to Sept. 6 is 92 da. ; from Apr. 1 to Oct. 1 is 183 da. ; from Aug. 26 to Dec. 26 is 122 da. The exact number of days between any two dates, leap years excepted, is found as in the following illustrations : 412. Examples, i. How many days from Mar. 1 to May 11? Solution. From Mar. 1 to May 1 is 61 da. From May 1 to May 11 is 10 da. 61 da. + 10 da. = 71 da., the required result. 2. How many days from July 26 to Oct. 6 ? Solution. From July 26 to Oct. 26 is 92 da. From Oct. 26 back to Oct. 6 is 20 da. 92 da. — 20 da. = 72 da., the required result. ORAL EXERCISE By the table find the exact number of day% from : 1. July 8 to Sept. 8. 7. 2. Jan. 6 to Mar. 6. 8. 3. Jan. 23 to June 23. 9. 4. Feb. 13 to July 13. lo. 5. Mar. 11 to Sept. 11. ii. 6. Mar. 21 to Aug. 21. 12. May 31 to Aug. 1. Feb. 23 to Sept. 23. Mar. 24 to July 12. May 11 to Aug. 31. Aug. 15 to Dec. 10. Nov. 25 to Mar. 25. BANK DISCOUNT 331 413. Examples, l. Find the proceeds of a note for 13000, payable in 78 da., discounted at 6%. Solution. 78 da. = the term of discount. $39 = the bank discount. $3000 — $39 = $2961, the proceeds. 2. A note for 16000 payable in 60 da. from May 10, 1915, with interest at 6%, is discounted May 25, at 6%. Find the maturity, the term of discount, the bank discount, and the proceeds. Solution. July 9, 1915 = the maturity. 45 da. = the term of discount. $ 60 = the interest on the note for 60 da. $6060 = the value of the note at maturity. $45.45 = the bank discount. $6014.55 = the proceeds. 414. The accompanying diagram illustrates a convenient outline for learning the proper method of computing bank dis- count. It will be observed that the first problem is an interest- bearing note, and the second problem a non-interest-bearing note. The items in black ink are taken from the problem, and the items in red ink are found as previously explained. WRITTEN EXERCISE 1. Assuming that the model note, page 9, was discounted July 2, at 6%, find the bank discount and the proceeds. 2. Assuming that the model note, page 314, was discounted Jan. 20, at 6%, find the bank discount and the proceeds. 3. Assuming that the model note, page 316, was discounted Aug. 26, at 6 %, find the bank discount and the proceeds. 4. Assuming that the model draft, page 326, was discounted May 15, at 6 % , find the bank discount and the proceeds. /PZ4^'>-rue>-t^''ti^^yui!CeLy / 2. J o&zi.?^ff/-;^i^i.^.^ ^J ?Ktt^ '■ xy^^€t<^ c^ '^t^^x-e,d^ ^JOO ^ioo ^i^/^i^-^y-lU^ X-'fut'. J-nuo T^^e^ ^fc^^^^S^i^.^ 6-/. :^^z.ti^ ^..St:^i.»t,x.t.^^^ C-/' iv: o,^Sz-£S. ff/.^3z^^^^ --^-^..-ftJk^.^:^^^ -^^TT-y ^ .^y ■ - - • — Ytiiue reeeioed 2. You gave the Union National Bank, of your city, your note, for $1200, at 60 da., indorsed by Williams & Rogers. How much cash will the bank advance you, if discount is deducted at the rate of 6% ? 3. Howe & Rogers, Buffalo, N.Y., borrowed il2,000 of Mer- chants National Bank on their demand note secured by 300 shares of Missouri Pacific Railway stock, at §50. If the rate of interest was 2| %, how much was required for settlement 39 da. after the loan was made ? 336 PRACTICAL BUSINESS ARITHMETIC 4. Jan. 2, 1915, C. W. Allen & Co., brokers, borrowed of First National Bank, Boston, Mass., $15,000 on the following collateral note. How much was required for full settlement of the loan 57 da. after it was made ? $Zj>^j2j2J:rrr^ Boston. Mass., (fr7^/ ^W ..-^^-gf^^ ^^fe Z'^^^^^?^ ^ - ■ Value received C. ^/2-(pr?r-;h7 .^ y r^ ^ ^ S)ollars g^-:?%i^t-^-'^'<^>^:^ , with interest at the rate of^^::i:,^:2£^per centum, per annum during the said=^A^Li3:2L^ and for such further time as the said principal sum or any part thereof shall remain unpaid. 342 PEACTICAL BUSINE!S8 AKITHMETIC \ ^ ^ ^ ^ ^ \ ,^ ■^ 1 .- ^ i! PARTIAL PAYMENTS 343 THE MERCHANTS' METHOD ORAL EXERCISE 1. A note for f 500 is dated July 1, 1915, payable in 1 yr. with interest at 6%. If no payments have been made, what is due on the note July 1, 1916 ? 2. A payment of 1300 was indorsed on the note Jan. 1, 1916. What was the amount of this payment at the time the note be- came due ? 3. If the value of the note at maturity is $530 and the value of the payment $309, what is the balance due ? 4. By the United States method what is the balance due at maturity on the note described in problems 1 and 3 ? How does this balance compare with the balance in problem 3 ? 421. The merchants' method is based on custom rather than on legal authority. It is used by niost banks and business men on short-time notes and other obligations. The principles of the merchants' method are suggested in problems 1-3. This method provides that : (1) the face of the note shall draw interest to the date of settlement; (2) interest shall he allowed on each payment from the time it is made to the date of settlement. 422. Example. On a note for $600, dated May 13, 1916, pay- able on demand, with interest 2A1 Qf^c, payments were made as follows: June 28, 1916, SlOO; Aug. 28, 1916, S200. What was due at settlement, Sept. 28, 1916 ? Solution Face of note May 13, 1916 $600.00 Interest from May 13, 1916, to Sept. 28, 1916 (4 mo. 15 da.) . . 13.50 Value of note Sept. 28, 1916, the date of settlement . . . $613.50 Payment June 28, 1916 $100.00 Interest on this payment from June 28, 1916, to Sept. 28, 1916 (3 mo.) 1.50 Payment Aug. 28, 1916 200.00 Interest on this payment from Aug. 28, 1916, to Sept. 28, 1916 (1 mo.) 1.00 Value of the payments Sept. 28, 1916, the date of settlement . . $302.50 Balance due Sept. 28, 1916, the date of settlement .... $311.00 344 PRACTICAL BUSINESS ARITHMETIC Some houses find the time by compound subtraction and some use the exact number of days. In the following exercise find the difference in time by compound subtraction in problems 1-2, and use the exact number of days in problems 3-7. WRITTEN EXERCISE 1. Solve problem a, page 341, by the merchants' method for partial payments. Compare the results by the two methods. 2. On a note for $1200, dated Apr. 16, 1916, payable on de- mand, with interest at 4| %, payments were made as follows: June 15, 1916, S500; July 18, 1916, $200. What was due at settlement, Sept. 16, 1916 ? 3. June 15 you borrowed $ 25,000 at Traders' National Bank on your demand note secured by a deposit of 300 shares of Illinois Central Railroad Stock at $110. June 27 you paid $5000, July 2, $10,000, and July 30, $5000. Aug. 2 you paid the remainder of the note and interest, and withdrew the collaterals. What was the amount of the last payment, money being loaned at 4i%? 4. The following is a partial page of the demand and loan register of a large bank. Copy it, supplying the amount of interest due Nov. 15, money being loaned at 4| %. Charles W. Sherman No. Date LOANEL Amount > Loaned Date of Payment Part of Loan Paid Balance of Loan Inter- est Collateral Value of Collat- eral 347 Apr. 1 20,000 00 May July Sept. Nov. 15 1 1 15 5,000 5,000 6,000 4,000 00 00 00 00 15,000 10,000 4,000 00 00 00 ??? ??? ??? ??? ??? ?? ?? ?? ?? I? 250 shares Peim. R.R. Stock . . 31,250 00 The balance due by the merchants' method may be found in the manner suggested by the above account. The interest is found on the face of the note to the date of the first payment. The payment is deducted and the in- terest found on the balance to the date of the second payment, and so on. The results obtained by this process are exactly the same as the results ob- tained by § 421. PARTIAL PAYMENTS 345 5. Solve problem 4 by the United States method and com- pare the result with the merchants' method. 6. Assuming that the collateral note, page 336, has the fol- lowing payments indorsed on its back, find the amount due at final settlement, Feb. 28, 1916. Indorsements: Jan. 15, 1916, $3000 ; Jan. 31, 1916, 15000 ; Feb. 5, 1916, $1000. 7. A collateral note dated at Philadelphia, Pa., July 10, 1916, for $20,000 payable at the Quaker City National Bank is in- dorsed as follows : Aug. 8, 1916, $3500 ; Sept. 12, 1916, $7500 ; Nov. 19, 1916, $4000 ; Dec. 31, 1916, $5000. What was due on the note Dec. 31, 1916, interest being at the rate of 4% ? To solve the problem copy and complete the following interest statement : ./O /) /) rA Philadelphia. <='^O^C-'^! >, ^^ , 19 To THE QUAKER CITY NATIONAL BANK. Dr. To interest on demand loans, as follows: ^ //^J-^^^ fra m ^/^ tn ^A 2. rj ^ days, $_ $ f ^ (P O ^ Src^rx^ ^/a tn 'V/g __ZZ__days. %_IJ^.LI_ $ J~^ ^ ^ -^ from ■''/?? \cs -VpP ? /> flays, $ ?F.?P Please send us the above interest on or Mnrp ....^ti^?^^^^ /^.4^^^-yi..-L^^ >rASHIFR I 8. Make an interest statement, similar to the above, for problem 6. 9. Make an interest statement, similar to the above, for problem 3. 10. Bring to the class a canceled note on which partial pay- ments are recorded. Find, by the United States method and by the merchants' method, the amount required to cancel the note. Which method is the better for the debtor? for the creditor? CHAPTER XXVIII BANKERS' DAILY BALANCES 423. Some commercial banks and trust companies pay inter- est on the daily balances of their depositors. Whether interest shall be allowed on a depositor's account is usually determined by the size of his daily balances. As a rule, no interest is allowed on small balances subject to check. All balances not subject to check usually draw interest. In an active account, that is, an account in which the balance changes frequently, interest is seldom allowed except on an even number of hundred dollars, and all parts of a hundred dollars are rejected. The form of the book in which accounts with depositors are recorded varies in different sections. What is known as the Boston individual ledger (see form, page 38) is extensively used. Another form of depositors' ledger is that shown in the example below. 424. Example. Verify the balance due on the following ac- count beginning Mar. 1, 1916, interest settlements being made monthly at 3%. M. W. Faknham Explanation Date F. Debit Balance Credit F. Date Explanation 1916 1056 25 1915-6 Dec. 31 1650 25 600 00 15 Jan. 7 Currency 2556 25 900 00 15 11 N. Y. draft Check Jan. 15 14 510 00 2046 25 3746 25 1700 00 17 Jan. 22 N. Y. draft Note Jan. 25 16 210 00 3536 25 Check 28 16 500 00 3036 25 3042 08 5 83 17 Jan. 31 Interest 4042 08 1000 00 21 Feb. 8 N. Y. draft Check Feb. 15 20 500 00 3542 08 Check 22 22 1340 00 2202 08 2209 49 7 41 23 Feb. 28 Interest Solution. The credit slip on page 347 shows a form used for recording the daily balances. Only two money columns are used, one for hundreds and the other for thousands. No interest is computed except on an even number of hundred dollars, and all parts of a hundred dollars are rejected. 346 BANKEKS' DAILY BALANCES 347 Beginning Jan. 1 the daily balance of M. W. Farnham's account for 6 da. was $1056.25; record $1000 on the credit slip as shown in the margin. A deposit of $600 was made Jan. 7, making the balance $1656.25 for the next 4 da.; record $1600 on the credit slip as shown in the margin. A deposit of $ 900 on Jan. 1 1 made the balance $ 2556.25 for the next 4 da.; record $2500 on the credit slip as shown in the margin. A with- drawal of $ 510 on Jan. 15 left a balance of $2046.25 for the next 7 da.; record $2000 on the credit slip as shown in the margin. A deposit of $1700 on Jan. 22 made the balance $3746.25 for the next 3 da.; record $3700 on the credit slip as shown in the mar- gin. A withdrawal of $210 on Jan. 25 left a balance of $3536.25 for the next 3 da.; record $3500 on the credit slip. A with- drawal of $500 on Jan. 28 left a balance of $3036.25 for the next 4 da. This records the balance for each day in January. Add- ing these balances the result is $70,000, and the interest on this sum for 1 da. at 3% is $ 5. 83. Adding $ 5. 83 to $ 3036. 25 gives the balance to the credit of the depositor Feb. 1 as $3042.08. Enter the daily balances for February as shown in the margin. The result is found to be $88,900, and the interest on this sum for 1 da. at 3% is $7.41. $7.41 added to the balance of the depositor's account Feb. 28 gives $ 2209.49 as the balance to his credit beginning Mar. 1. In practice the daily balances are usually written as shown in the February column of the accompanying credit slip. The total is then found by multiplication and addi- tion. Thus, the total of the February col- u mnis7 x § 3000 + 7 x $4U00 + 7 x $3500 -h 7 X $2200, or $88,900. Some accountants also use the pure interest method in finding the amount due. Thus, the interest on $3000 for 7 da., plus the interest on $4000 for 7 da., plus the interest on $3500 for 7 da., plus the interest on $2200 for 7 da. equals $7.41, the same as by the first method. In the examples which follow the student may use either of the three methods suggested. DAILY CREDIT BALANCES M. W. Farnham 1007 Jan. Feb. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 Total 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 1 3 3 6 6 6 6 5 5 5 5 T < 7 7 5 5 5 3 4 8 2 5 2 70 88 9 41 Interest 5 83 7 348 PKACTICAL BUSINESS ARITHMETIC WRITTEN EXERCISE , 1. The Rochester Trust and Safe Deposit Co. allows inter- est to its depositors on daily balances at 3 % per annum, pay- able quarterly. Find the cash balance of the following account with Chas. M. Sherman, Apr. 1, 1916. Jan. 1, 1916, deposited 11200; Jan. 12 drew out 1400; Jan 30 deposited 1800; Jan. 31 drew out 1400; Feb. 10 deposited 1800; Feb. 25 drew out $100 ; Mar. 10 deposited 1800 ; Mar. 20 drew out $900 ; Mar. 25 deposited |300. 2. At the close of an interest period, Feb. 28, 1916, Harvey & Smith's balance with the Fidelity Trust Co. was $2246. During the month of March they made the following deposits : Mar. 3, $2500; Mar. 9, 11750; Mar. 24, 12645.75; Mar. 28, $1310.50 ; Mar. 30, $500. They also drew out by check as fol- lows: Mar. 4, $1050; Mar. 6, $2000; Mar. 8, $720; Mar. 12, $840.50; Mar. 16, $450; Mar. 19, $430; Mar. 23, $1000; Mar. 26, $150; Mar. 29, $267. How much interest should be credited Mar. 31, the rate being 3% per annum? What was the balance of the account after the interest was credited? 3. Find the cash balance of the following account May 31, 1916, assuming that interest is allowed on daily balances at 3 % and added to the account monthly. A. S. OSBORN Explanation Date F. Debit Balance Credit F. Date Explanation 1916 1200 00 1916 Feb. 28 Check Mar. 12 100 00 1500 2000 00 00 400 500 00 00 Mar. 12 25 Currency Currency Check . 31 100 00 2400 ** 500 * 00 31 31 N. Y. draft Interest **** ** 700 00 Apr. 15 N. Y. draft Note Apr. 20 50 00 **** ** 200 00 20 N. Y. draft Check 30 1200 00 **** ** * ** 30 Interest **** ** 250 00 May 10 Currency Check May 31 500 00 **»* ** * ** 31 Interest CHAPTER XXIX SAVINGS-BANK ACCOUNTS 425. A savings bank is an institution, chartered by the state, in which savings or earnings are deposited and put to interest. The deposits in a savings bank are practically payable on demand. Most banks reserve the right to require notice of withdrawal from 30 to 60 da. in advance ; but this right is seldom exercised. The period of time which must elapse before dividends of interest are declared is called the interest term. Dividends of interest are usually de- clared semiannually; but in some sections they are declared quarterly. The stated days on which balances begin to draw interest are called interest days. In some savings banks deposits begin to draw interest from the first of each quarter ; in others, from the first of each month. In nearly all savings banks, only such sums as have been on deposit for the full time between the interest days draw interest. Thus, if the interest days begin on the first of each quarter, only those sums that have been on deposit for the full quarter draw interest. 426. Interest is computed on an even number of dollars, and all fractions of a dollar are rejected. When interest is not withdrawn it is placed to the credit of the depositor and draws interest the same as any regular deposit. Savings banks there- fore allow compound interest. 427. Examples, l. In the Walker Institution for Savings the interest term is 6 mo. and the interest days are Jan. 1, Apr. 1, July 1, and Oct. 1. Verify the balance due on the following account Jan. 1, 1916, at 4 %. Solution. The account was opened July 1, 1915, by a deposit of $500. July 10 this sum was increased by a deposit of $10, making the balance $510; Aug. 14 this sum was diminished by a withdrawal of $ 20, making the balance $490; Oct. 4 this sum was diminished by a withdrawal of $200, making the balance $ 290. The account was similarly increased and diminished until Dec. 31, when there was a balance of $300.75 due the depositor. 349 350 PRACTICAL BUSINESS AEITHMETIC *Jhe nalken institution for Savings in account with ( \ DATE DEPOSITS INTEREST PAYMENTS BALANCE ^/f/^ / ,ro ^ v:f77/^ /^ / / /? / ^ _ .r/ ^ /^ 2 ^ „ U£? r; r^2 ^A Z/0 _ 7 ^ _ //7 -7 7^^ / J 6/9 '7S' ^^^ /r A^^ A^/^ r> / J/ / lO ^ .3 r7^ / Q^^^y?^ / y Jr'n >? fJ ^ ^ The smallest balance for the first interest period, July 1 to Oct. 1, was $490. The interest on $490 for 3 mo. at 4% is $4.90. The smallest balance for the second interest period, Oct. 1 to Jan. 1, was $290. The interest oh $290 for 3 mo. at 4% is $2.90. $4.90 plus $2.90 equals $7.80, the dividend of interest due the depositor Jan. 1. Since this sum is not withdrawn, it is placed to the credit of the depositor, making his balance $308.55. 2. In the Warren Institution for Savings interest dividends are declared semiannually and the interest days are Jan. 1, Apr. 1, July 1, and Oct. 1. Verify the balance due on the following account Jan. 1, 1916, at 4%. Cj)e 3S^an:m institution for ^atainsa; ^, in account iiit^ / DATE DEPOSITS INTEREST PAYMENTS BALANCE / .^/^/7 . .r/^^ . . 4.. / ,3/0/9 __ r^0 _ jYt^^y //? / /O /O _ <^/y^ (L.2. / /.t? , ^ ^/,3 , , '^fi:?^ / /t ?Y / ;^^ .j^M^n^, v SAVINGS-BANK ACCOUNTS 351 Solution. The smallest balance for the first interest period was $500 ; the interest on $ 500 for 3 mo. at 4 % is $ 5. The smallest balance for the second interest period was $800; the interest on $800 for 3 mo. at 4% is $8, $ 5 + $ 8 = $ 13, the total interest due the depositor July 1. $900 + $ 13 = $ 913, This balance remained unchanged for the next 6 mo. The interest on $913 for 6 mo. at 4 % is $ 18.26. $ 913 + $ 18.26 = $ 931.26, the amount due the depositor Jan. 1, 1916. WRITTEN EXERCISE 1. Solve example 1 above, assuming that the interest days are the first day of each month ; also example 2. 2. Copy the following account, supplying the missing amounts. Interest at 4| % ; interest days, Jan. 1, Apr. 1, July 1, and Oct. 1. MANHATTAN SAVINGS BANK In Account with Mr. Chas. B. Sherman Date Deposits Interest Payments Balance 1915 Jan. 1 600 00 * * * * * Jan. 31 100 00 * * * * * Mar. 1 250 00 * * * * * May 6 50 00 * * * * * May 31 100 00 * * * * * July 1 * * * * * * * * * 3. Copy and complete the following account. Interest at 4% ; interest days, Jan. 1, Apr. 1, July 1, and Oct. 1. FIDELITY SAVINGS BANK In Account with Mr. Frank M. Ellery Date Deposits Interest Payments Balance 1915 Jan. 1 300 00 * * * * « Mar. 6 200 00 * * * * * Mar. 30 125 00 * * * * * Apr. 17 165 50 * * * * * July 1 100 00 * * * * * * 4^ * * Aug. 15 75 00 * * * * * Auff. 31 58 40 * * * * * Oct. 1 250 00 * * * * * Dec. 1 110 50 * * * * Ma 1916 Jan. 1 * * * * * * * * * 352 PEAOTICAL BUSINESS AEITHMETIG POSTAL SAVINGS BANKS 428. The law establishing postal savings banks became effec- tive in the United States, January 3, 1911. Herewith are some of the leading provisions of this law. 429. An account may be opened and deposits made by any person of the age of 10 yr. or over. 430. Deposits will be accepted only from individuals, and no account will be opened in the name of a corporation, associa- tion, society, firm, or partnership, or in the name of two or more persons jointly. 431. Deposits may be accepted without regard to the resi- dence of the depositor or the post office of which he is a patron, but a person can have but one postal savings account, either at the same office or at different offices. 432. No account may be opened for less than SI, nor will fractions of a dollar be accepted for deposit at any time. 433. Postal savings deposits will be evidenced by certificates in fixed denominations of $1, S2, S5, $10, S20, $50, issued in the name of the depositor. Such certificates are non-transferable and non-negotiable. Each certificate must bear the depositor's name, the number of his account, the date of issue, the name of the office receiving the deposit, and the date on which inter- est will begin. .Interest will begin on each deposit the first day of the month following the deposit. A deposit on March 1 will not begin to draw interest until April 1. 434. Interest at the rate of 2% per annum shall be allowed and paid on the amount represented by each postal savings cer- tificate for each full year that it remains on deposit. No interest will be allowed for a fractional portion of a year. Compound in- terest is not allowed, but a depositor may withdraw interest accrued and make a new deposit of it which will then draw interest. 435. A postal savings card with nine postal savings stamps affixed may be presented and accepted as a deposit for $ 1, either in opening an account or in adding to an existmg account, or it may be redeemed in cash. SAVmGS-BANK ACCOUNTS 353 436. Postal savings cards and stamps are transferable and need not be presented for deposit by the original purchaser. They may be sold to any person in any quantity desired. 437. A depositor may surrender his deposits in whole or in part, in the sum of S 20 or any multiple thereof up to $ 500, and receive in heu of such surrendered deposits postal savings bonds in appropriate denominations. Such exchange may be made by a depositor as of January 1 and July 1 of each year, but appli- cations therefor shall be made at least 1 mo. previously. These bonds bear interest at the rate of 21 % per annum, payable semi- annually. WRITTEN EXERCISE 1. If John A. Sellman deposited S 7 on the tenth day of each month for the year 1911, begmnmg Jan. 10 and making his last deposit on Dec. 10, what sum would be to his credit on March 1, , 1912? on Sept. 1, 1912? 2. If John A. Gilson deposited $12 on the first day of each alternate month for the year 1913, begmning Jan. 1, what sum would be to his credit on Jan. 1, 1914 ? on April 1, 1914 ? 3. If no additional deposits were added to the account in problem 2, what sum would be to the credit of Mr. Gilson on Jan. 1,1915? 4. Ralph C. Yarner made the following deposits and received postal savings certificates therefor: Nov. 4, 1911, S15; Mar. 12, 1912, $25; July 11, 1912, $30; Oct. 2, 1912, $23. What was due on this account July 1, 1915 ? 5. Henry M. Werner made the following deposits and received postal savings certificates therefor: Mar. 1, 1914, $11; June' 4, 1914, $19 ; Sept. 8, 1914, $10 ; Dec. 23, 1914, $10. What was due on this account Jan. 1, 1915 ? on Apr. 1, 1915 ? CHAPTER XXX EXCHANGE DOMESTIC EXCHANGE ORAL EXERCISE 1. Mention some objections to sending actual money by express. 2. If $50 sent by mail in a registered letter is lost, to what extent are the postal authorities liable ? 3. In what ways may you pay a debt at any distant point without actually sending the money ? 438. The process of settling accounts at distant points with- out actually sending the money is called exchange. Money Orders 439. Money orders, as issued by post offices, express com- panies, and banks are frequently used in making payments at a distance. 440. A postal money order is a government order for the payment of money, issued at one office and payable at another. 6T59S^ Westfield, Sta.l.Mass. 32^^ United States Postal Money Order RECEIVEO PAYMENT: FACSIMILE. OF NO VALUE Westfield, Sta.1. Mass. 3746^ J61596 ^Liy "" """"" Coupon for Payings Office THIS MONEY ORDER IS NOT OOOO • FOR MORE THAN LARGEST AMOUNT ■^ INDICATED ON LEFT-HAND MAROiNl i or THE ORDER AND / HON OK ERASURE! I IT VOID 354 EXCHANGE a55 The fees (rate of exchange) charged for postal money orders are : For orders for sums not exceeding 12.50 3^ Over 2.50 to $ 5.00 hf Over 5.00 to 10.00 ^9 Over 10.00 to 20.00 10^ Over 20.00 to 30.00 VI f Over $30.00 to % 40.00 15;* Over 40.00 to 50.00 \^f Over 50.00 to 60.00 20;* Over 60.00 to 75.00 25;* Over 75.00 to 100.00 30;* The maximum amount for which a single postal money order may be issued is $ 100. When a larger sum is to be sent, additional orders must be obtained. When an order is issued, the money is not sent from one post office to another. The transfer is merely a matter of bookkeeping, the money being received by the government at one office and paid out at another. If a postal money order is lost, a duplicate may be obtained from the Post Office Department at Washington. 441. An express money order is an order for the payment of money, issued by an express company and payable at any of its agencies. I When Countersigned SrAOENTATPOINTOFtSSUe PaYTO THE ORDER 0F_^ EXPRESS MONEY ORDER The Sum of /.Lil^^;^^.^^..^'^ ^^ ju.?i VoT GOOD fOR MORE TMAH THE HIGHEST PRllilTtB HAg '"(^Tf^^S^^yt^^^J^ ^lA^^^T^d^^iP^.--'?^'^. . . State orj^ The fees charged for express money orders are the same as those for postal money orders. The maximum amount for which a single express money order may be issued is $50. A postal money order must not bear more than one indorsement; but an express money order may bear any number of indorsements. 442. A bank money order (see form, page 356) is an order for the payment of money issued by a bank and payable at certain other banks in different parts of the country. The charge for a bank money order is usually the same as that for a postal money order. 356 PRACTICAL BUSINESS ARITHMETIC wmiiiwi/iiiiii/wwwiiiiitmiiiiiijwiijtiwi/iiiuwiiiiiiiiwuwiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiwii 443. A telegraphic money order is a telegram of an express or telegraph company, at any given place, ordering the pay- ment of money at another designated place. THE UNION TELiLGRAPH CO. INCORPORATED- 23,000 OFFICES IN AMERICA CABLE SERVICE TO ALL THE WORLD ROBERT C. CLOWRY, President and General Manager W ti IM U the following message subject to the terms on back hereof, which are hereby agreed to. T-Q The Union Telegraph Co. Boston, Mass., July 27, -19 Rochester, N.Y. Findable Findelkind Charles Osgood ten East Fichant The Union Telegraph Co. These telegrams are usually in cipher; that is, in a language not under- stood by those who are unfamiliar with the system of abbreviations (code) used. The sender and the receiver must each have a code. The following code will illustrate the principle of telegraphing in cipher : Code Word Meaning Fichant One hundred dollars Ficheron One thousand dollars Findable Please pay of your city % . Findelkind On production by him of positive evidence of his personal identity. The principle of a telegraphic money order is the same as that of a postal money order; no money is transferred from one place to another. The charge for an order is usually 1% of the amount to be transmitted plus twice the rate for a single ten-word message. EXCHANGE 357 The following are the rates for a ten-word message from Boston to the places named : New York $0.30 ' Chicago $0.50 Galveston $0.75 Philadelphia $0.35 San Francisco $1.00 Rochester $0.40 ORAL EXERCISE 1. What was the total cost to the sender of the postal money order, page 354? the express money order, page 355? the telegraphic money order, page 356? the bank money order, page 356 ? 2. What will be the total cost of a postal money order for 27f? $2.19? i5.28? $10.40? $18.90? $45.10? $35.89? $125 ($100-f-$25)? $75.29? $49.82? $127.16? 3. What will be the total cost of an express money order for $6.20? $28.80? $19.50? $27.95? $48.90? $&5 ($504-$15)? $111? $37.59? $41.72? $65.59? $114? 4. What will be the total cost of a telegraphic money order from Boston to New York for $50? $75? $100? $125? $150? $200? $300? $400? $450? $500? from Boston to Phila- delphia? from Boston to San Francisco? from Boston to Chicago ? 5. Translate the following telegraphic money order : Find- able F. J. Reed^ 20 Park St. ficheron findelkind. How much will it cost for such an order from Boston to Galveston? from Boston to Chicago? from Rochester to Boston? WRITTEN EXERCISE 1. Find the total cost of 5 postal money orders for the fol- lowing amounts : $3.10; $8.19; $25.06; $18.50; $20. 2. Find the total cost of six express money orders for the following amounts : $1.25; $10; $6.80; $16.25; $80; $19.50. 3. Find the total cost of the following telegraphic money orders: one from Boston to New York for $50; one from Boston to Philadelphia for $500; one from Boston to San Francisco for $175; one from Boston to Galveston for $300; one from Boston to Rochester for $250. 358 PRACTICAL BUSINESS AEITHMETIC Checks and Bank Drafts 444. Business men usually keep their money on deposit with a commercial bank or trust company and make most payments, at home and at a distance, by check; that is, an order on a bank from one of its depositors for the payment of money. Cfje jfirst Rational Bank l^o.-^i^Z. W.-^^^ to the orl»cr of ^.^y ^^p^ - Z^-?:>^ , ^^^ i£^ n^z:^^^ SDoflaritf A check may be drawn for any amount so long as it does not exceed the balance on deposit to the credit of the drawer. It may be drawn payable to : (1) the order of a designated payee, in which case the payee must indorse it before the money will be paid over; (2) the payee, or bearer, in ■which case any one can collect it ; (3) " Cash," in which case any one can collect it. C. B. Sherman & Co. and E. H. Robinson & Co. in the foregoing check both reside in Boston. On receiving the check, E. H. Rob- inson & Co. indorse it and de- posit it for credit with their bank, say the National Shawmut Bank. The First National Bank and the National Shawmut Bank, as well as each of the other banks in the city, has many depositors who draw INTERIOR View of a Clearing House. checks upon it which are de- posited by the payees in various other city banks, and it also receives daily for credit from its own depositors checks drawn upon various other city banks. Each bank therefore has a daily balance to settle or to be settled with each of the other banks. To some it has payments to make and from others it has payments to receive. If these balances were adjusted in money, each bank would have to send a messenger to each of the debtor EXCHANGE 359 banks to present accounts and receive balances. This would be a risky and laborious task. To facilitate the daily exchanges of items and settle- ments of balances resulting from such exchanges there has been established in every large city a central agency, called a clearing house. This agency is an association of banks which pay the expense of conducting it in pro- portion to the average amount of their clearings. Suppose, for example, that the banks constituting a clearing house are Nos. 1, 2, 3, and 4. No. 1 presents at the clearing house items against Nos. 2, 3, and 4, and Nos. 2, 3, and 4 present items against No. 1. So, likewise, with No. 2 and each of the other banks. In the clearing house there are usually two longitudinal columns containing as many desks as there are banks in the association. At a given time a settling clerk from each bank takes his place at his desk inside of one of the columns and a delivery clerk from each bank takes his place outside the column. Each delivery clerk advances, one desk at a time, and hands over to each settling clerk his exchange items against that bank. After the circuit of the desks has been completed each delivery clerk is at the point from which he started, and each settling clerk has on his desk the claims of all of the other banks against his bank. Each settling clerk then compares his claims against other banks with those of other banks against him and strikes a balance. This balance may be in favor of or against the clearing house. If No. 1 brought claims against Nos. 2, 3, and 4 aggregating ^211,000 and Nos. 2, 3, and 4 brought claims against No. 1 aggregating $200,000, there is $11,000 due No. 1 from the clearing house. But if No. 1 brought to the clearing house exchange items aggregating $200,000 and took away exchange items aggregating $211,000, there is $11,000 due the clearing house from No. 1. So, likewise, with No. 2 and each of the other banks. When all of the exchanges have been completed, the clearing house will have paid out the same amount that it has received. But all checks received by banks are not payable in the city. Suppose that A. W. Palmer, of Chicago, 111., owes C. B. Andrews, of Westfield, Mass., $ 500 and that the amount is paid by a check on the City National Bank of Chicago. C. B. Andrews receives the check and offers it for credit at the Farmers and Traders Bank of Westfield, Mass. The Westfield Bank has no account with any Chicago bank, but it has with the First National Bank of Boston, and the check is sent to that bank for credit. The First National Bank wishes *to increase its New York balance and the check is forwarded to Chemical National Bank of New York for credit. Chemical National Bank next mails the check to Commercial National Bank of Chicago, the 360 PRACTICAL BUSINESS ARITHMETIC bank with which it has regular dealings in that city. Commercial National Bank sends the check to the clearing house and it is carried to the City National Bank by a messenger from that bank. Thus, all of a depositor's checks will in time be presented to the bank on which they are drawn. When presented, they will be charged to the depositor, cancelled, and later returned to him to be filed as receipts. Banks frequently charge their depositors a small fee (rate of exchange) for collecting out-of-town checks. This fee is rarely over ^jj %, but there is no uniformity in the matter. Sometimes when a- customer keeps a large bank account, no charge whatever is made for the collection. 445. It often happens that a person will find it necessary to make payment to one who does not care to take the risk of a private check or to one who should not be called upon to pay the cost of cashing a check. In such cases some other form of instrument of transfer must be used. A very common and con- venient method of making a remittance is by means of a check of one banking institution upon another called a bank draft. wMMMMjjz imiMMmiimmimmmmmMmmMmmiiJ' tjjosfon, >^/rtass. Uraders U\ational njjank J 9?atf to tAe order ^f """^ ""t^- ~(^ ^^^^ ^^^^-^^^^-^^ ^A^^M ^^^?^-^^^-^-^ -r^y-^^^f^-g.^^^^^^^^^ — 9)oaa J\few York j ^ ^^ — " on the return of this certificate properly indorsed. ea. .^ — ^jt; — 7f/~ — /J The payee in a certificate of deposit will have no difficulty in getting the certificate cashed or the amount credited to him by his bank. 362 PRACTICAL BUSINESS ARITHMETIC ORAL EXERCISE 1. Assuming that the bank which cashed the check on page 5 charged ^ % collection, what was the amount credited to the depositor ? 2. Silas Long of New York deposited the following check. The bank deducted ^^ % for collection. How much was placed to Silas Long's credit? %\^z Virion 33anfe l^ar^to ti^e otDet of. a. (?z'^C->^-<& :^^^^-<^i ^^:^ ^ 3. B deposited three out-of-town checks in his bank as fol- lows: $300; 1700; $750. If the bank charged ^0% collec- tion, what amount was placed to B's credit? 4. Bring to the class a number of canceled checks and take several of them and trace them from the time they w^ere issued until they were filed as receipts by the drawer. Show why a canceled check is the best kind of a receipt for the payment of money ? 5. How much did the bank draft on page 360 cost the pur- chaser if the exchange was at ^^o % premium ? WRITTEN EXERCISE 1. Find the cost of a bank draft for $3958.75 at J^- % pre- mium; of a bank draft for $679.80 at gV % premium; of a bank draft for $768.54 at 50^ per $1000 premium. 2, To cover the cost of a bank draft bought at ^0% P^®" mium, I gave my bank a check for $250.25. What was the face of the draft ? What was the rate of premium per $1000? EXCHANGE 363 3. How large a bank draft can be bought for $850.85, ex- change being at -^q % premium ? 4. Find the proceeds of the accompanying deposit, ^^ % col- lection and exchange being charged on the out-of-town checks. When the receiving teller takes a, deposit from a customer, he classifies the items on the deposit ticket, as shown in the accompanying illustra- ' tion. If the coin and bills passed in count right, these items are checked (V) on the deposit slip ; if a check on a clearing house bank is received, it is marked with the number of that bank ' in the clearing house ; if a check on the teller's bank is received, it is marked "B"; if a check on an out-of- town bank is received, it is marked «X." [ THE UNION NATIONAL BANK DEPOSITED SY Boston,. uyc^_^ / ■^^^^^ Specie . Bills . . Checks . . 'sdCui^^.e^^^^ . /^ t^o^-^SW^ i^ 2l '.-ti<<.-rryj^ M, -,<^^ r^:^ -t//?A^^J/ ^^<^i.^ ^ty/o -^-^ e ? ^ ? 12. 5. Write a bank draft using the following data : your ad- dress and the current date; drawer, Central National Bank; drawee. Chemical National Bank, New York; amount, $711.94; payee, C. E. Denison; cashier, your name. How large a check will pay for the draft at J^ % premium ? Write the check. 6. Suppose that the members of the class whose surnames be- gin with the letters from A to G inclusive have a deposit Avith Traders National Bank ; that the members whose surnames begin with the letters from H to N inclusive have a deposit with City National Bank ; that the members whose surnames begin with O to S inclusive have a deposit with First National Bank; and that the members whose surnames begin with T to Z inclusive have a deposit with Central Bank. Let each student write a check on his bank in favor of one of his classmates, and let this classmate indorse the check and deposit it with his bank. Then form a clearing house, strike a balance between the different banks, and have these balances adjusted by the payment of school money. 364 PEACTICAL BUSINESS ARITHMETIC Commercial Drafts 448. Business men frequently employ the commercial draft as an aid in the collection of accounts that are past due. . (^^^/^^^.^^^^ — — -^gy to the order of . '^^^^■r^ryA^.^T^ ^ ^ ^^-^<^^J^^ "Z^. — — CD„//„^ Value received and charge to account of So, (^^^g^^^gg- J/^..Al/^S)ue. /2r ^ The above is a commoii form of draft used for collection purposes. Edgar McMickle owes Wilbert, Closs & Co. % 260.50. The amount is due, and Wilbert, Closs & Co. draw a draft on Edgar McMickle and leave it with their Springfield bank for collection. The Springfield bank forwards it to its correspondent in Paterson and this bank sends it by messenger to Edgar McMickle. When he pays the draft, the Paterson bank notifies the Spring- field bank, and that bank deducts a small fee (collection and exchange) for collecting the draft, and credits Wilbert, Closs & Co. for the proceeds. 449. It has been seen (page 327) that the time draft is fre- quently used in connection with sales of merchandise. C ^: =yA^^-^y .gZ^g>g^:U>n I ^^ (( tl 90(' jLu'- I i u 8760 50 \ 8 '^500 I 00 I oo ^- ip 'H: '■<• I ■%■ --K- 370 PRACTICAL BUSINESS ARITHMETIC FOREIGN EXCHANGE Foreign Money oral exercise 1. Repeat the table for English money ; for French money ; for German money. (See Appendix B, page 451.) 2. What is the value of a pound sterling in United States money ? of a franc ? of a mark? 3. Express $4866.50 in English money; ^100 in United States money. Express $ 1930 in French money ; 1000 fr. in United States money. Express $238 in German money; 10000 M. in United States money. A pound sterling is commonly thought of as about $5; a shilling or a mark as about 25 f ; a penny as about 2 ^ ; a franc or lira as about 20 )^ ; a guilder as about 40 f . In problems 4-6 use these approximations. 4. Express $100 as English money; as German money; as French money; 1500 guilders in United States money. 5. Express as United States money : X 15 ; £8 5s. ; £25 10s.; 100 M.; 1500 M. ; 1750 M. ; 75 fr. ; 350 fr. ; 200 fr. 6. A and B while abroad spent 3 wk. in Naples, Italy. If their expenses here averaged 25 lire apiece per day, how much was this in United States money for the 3 wk. ? WRITTEN EXERCISE 1. Express as pounds and decimals of a pound : X25 6s. ; £150 15s.; X200 10s. 6d.; X 300 12s. 9c?. 2. Reduce to United States money : X25 10s. ; X120 9s. 3. Reduce to United States money: 275 M.; 1500 M. 75 pf.; 315 fr.; 725 fr.; X115 10s. 6d. Reduce $1250 to English money ; to French money ; to German money. 4. In a recent year the funded debt of the German Empire amounted to 2,733,500,000 M., of which 1,240,000,000 M. bore interest at 3|% and 1,493,500,000 M. at 3%. Express in United States money the interest on the funded debt for 1 yr. j:xchange 371 The Metric System 452. The metric system is a system of measures having a decimal scale of relation. It was invented by France, and is now used in practical business in a large part of the civilized world. It has been authorized by law in Great Britain and the United States, but is not generally used in these countries except in foreign trade and in scientific investigations. The principal units of the system are the meter for length, the liter for capacity, and the gram for weight. Submultiples and multiples of these units are easily learned when the meaning of the prefixes is known. The Latin prefixes, deci, centi, and milli mean respectively 0.1, 0.01, and 0.001 of the unit. The Greek prefixes deca, hekto, kilo, and myria mean respectively, 10, 100, 1000, and 10,000 times the unit. Table of Length 10 millimeters (mm.) 10 centimeters 10 decimeters 10 meters 10 dekameters 10 hektometers 10 kilometers 1 centimeter (cm.) = = 1 decimeter (dm.) = = 1 meter (m.) = = 1 dekameter (Dm.) = = 1 hektometer (Hm.) = = 1 kilometer (Km.) = = 1 myriameter (Mm.) = 10,000 The units in common use are indicated by black-faced type. Table of Square Measure .01 . meter. .1 meter. 1. meter. 10. meters. 100. meters. 000. meters. ,000. meters. .0001 sq. meter. .01 sq. meter. 1 . sq. meter = 1 centare. sq. meters = 1 are. sq. meters =lhectare. sq. meters. sq. meters. 100 sq. millimeters =1 sq. centimeter (sq. cm.) 100 sq. centimeters =1 sq. decimeter (sq. dm.) 100 sq. decimeters =1 sq. meter (sq. m.) 100 sq. meters =1 sq. dekameter (sq. Dm.) = 100. 100 sq. dekameters =1 sq. hektometer (sq. Hm.)= 10,000. 100 sq. hektometers=l sq. kilometer (sq. Km.) = 1,000,000. 100 sq. kilometers =1 sq. myriameter (sq. Mm.) =100,000,000. The centare, are (a.), and hektare are common terms in land measure- ments. Table of Cubic Measure 1000 cu. millimeters 1000 cu. centimeters 1000 cu. decimeters 1000 cu. meters 1000 cu. dekameters 1000 cu. hektometers 1000 cu. kilometers The cubic meter is also called a stere, a unit used in measuring wood. cu. centimeter (cu. cm.) = .000001 cu. m. 1 cu. decimeter (cu. dm.) = .001 cu. m. 1 cu. meter (cu. m.) = 1. cu. m. 1 cu. dekameter (cu. Dm.) = 1000. cu. m. 1 en. hektometer (cu. Hm.) = 1,000,000. cu. m. 1 cu. kilometer (cu. Km.) = 1,000,000,000. cu. m. 1 cu. myriameter (cu. Mm.) = 1,000,000,000,000. cu. m. ;72 PRACTICAL BUSINESS ARITHMETIC Table of Capacity 10 milliliters (ml.) = 1 centiliter (cl.) = .01 liter. 10 centiliters = 1 deciliter (dl.) = .1 liter. 10 deciliters '= 1 liter (1.) :=. 1. liter. 10 liters = 1 dekaliter (DL) - 10. liters. 10 dekaliters = 1 hektoliter (HI.) = 100. liters. 10 hektoliters = 1 kiloliter (Kl.) = 1000. liters. A liter is the same as a cubic decimeter. Table of Weight 10 milligrams (mg.) = 1 centigram (eg.) 10 centigrams 10 decigrams 10 grams 10 dekagrams 10 hektograms 10 kilograms 10 myriagrams 10 quintals = 1 decigram (dg.) = 1 gram (g.) = 1 dekagram (Dg.) = 1 hektogram (Ilg.) = 1 kilogram (Kg.) = 1 myriagram (Mg.) = 1 quintal (Q.) = 1 tonneau (T.) .01 gram. .1 gram. 1. gram. 10. grams. 100. gi-ams. 1000. grams = 10,000. grams. = 100,000. grams. = 1,000,000. grams The tonneau is usually called a metric ton. Table of Approximate Values A meter = 3i ft. or 1 1 yd. A stere = y\ cd. A kilometer = f mi. A gram = 15| gr. A square meter = 14 sq. rd. A kilogram = 2i lb. ay. An are = 4 sq. rd. A liter = 1 qt. An hectare = 2| A. An hektoliter = 2^ bu. A cubic meter = 1.3 cu. yd. A meti-ic ton = 2200 lb. ORAL EXERCISE 1. Name the prefix which means 10,000; 0.001; 100; 0.01; 10; 0.1; 1000. 2. Read the following: 2.5m.; 72 mm.; 95.5 cm.; 302.05 km. Express 475.125 m. in millimeters ; in hek- tometers. 3. Which of the divisions of the following scale are millimeters? centimeters? 1 2 3 ■4 5 6 7 8 y ,:o 1 1 1 1 III! 1 : 1 decimeter excha:^ge , 373 4. A certain tower is 200 in. high; this is approximately how many feet? 5. How many square meters in 1 a. ? how many ares in 5 Ha. ? in 25 Ha. ? 6. How many liters in 1 cu. m.? in 5 cu. m.? Find the cost of 5 Kl. of milk at 5)^ a liter ; at 4^ a liter. 7. Find the length of your schoolroom in meters; the weight of any familiar object in kilograms. 8. Bought 1000 m. of cloth. How many yards was this ? 9. An importer bought 1000 1. of liquors at 80^ a liter. If he sold it at 13.50 per gallon, did he gain or lose, and how much? 10. The distance from Paris to Cologne is 510 Km.; from Cologne to Mainz 150 Km. Express these distances in miles. WRITTEN EXERCISE 1. At $ 75 an acre find the cost of 75 Ha. of land. 2. Find the cost of 175.75 m. of lace at 65^ a meter. 3. How many steres of wood in a pile 12 m. long, 1.5 m. wide, and 3 m. high? How many cords? 4. A merchant bought cloth at $1.14 per meter, including duties. For how much must he sell it per yard to gain 33^%? 5. I imported 1000 m. of silk dress goods (see duties, page 294) at 10 fr. per meter and sold it at $ 3 per yard. Did I gain or lose and how much, the silk being 1 yd. wide ? 6. The distance between two places on a map is 15.5 cm. ; this is - — i— -- of the actual distance. What is the actual dis- tance in miles? 7. C bought cloth at $2 per meter, including duties, and sold it by the yard at a gain of 25%. What was the selling price per yard? 8. The speed rate of a certain express train is 64 Km. an hour ; of a certain mail train, 48 Km. an hour. In a journey of 384 Km. what time will be saved by taking the express instead of the mail train. 374 PKACTICAL BUSINESS ARITHMETIC Foreign Money Orders 453. Small sums are frequently sent from one country to another by means of foreign money orders. The international postal money order and the foreign express money order or check are both extensively used for this purpose. These orders are usually drawn payable in the money of the country on which they are issued. They are similar in form to domestic money orders, but are issued on prac- tically the same principle as the ordinary bank draft. ORAL EXERCISE 1. D in Chicago wishes to send E in Havre, France, 780 fr. At 19.5^ to the franc, how large an express money order (in U.S. money) can he buy ? 2. B in New York wishes to send $120 to C in Leipzig, Germany. At 24^ to the mark, how large an express money order (in marks) can he buy ? 3. At 1% premium find the cost of an international money order, payable in Great Britain, for each of the following amounts: |40; $50; 175; 1100; $150; 1200. 4. A in Boston bought an international money order for $20 and sent it to a friend in Liverpool, England. At 1% premium, what did the order cost? For how many pounds sterling (approximately) was it issued ? WRITTEN EXERCISE e 1. I wish to send $100 to G in Holland. At 40^^ to the guilder, how large an express money order can I buy ? 2. I wish to send $50 to a friend in Scotland. At $4.87 to the pound, how large an express money order can I buy ? 3. C in Chicago sent D in Geneva an express money order for 256.41 fr. At 19.5^ to the franc, how much did the order cost C ? 4. E in Philadelphia sent F in Naples an international postal money order for 128.21 lira. At 19.5^ to the lira, how much did the order cost E ? EXCHANGE 375 Bills of Exchange 454. Drafts of a person or a bank in one country on a person or a bank in another country are usually called bills of exchange. fe^^ JUL !Q,1915l B ^nSriA-l 455. Bills of exchange may be divided into three classes: (1) bankers' bills, which are drawn by one banker upon an- other ; (2) commercial bills, which are drawn by one mer- chant upon another ; (3) documentary bills, which are drawn by one merchant upon another and secured by the assignment and transfer of a bill of lading and policy of insurance covering merchandise on its way to the market. Theforegoing form is a bankers' demand draft or check. Bankers' bills of exchange are frequently issued in duplicate ; that is, in sets of two of like tenor and amount. These bills are sometimes sent by different mails; but more frequently the original is sent and the duplicate is placed on file to be sent in case of necessity. Duplicate bills are so con- ditioned that the payment of one of them cancels the other. The bankers' sole bill of exchange is also used. This is preferred by many, inasmuch as it may be more easily negotiated by the payee when he resides in a city other than the one drawn upon. Commercial and documentary bills of exchange are usually issued in duplicate. 456. The mint par of exchange is the actual value of the pure metal in the monetary unit of one country expressed in terms of another. 376 PRACTICAL BUSINESS ARITHMETIC The mint par of exchange is determined by dividing the weight of pure gold in the monetary unit of one country by the weight of pure gold in the monetary unit of another. Thus, the United States gold dollar contains 23.22 troy grains of pure gold and the English pound sterling, 113.0016 troy grains. 113.0016 h- 23.22 = 4.8665. Since there is 4.8665 times as much pure gold in the pound sterling as in the gold dollar, the pound sterling is worth 4.8665 times $1, or f 4.8665. The mint par of exchange is used mainly in determining the values on which to compute customs duties. 457. The rate of exchange is the market value in one country of the bills of exchange on another. The price paid for bills of exchange fluctuates. When the United States owes Great Britain exactly the same amount that Great Britain owes the United States, the debts between these countries can be paid without the transmission of money, and exchange is at par. But w'hen Great Britain owes the United States a greater amount than the United States owes Great Britain, exchange in the United States is at a discount and in Great Britain at a premium, and vice versa. The rates of premium or discount are limited by the cost of shipping gold bullion from one country to another. The cost of shipping gold from New York to London is about f %. There- fore, when A in New York owes B in London, and A cannot buy a bill of exchange on London for less than $4.88^ to $4.89, it is cheaper for him to export gold. On the other hand, if D in l^ondon owes C in New York and C cannot sell a draft on D for more than |4.83| to $4.84, it is cheaper for him to import gold. The greater part of exchange is drawn on Great Britain, France, Germany, Holland, Belgium, and Switzerland. Because London is the financial center of the world, probably more foreign exchange is drawn on Great Britain than on all the other countries combined. 458. Exchange on Great Britain is usually quoted at the number of dollars to the pound sterling ; exchange on France, Belgium, and Switzerland, at the number of francs to the dollar ; exchange on Germany, at the number of cents to each four marks; exchange on Holland, at the number of cents to each guilder. The accompanying foreign exchange rates were quoted recently. In Great Britain 3 da. of 60 Days Demand grace are allowed on all bills GennalyrreiciismarksV/////////////.%?y8 *'953| gxa^c aic aiiuwcu uii an uxiia Germany, reichsmarks 947/8 drawn payable after sight, but gg^Yum ^'^*"''' .' " *5i sf drafts on Great Britain payable Switzerland, francs 5.I884 5.15% ^ . ,^ T 11 Holland, guilders 40 40% at sight or on demand have no grace. There are no days of grace allowed on any drafts drawn on Germany, and nearly all Europe, excepting Holland, where 1 da. of grace is allowed. EXCHANGE 377 WRITTEN EXERCISE 1. Using the foregoing table of quotations, or current quota- tions clipped from any daily newspaper, find the cost of de- mand drafts for each of the following amounts : a. £100. d. 160 guilders. g. 200 M. j. 6000 M. h. X1200. e. 240 guilders. h. 160 M. k, 4000 M. c. £1800. /. 1200 guilders. ^. 2000 M. I. 12000 M. 2. Find the cost of a 60-da. draft for each of the amounts in problem 1. WRITTEN EXERCISE 1. F. M. Cole & Co., importers, Boston, owe Richard Roe, London, £525 10s., 6J., buy by check the draft illustrated on page 375, and remit it in full of account. If exchange on London is ^4. 87 J, what was the amount of the check ? 2. Jordan, Marsh & Co. wish to import a quantity of woolen goods from Bradford, England. They make up an order and inclose in payment the following draft which they buy by check, at $4.85 J. What was the amount of the check ? f BKOfWBHOTHERS&CO :^^^^H I % Sfioo — 'M^ f 3ttESS9?BROTI^,SlIIHJEir&CO. /7^ ^^^ 4 JVb._3497___ VcgSOQf^. Brother3 ^ Co. 3. 45 da. before the draft was due (problem 2) John Smith & Co. sold it to Baring Bros, at 2% discount. How much (in English money) did they receive ? Write the indorsements which Would appear on the back of the draft. 37 PEACTICAL BUSINESS ARITHMETIC 4. D. M. Knowlton & Co. drew the following commercial : exchange and sold it to How much was received for it ? bill of exchange and sold it to Kidder, Peabody & Co. at 96| Commercial bills of exchange are usually drawn by exporters against funds abroad which have accumulated to their credit from sales previously made. The exporter generally waits until the rates of exchange are high and then draws the draft as above. 5. Aug. 1 T. H. Reed & Co., exporters, Minneapolis, Minn., bought through their broker, 24,000 bu. No. 1 wheat at 84^ per bushel and paid for same by check. What was the amount of the check, the broker's commission being J ^ per bushel ? 6. Aug. 2 the wheat was delivered and placed with City Elevator for storage. The storage rates were |^ per bushel for the first 10 da. or fraction thereof, and -^^j^ per bushel for each additional day thereafter. On Aug. 15 tlie wheat was withdrawn from the City Elevator and delivered to the Soo Freight Line for shipment to W. B. Radclitfe & Son, Liver- pool. What was the amount of the storage bill ? 7. The wheat was sold to W. B. Radcliffe & Son at £1 12s. 2d, per quarter (8 bu. or 480 lb.). Make out the bill under date of Aug. 15. 8. On Aug. 15 a through bill of lading in duplicate was re- ceived from the Soo Freight Line. If the through freight rate from Minneapolis to Liverpool was 2d. per hundredweight, what was the amount of the freight bill ? EXCHANGE 379 9. Aug. 16, upon presentation of the bill of lading to the Western Assurance Co., the goods were insured for 10% more than their billed value and a certificate of insurance issued. What was the amount of the premium, the rate being 1J% ? 10. T. H. Reed & Co., drew the following draft on W. B. Radcliffe & Son and attached it to the bill of lading and cer- tificate of insurance. These documents, which constitute what is called a documentary bill of exchange, were then offered for sale and later sold to Kidder, Peabody & Co., at the rate of H.84| per pound. How much was received for the bill? sold the draft to 11. Aug. 17 Kidder, Peabody & Co American Express Co. at f4.84J. If the American Express Co. paid by check, what was the amount of the check? 12. American Express Co. forwarded the bill to Provincial Bank, Liverpool, for collection, and this bank presented the draft to W. B. Radcliffe & Son for acceptance. Sept. 1 the wheat arrived by steamer and as the draft was stamped "Sur- render documents only upon payment of draft" W. B. Rad- cliffe & Son had to pay the draft before they could get the docu- ments or the goods. As the draft has 47 da. yet to run, the bank allowed W. B. Radcliffe & Son 1% discount. What was the amount paid by W. B. Radcliffe & Son ? Such drafts are frequently stamped "Surrender documents upon accept- ance of the draft." In such cases the documents would be delivered to the consignee upon the acceptance of the draft, and he could then obtain pos- session of the goods. 380 PRACTICAL BUSINESS ARITHMETIC 13. What was T. H. Reed & Co.'s net gain or loss on the transactions in problems 5-10 ? Letters of Credit and Traveler's Checks 459. A traveler's letter of credit is an instrument issued by a banker instructing his correspondents in specified places to pay the holder funds in any amount not exceeding a specified sum. ULAIl LETTER OF C ^i?*/B 13.683 ClRCULAIl LETTER OF CREDIT ^ ckkw-^Ua^.^JufuAt 2l^y0/S %A I 123 J^llMall.L -^X/t-a-T-^O^rr-ii-xCstx'^-w^ NDON; ^a^i^c 'Messrs BROWN, S H I PLEY.^ Co. 'cnTiyOuleJote' Ou/ytiL' 30 ' — ^yony ec/^ /o^/.2.oo-/ EXCHANGE 381 The purchaser of a letter of credit is required to subscribe his name upon the document as a means of identification later on. Other copies of the signature are left and forwarded to the leading foreign banks drawn upon. When the traveler desires funds, he presents his letter to the proper bank at the place in which he is stopping. The letter itself always specifies the banks that will honor the draft. When the letter is presented to a foreign banker for payment, he draws a sight draft on the London banker, which draft the traveler is required to sign. If the signatures on the letter and on the draft are identical, the amount desired is promptly paid and indorsed on the back of the letter. The indorsements on. the back of a letter show at all times the balance available for the traveler. The bank making the last payment retains the letter to send to the drawee in London. Letters of credit are usually drawn payable in pounds ster- ling, but they are paid in the current money of the country in which they are negotiated. Banks usually charge 1% commission for issuing a letter of credit. 460. Another instrument frequently used by travelers is what is called a traveler's check. When a check is purchased, the buyer signs bis name in the upper left- hand corner. When he wishes funds, he presents his check to the cor- respondent of the express company or bank and signs his name either in the upper left-hand corner or on the back of the check. On the form above, he would sign his name in the lower left-hand corner; but on the form on page 382 he would sign his name on the back. The lat- ter form is considered better because it is more diflBcult to forge an- other's signature when there is no signature near at hand from which to copy. The terms of issue are cash for the face amount plus 1% commission. 382 PEACTICAL BUSINESS AEITHMETIC ORAL EXERCISE 1. At $4.85 to the pound sterling plus 1% commission, what did the letter of credit on page 380 cost? 2. At the same rate, find the cost of a letter of credit for ^500; XIOOO. 3. At 1% commission, what will be the total cost of 10 checks like the sample on page 381? of 20 checks? of 25 checks ? 4. At f 4.85 to the pound plus | % commission, what was the cost of a traveler's check on page 382 ? of a book of 10 checks like the sample on page 382 ? WRITTEN EXERCISE 1. On the letter of credit, page 380, the following payments are recorded on the back : Aug. 31, c£ 200 ; Sept. 9, <£ 400 ; Oct. 15, X 250 ; Nov. 1, X 100 ; Nov. 12, £ 200. The holder returns to New York on Nov. 20 and presents the letter to Brown Brothers & Co. for the refund. At S4.85 to the pound, how much Avill Brown Brothers & Co. pay on the letter? In this problem it is assumed that Brown Bros. & Co. refund 1 % commis- sion on the unused portion of the letter. EXCHANGE 383 2. At 25^ per word and 1% of the amount, find the cost of a twenty -one word cable money order from Boston to Paris for 25,000 fr. when exchange is quoted at 5.15|. Money may be cabled from one country to another on the same principle that it is telegraphed from one part of any country to another part. In a cable message a charge is made for each word in the address of the one to whom it is sent. WRITTEN REVIEW EXERCISE 1. A broker sold for me a bill on Manchester, England, at f 4.84i and charged |% brokerage. What was the face of the bill, if the proceeds were $5218.50? 2. How much remains in the bank to the credit of H. B. Claflin & Co. after the following check was issued ? Bn.JAj2 amount. $ ^liamfii Cru£(t Company to tf>e otUrr iA^&n<^fr^t^^^,i^^-n^J>^ / ,' ,' F -^ l'£yL^tY--'^-^'<^'!^(^^''^- ^^^ * * * ^^aWoWat^ >^,>^H^^ 3. My agent in Brussels, Belgium, purchased for me carpet amounting to 35,000 fr., and his commission was 5%. I re- mitted him a draft to cover the cost of the carpet and the commission for buying. K exchange was 5.15|, and I paid for the draft by check, what was the amount of the check? 4. My agent in Rotterdam sold for me 525 kegs of tobacco, each containing 50 lb., at J guilder per pound, and charged me a commission of 41%. I drew on him for the proceeds and sold the draft to a broker at 40|. If the broker charged |% for his services, what did I receive as proceeds of the draft ? EQUATIONS AND CASH BALANCE CHAPTER XXXI EQUATION OF ACCOUNTS ORAL EXERCISE 1. How long will it take 1 5 to produce the same interest as $10 for 10 da. ? , The use of $100 for 1 mo. is equivalent to what sum for 2 mo. ? 2. If I have the use of 150 of A's money for 30 da., how much of my money should he have the use of for 15 da. in return for the accommodation ? 3. The interest on $40 for 2 mo. plus the interest on $40 for 4 mo. is equal to the interest on $80 for how many months ? 4. D owes E $100; $50 is due in 2 mo. and the balance in 4 mo. In how many months may the whole be paid without loss to either party ? 5. On Apr. 1 I bought a bill of goods amounting to $200, payable as follows: $100 in 3 mo. and the balance in 5 mo. In how many months may the whole sum be equitably paid ? 6. A owes B $400 and pays $200 30 da. before the account is due. How long after the account is due may B have in which to pay the balance ? 461. The process of finding the date on which the settle- ment of an account may be made without loss of interest to either party is called equation of accounts. Sometimes one or more of the items in a personal account are not paid at maturity and the holder of the account suffers a loss ; sometimes one or more of the items are paid before maturity and the holder of the account realizes a gain. To equitably adjust these items of loss and gain, accounts are equated. Retail accounts are not often equated ; but wholesale and commission accounts are frequently equated, particularly foreign ones. 384 EQUATION OF ACCOUNTS 385 462. The time that must elapse before several debts, due at different times, may be equitably paid in one sum is called the average terin of credit ; the date on which payment may be equitably made, the average date of payment, the equated date, or the due date. 463. Any assumed date of settlement with which the several dates in the account are compared for the purpose of deter- mining the actual due date is sometimes called the focal date. The face value of each item should always be used in equating accounts. Items not subject to a term of credit and interest-bearing notes are worth their face value on the day they are dated. Items subject to a term of credit and non-interest-bearing notes are not worth their face value until maturity. SIMPLE ACCOUNTS ORAL EXERCISE 1. If I owe $200 due Jan. 1 and |400 due Jan. 31, when may both accounts be equitably paid in one sum ? Solution. On Jan. 31, there is legally due $600 -f $ 1 (the interest on $200 for 30 da.). Since more than the face of the account is due, the equitable date of settlement is before Jan. 31. It will take $600 one third as long as $200 to produce $ 1 interest, i of 30 da. = 10 da. The whole account may therefore be paid 10 da. before Jan. 31, or Jan. 21, without loss to either party. 2. You sold Baker, Taylor & Co. goods as follows : Apr. 20, 1600; Apr. 30, $600. How mucli is legally due on the ac- count Apr. 30 ? On what day may the whole account, i 1200, be paid without interest ? 3. When is the following account due by equation ? A. B. Comer . 19— Sept. To mdse. To mdse. 300 300 4. Rowland & Hill bought goods of you as follows : Oct. 16, $400; Oct. 31, $800. How much was legally due on the ac- count Oct. 31 ? On what date can the whole of the account, $ 1200, be paid without interest ? 386 PKACTICAL BUSINESS ARITHMETIC 464. Example. On what date may the total of the following account be paid without interest ? F. M. Pratt & Co. 19- Jan. 1 9 15 21 26 To mdse. To mdse. To mdse. To mdse. To mdse. 30 120 150 300 60 00 Solution. Take the latest date, Jan. 26, as the focal date. If settle- ment was made on Jan. 26, the holder of the account might charge interest on each item as shown in the accompanying statement. The holder loses $0.11 per day as long as the account remains un- settled. If settlement was made Jan. 26, the loss would be $ 0.99, or 9 days' interest; therefore if the ac- count were settled 9 da, before Jan. 26, the holder would lose nothing. Date Amount Days Interest Jan. 1 130 25 i.125 9 120 17 .34 15 150 11 .275 21 300 5 ,25 26 60 $660 1.99 The amount of the account = $ 660. The interest on $660 for 1 da. = $0.11. $ 0.99 -=- $ 0.11 = 9, or the number of days. Jan. 26—9 da. = Jan. 17, the equated date. Proof. The proof of the problem must show that the interest on the items dated before Jan. 17^ the equated date, is offset by the discount on the items dated after Jan. 17. The following items are dated before Jan. 17 : Date Interest Period Item [nterest Jan. ltol7 16 da. $30 $.08 9 to 17 8 120 .16 15 to 17 2 160 .05 Total interest $.29 nng items are dated after Jan. 17: Date Discount Period Item Discount Jan. 17 to 21 4 da. $300 $.20 17 to 26 9 60 .09 Total discount, $ .29 The proof shows that the equated date, Jan. 17, is correct. Any rate of interest may be used in equating an account. As a matter of convenience, always use 6 %. If items are subject to terms of credit, add the time to the date of the items before beginning to equate. EQUATION OF ACCOUNTS 387 WRITTEN EXERCISE In each of the following problems find the equated date and prove the work. Assume that all the dates are in 1916. 1. F. M. Drake, Di Mar. 2, To mdse. 8, To mdse. 11, To mdse. 17, To mdse. 23, To mdse. 3. Geo. M. Barton, Dr. Aug. 3, To mdse., 60 da. 1360. 6, To mdse., 30 da. 240. 11, To mdse., 30 da. 19, To mdse., 30 da. 24, To mdse., 30 da. 5. Carter & Co., Dr. May 5, To mdse. 12, To mdse. 16, To mdse. 20, to mdse. 23, To mdse. 1\ Brigham & Co., Dr. Sept. 4, To mdse., 60 da. $600. 9, To mdse., 60 da. 450. 12, To mdse., 60 da. 17, To mdse., 60 da. 22, To mdse., 30 da. 30, To mdse., net, 9. Brown, Kerr & Co., Dr. Oct. 1, To mdse., 3 mo. |210 5, To mdse., 60 da. 840 13. To mdse., 60 da. 720 21, To mdse., 60 da. 24, To mdse., 60 da. 31, To mdse., net, 1120. 180. 60. 240. 150. 300. 60. 180. 1180. 300. 230. 270. 360. 350. 400. 500. 150. 2. Louis M. Allen, Dr. Apr. 3, To mdse. . . $160. 9, To mdse. . . 250. 13, To mdse. . . 100. 19, To mdse. . . 280. 23, To mdse. . . 420. 4. Leon H. Hazelton, Dr. June 6, To mdse. . 9, To mdse. . . 300. 14, To mdse. . . 400. 24, To mdse. . . 600. 27, To mdse. . . 330. 6. Lamson & Roe Co., Dr. Dec. 1, To mdse., 3 mo. 1 294.20. 10, To mdse., 3 mo. 698.40. 20, To mdse., 60 da. 136.60. 24, To mdse., 60 da. 740.60. 28, To mdse., 60 da. 700.40. 8. D. H. Beckwith & Co. Dr. Nov. 3, To mdse., 2 mo. 1 750.50. 8, To mdse., 2 mo. 432.25. 17, To mdse., net, 275.50. 22, To mdse., 2 mo. 210.50. 25, To mdse., 1 mo. 168.30. 28,Tomdse.,lmo. 240.50. 10. D. M. Smith & Co., Dr. 660. 540. 300. July 3, To mdse. 8, To mdse. 11, To mdse. 16, To mdse. 25, To mdse. 29, To mdse. $420.30. 325.70. 417.25. 186.24. 240.60. 126.84. PEACTICAL BUSINESS ARITHMETIC COMPOUND ACCOUNTS ORAL EXERCISE 1. The following is your account with John D. Foster. Had no payment been made, when would the account have been due? Smce no payment was made until after maturity, you have lost the use of $ 400 for how many days ? To offset this loss what should be the date of an interest-bearing note given to cover the balance of the account? Jan. 16 — 30 da. = Dec. ?, the date of an interest-bearing note given to cover the balance of the account. 2. The following is your account with Walter H. Wood. Walter H. Wood 19— Apr. Tomdse.,30da. 600 00 19— Apr. 16 By Cash 300 00 Had no payment been made, when would the account have matured? By the payment recorded you have gained the use of $300 for how many days ? To offset this gain, you should allow Walter H. Wood to keep the balance of the account how many days after maturity? May 1 + 15 da. = May ?, the date on which the balance is equitably due. 3. May 1 B sold C goods amounting to I 500. Terms : 30 da. May 11 C made a payment of $ 250 on account. On what date is the balance of the account due ? 4. Find the date of an interest-bearing note given for the balance of each of the following accounts, assuming that the terms in each case are 30 da.; assuming that the terms are cash. Name a. H. H. Howard b. W. H. Lyman & Co. c. R. H. Delaney & Son Dr. Jan. 1, $400 Jan. 1, $400 Jan. 1, $400 Cr. Jan. 16, 1 300 Jan. 16, $ 100 Jan. 16, 1 200 EQUATION OF ACCOUNTS 389 465. Examples, l. Find the equated date for the following : y^^'y?^.'f:Cd■.^^.icl■tCyyi^6!6<£^y./0.<:^'ay- 360 J!2f / i?f'0 ?y^^^^t?z,<^<#C' 3Co A^ZC> X^/^^^w^ .y_ 1 r=i n .y_ F=^ r=j 1 1 v= /^ /o -^ff->99%-^z.S?::^V~^^^^^ '?— 1 =\ 'f — 1 1 r= P^ta^ Z3 -i^tryy-rua^^i.^-. y^iU^ cfjr /J^O — ?Uc^^ ZS -I^^CiZ^lX' ^/// / iTi) - Jn It >/ Jo^a^ ^^l fOO — ^Unu. 2f // // €Mi ^^^O — JUu C rf >f t> If ^Ji / O(>0 ~ ^4 s- // >> €yo ^ATO — zz. ff /> tf '1 /-./ J-uo&-un^i^ (&. /^ational CXjank. Z=^S)oU€trs S>ioid4!nd J{o.Jz^ feasurer 5. A company with 11,000,000 capital declares quarterly dividends of 1^ % . What are the annual dividends ? What is the amount received annually by D, who owns 475 shares ? 6. A corporation with a capital of 1 125,000 loses $2500. What per cent of his stock must each stockholder be assessed to meet this loss? How much will it cost A, who owns 150 shares ? 7. A company with a capital of % 750,000 declares a semi- annual dividend of 3^%. How much money does it distribute among its stockholders annually? What is the annual income of a man who owns 200 shares ? STOCKS AND BONDS 401 8. If the Pennsylvania Railroad declares a semiannual divi- dend of 2i% x)n a capital stock of S 500,000,000, what amount is annually distributed among the stockholders ? What is the annual income to J. P. Morgan from this stock if he owns 7,500,000 shares having a par value of 1 50 each? 9. During a certain year a manufacturing concern with a capital of -i) 750,000 earns •$ 75,500 above all expenses. It decides to save §15,500 of this for emergencies and to divide the remainder in dividends. What is the rate ? What would be the amount of A's dividend check if he owns 125 shares ? 10. The capital stock of the Gramercy Finance Company is $1,500,000. The gross earnings of the company for a year are §375,000 and the expenses 1215,000. What even per cent of dividend may be declared and what would be the amount of un- divided profits if 10% of the net earnings are first set aside as a surplus fund ? (An even per cent is a per cent without a fraction.) 11. A railway company has a capital of §3,500,000 and declares dividends semiannually. During the period from Jan. 1 to July 1 of a certain year the net earnings of the com- pany were §191,000. Of this amount 10 % is carried to surplus fund. What even rate per cent of dividend may be declared on the balance and how much will be carried to undivided profits ? 12. A company with a capital stock of §500,000 gains during a certain year §38,750. It decides to carry §5000 of the profits to surplus fund and to declare an even per cent of dividends on the remainder. What sum was divided among the stockholders, and what sum was carried to undivided profits account ? What was the annual income to F from this stock if he owned 500 shares ? 13. During a certain year the gross earnings of a railroad having a capital stock of §100,000,000 were §65,150,000, and the operating expenses §45,150,000. If the company declared a semiannual dividend of 3^ % and carried the balance of the net earnings to undivided profits account, how much was divided among the stockholders ? How much was the working capital of the company increased ? 402 PRACTICAL BUSINESS ARITHMETIC 14. The capital stock of the First National Bank is S 3,000,000, and dividends are declared semiannually. The profits of the bank for a certain six months are $185,750. Of this sum 10% is carried to a surplus fund. The directors then vote to declare a semiannual dividend of 3|^% and carry the balance of tlie profits to undivided profits account. What amount was carried to surplus fund account? to dividend account? to undivided profits account? Buying and Selling Stock 480. The following is an abbreviated form of the stock quo- tations for a certain day on the New York Stock Exchange : Table of Sales and Range of Prices Sales Stocks Open. High. Low. Clos. Net Change 2,600 Am. Sugar .... lOOi lOOi 99i 99f -f 200 Am. Sugar (pfd.) 110 llOir 109i 109i -1 10,200 Atchison .... 95^ 95i 91f 92 -3i 300 Atchison (pfd.) . . 100 100 100 .100 900 At. Coast Line . . 121i 120 116 116 -4i 13,600 Baltimore & 0. . . 88i 881 87i 88 -i 600 Baltimore &0. (pfd.) 80i 81 80i 80i -i 147,100 Canadian Pacific . . 1931 200f 188i 1891 -3f 20,200 Chic. M. & St. P. . 98| 98+ 94i 95 -3f 300 Chic. M.& St. P. (pfd.) 137f 135 134^ 134i -2 200 General Chem. (pfd.) 108 109 108i 109 + 1 2,500 General Electric . . 144 144 141 141 -3 15,600 Gt. Northern (pfd.) . 122 121f 119 119i -2i 1,600 Illinois Central . . 110 110 107i 107f -2| 59,800 Lehigh Valley . . 136i 136i 132i 134f -If 650 Louisville & Nash. . 135f 135i 131i 131i -H 2,100 NatU Biscuit . . . 131 130i 125 125 -5 100 Nat'l Biscuit (pfd.) . 123 123i 123f 123^ + i 69,200 South. Pacific . . . 92i 9H 86i 87i -5i 300 South. Pacific (pfd.). lOOi 97i 97i 97i -2f 210,100 Union Pacific . . . 154i 154i im 1491 -4 400 Union Pacific (pfd.) . 82i 82i 82 82 -i 390,100 U.S. Steel .... 58i 58f 56 56f -2| 4,200 U.S. Steel (pfd.) . . 109 109i 107i 107i -n In the first column is shown the number of shares of stock sold ; in the second, the name of the stock ; in the third, fourth, fifth, and sixth, respec- tively, the opening, the highest, the lowest, and the closing prices of the day ; in the last, the net changes between the closing price of yesterday and to-day. Thus, 2600 shares of American Sugar stock were sold. The opening price was 1100.50 per share ; the highest price $ 100.50 ; the lowest, 199.25 ; the closing, $99.75, which shows a decline of 75)* from the preceding day. STOCKS AND BONDS 403 ORAL EXERCISE 1. Find in the table (page 402) three eases where a quo- tation both for common stock and for preferred (^})fd. stands for preferred) stock of the same company is given. Which is worth the more in each case ? The par value of all shares is SI 00. If the profits of a concern are so great that a large per cent may be paid on the common stock, after paying tlie fixed rate on the preferred stock, then the common stock may sell for a higher figure than the preferred. 2. What would 100 shares of American Sugar (common) cost if bought through a broker at the lowest price for the day, brokerage being |-%. 3. What would the seller of the stock realize on the sale ? Suggestion. The seller would receive the price for which it was sold minus the brokerage, \ %. 4. State the cost, at the opening price in the table, of 100 shares each of the following stocks, assuming that the transac- tions take place through a broker who charges '^ % commission : Baltimore & Ohio ; Canadian Pacific ; General Electric ; Lehigh Valley. (Base the calculations on the common stock.) 5. At the highest price in the table, state the amount that would be received from the sale of 100 shares of each of the following stocks, assuming that they were sold through a broker who charged |^'% commission: Southern Pacific; U.S. Steel (pre- ferred); Great Northern (preferred) ; National Biscuit; Ameri- can Sugar (preferred) ; Atchison ; General Chemical (preferred) ; Illinois Central ; . Union Pacific. (If preferred is not named, common stock is referred to.) WRITTEN EXERCISE Find the cost, at the closing price in the table, of 2500 shares of the following stocks, including brokerage : 1. Canadian Pacific. 4. Baltimore & Ohio (pfd.). 2. American Sugar (pfd.). 5. Atlantic Coast Line. 3. National Biscuit (pfd.). 6. United States Steel (pfd.). 404 PRACTICAL BUSINESS ARITHMETIC At the closing price for the day find the amount received from the sale of 3500 shares of the following stocks sold through a broker : 7. Illinois Central. il. Atchison (pfd.). 8. Louisville & Nashville. 12. General Electric. 9. Southern Pacific. 13. Southern Pacific (pfd.). 10. Lehigh Valley. 14. Great Northern (pfd.). 481. Example. I bought 1000 shares Chicago, Milwaukee, & St. Paul preferred stock, at the lowest price in the table, and sold the same at 1401. Allowing for brokerage both for buying and selling', did I gain or lose, and how much ? S140 371 Solution. Since I bought through a broker, each share * 2 cost me $ 134.871 + |0.12^, or $ 135 ; and since I sold through 1^5.00 a broker, the proceeds of each share sold was $140.50 — .^0.12^, S 5.37i- or $140.37|. $ 140.371 - $135.00 := S5.37|, gain on each 1000 share. Since 1 5.37^ is gained on each share, 1000 times |5.37i, or $5375, is gained on 1000 shares. ^bdlb. In the following exercise it is understood that all sales and purchases are made through a broker, who charges a commission of i% both for buying and for selling. WRITTEN EXERCISE Find the gain or loss on 500 shares of each of the following stocks bought at the opening price and sold at the price here given : 1. Illinois Central, 108|. 5. American Sugar (pfd.), 103. 2. General Electric, 147|. 6. National Biscuit, 134i. 3. Southern Pacific (pfd.), 89. 7. Baltimore & Ohio, 90|. 4. General Chemical (pfd.), 110. 8. Canadian Pacific, 200^. 9. United States Steel (pfd.), 112 1. 10. Atlantic Coast Line, 115|. 11. Great Northern (pfd.), 125. 12. National Biscuit (pfd.), 126|. 13-24. Find the gain or the loss on 1000 shares of each of the above stocks bought at the lowest price and sold at the highest price, in the table. 25. John R. West bought 400 shares of United States Steel, (common) at the opening price in the table and sold it so as to gain $300. What was the quoted price when he sold it? STOCKS AND BONDS 405 26. I bought some United States Steel (preferred) at the opening price in the table and sold it for 112i. If I gained S650 by the transaction, how many shares did I buy? 27. I bought 2500 shares of General Electric at the lowest price in the table, held it for a year, received 5 % in dividends, and then sold it at 139|. If money was worth 41 %, did I gain or lose, and how much ? The interest is to be computed on the cost of the stock, the dividend on the par value. 28. I gave my broker orders to buy 1500 shares of Atchison (preferred) and to sell 2000 shares of Canadian Pacific. If he bought at the lowest price in the table and sold at the highest price, what balance will he put to my credit ? BONDS 482. A bond is an instrument by which a government, a municipality, or a corporation contracts and agrees to pay a specified sum of money on a given date, at a specified rate of interest. — Rollins. Bonds are generally issued at a face value of $ 1000 ; less frequently, of •$500 ; occasionally, of f 100. All bonds of the same issue usually have the same rights and security. Bonds, the payment of which depends only on the unsecured credit of the issuing company, are called debenture bonds; those that have their pay- ment secured by a mortgage on the property of the issuing corporation are called mortgage bonds ; those that are secured by a deposit with a trustee of collateral are called collateral trust bonds ; those that provide that the interest on them shall be paid only if earned are called income bonds. Bonds of a national govermnent are called government bonds; of a state, a city, a town, or other municipal organization, municipal bonds. The names of the different government bonds are usually derived from the interest they bear and the time when they mature. Thus, " U. S. 2s, 1930," are United States bonds bearing interest at 2% and maturing in 1930. From the gross earnings of a company the operating expenses are first deducted; from the net earnings are deducted all fixed charges, such as interest on bonds ; then the dividends on preferred stock are paid ; and finally out of the remainder dividends on the common stock are paid. 406 PRACTICAL BUSINESS ARITHMETIC 483. With reference to the form of contract for the payment of principal and interest there are two kinds of bonds : coupon and registered. 484. A coupon bond is a bond to which are attached interest notes, or coupons, representing the interest due on the bond at stated periods of payment. STOCKIS AND BONDS 407 The interest notes may be cut off from the bonds at maturity and the amount of interest which they represent collected through a bank. If these notes are not paid when due, they bear interest at the legal rate. 485. A registered bond is a bond which has no separate con- tract for the payment of the interest. Such a bond must be recorded on the books of the corporation in the name of the holder to whom the mterest is sent by check. Coupon bonds may be made j>ayable either to bearer or registered as to principal only (the first custom prevails generally), and may be transferred by delivery or indorsement accordingly. Registered bonds are always drawn payable to some designated person and can be transferred only by assignment and registry on the books of the corporation. ORAL EXERCISE 1. Examine the bond on page 406. With reference to tlie form of contract, what kind of a bond is it ? 2. How many interest notes (coupons) Avould be attached to the full bond? 3. When was the bond issued ? What date (of maturity) should be written on each interest note ? 4. What is the face of the bond ? What rate of interest does it bear ? What sum should be written on each interest note ? 5. How may coupon bonds be transferred ? registered bonds ? All bonds are bought and sold " and interest " ; that is, interest should be reckoned on the par value from the date of the last interest payment to the date of the purchase or sale, at the rate which the bond pays. 6. If the bond on page 406 was quoted at 105|^ when it was purchased, how much did it cost, including 1 % brokerage ? How much did the seller realize on it, if sold Aug. 1. 1915 ? 7. Has the city or town in which you live any bonded in- debtedness (mdebtedness secured by bonds) ? If so, what are these bonds called, and what rate of interest do they pay ? 8. What is the difference in the meaning of government bond and municipal bond ? Upon what authority does the government issue bonds ? Upon what authority does a town or a city issue bonds ? Must the bond issue be approved by the state in which the town or the city is located ? 408 PEACTICAL BUSINESS ARITHMETIC The Use of Bond Tables 486. The use of tables for finding tlie interest on notes, bonds, etc., is common among bankers and brokers. No interest tables are illustrated in this connection because they are too extended and complex for a textbook. Referring to the bond table, page 409, the per cents at the top of the table represent the income on the face of a bond at one of the given rates, and the per cents given in the column at the left represent the income that will be realized when a bond is bought at a certain market price. This table is for a bond maturing 20 yr. from date, with interest payable semiannually. 487. Example. What will be the net income on a 5 % bond bought at 97.53? Solution. In the column headed 5% find the price named, 97.53, then fol- low this line to the left and note that in the Ter Cent per Annum column 6.20 is given; the net income on the price paid for the bond, 97.53, will be 5.2%. ORAL EXERCISE He/er to the table and find the cost of: 1. A 6 % bond that will net 61 %. 2. A 3 % bond that will net 5 %. 3. A 41 % bond that will net 4.8 %. 4. A 4 %, bond that will net 51 %. 5. A man purchased 4 bonds, as follows : a 3 % bond that would net 4.6 % ; a 41 % bond that would net 4:%; a 5 % bond that would net 41 %. What did he pay for each bond ? Refer to the table and find the net income of : 6. A 5 % bond that will cost $91.15. 7. A 7% bond that will cost S125.10. 8. A 3% bond that will cost S 79.95. 9. A 6 % bond that will cost S 106.02. 10. A man purchased 5 bonds each of which netted him 5 % income. If the bonds which he bought yielded, on the face value, the following rate of income, what did he pay for each one : 4 %, 31 %, 5 %, 6 %, and 7 % ? STOCKS AND BONDS 409 A BOND TABLE 20-YEAR. Interest Payable semiannually Per Cent PER Annum 3% ^% 4% H% 5% 6% 7% 3.70 90.17 97.19 104.21 111.24 118.26 132.30 146.35 31 89.51 96.50 103.50 110.49 117.48 131.46 145.44 3.80 88.80 95.82 102.78 109.74 116.70 130.63 144.55 H 87.90 94.81 101.73 108.64 115.56 129.39 143.22 3.90 87.58 94.48 101.38 108.28 115.18 128.98 142.78 4. 80.32 93.16 100.00 106.84 113.68 127.36 141.03 4.10 85.09 91.86 98.64 105.42 112.20 125.76 139.32 4i 84.78 91.54 98.31 105.07 111.84 125.37 138.90 4.20 83.87 90.59 97.31 104.03 110.75 124.19 137.63 H 83.27 89.96 96.65 103.35 110.04 123.42 136.80 4.30 82.68 89.34 96.00 102.66 109.33 122.65 135.98 4f 81.80 88.42 95.04 101.65 108.27 121.51 134.75 4.40 81.51 88.11 94.72 101.32 107.93 121.14 134.35 H 80.35 86.90 93.45 100.00 106.55 119.65 132.74 4.00 79.22 85.72 92.21 98.70 105.19 118.18 131.16 H 78.94 85.42 91.90 98.38 104.86 117.82 130.77 4.70 78.11 84.55 90.99 97.43 103.86 116.74 129.61 4f 77.57 83.98 90.39 96.80 103.20 116.02 128.84 4.80 77.02 83.40 89.79 96.17 102.55 115.32 128.08 4| 76.22 82.56 88.90 95.24 101.59 114.27 126.95 4.90 75.95 82.28 88.61 94.94 J01.27 113.92 126.58 5. 74.90 81.17 87.45 93.72 100.00 112.55 125.10 5.10 73.86 80.09 86.31 92.53 98.76 111.20 123.65 5i 73.61 79.82 86.03 92.24 98.45 110.87 123.29 5.20 72.85 79.02 85.19 91.36 97.53 109.87 122.22 5i . 72.34 78.49 84.64 90.78 96.93 109.22 121.51 5.30 71.85 77.97 84.09 90.21 96.33 108.57 120.81 5f 71.11 77.19 83.27 89.36 95.44 107.60 119.77 5.40 70.87 76.94 83.01 89.07 95.14 107.28 119.42 H 69.90 75.92 81.94 87.96 93.98 106.02 118.06 51 68.72 74.68 80.64 86.59 92.55 104.47 116.38 5f 67.57 73.46 79.36 85.26 91.15 102.95 114.74 51 66.43 72.27 78.11 83.95 89.78 101.46 113.13 6. 65.33 71.11 76.89 82.66 88.44 100.00 111.56 6i 64.25 69.97 75.69 81.41 87.13 98.57 110.01 Qi 63.19 68.85 74.51 80.18 85.84 97.17 108.50 6| 62.15 67.76 73.36 78.07 84.58 95.79 107.01 6^ 61.14 66.69 72.24 77.79 83.34 94.45 105.55 6f 60.14 65.64 71.14 76.64 82.13 93.13 104.12 61 59.17 64.62 70.06 75.50 80.95 91.83 102.72 6i 58.22 63.61 69.00 74.39 79.78 90.57 101.35 7. 57.29 62.63 67.97 73.31 78.64 89.32 100.00 410 PRACTICAL BUSINESS ARITHMETIC Buying and Selling Bonds 488. Bonds are generally bought and sold through invest- ment bankers or private bankers. Tlie commission for buying and selling bonds is the same as for buying and selling stocks. 489. The following table is an abbreviated form of the sales, and the opening, highest, lowest, and closing prices of bonds traded in on the New York Exchange on a recent date. Table of Sales and Range of Prices Sales Bonds Open, High. Low. Clos. Net Chance 5,000 Am. Hide & Leather 6s 103i 103i 103 104 + f 8,000 Brooklyn Rapid Tran- sit con. 5s . . . . 103 103 102f 103 6,000 Chesapeake & Ohio 5s 1061 107i 1061 107i + f 81,000 Chicago, Burlington & Quincy 4s . . . 93i 93i 92f 92f - 1 15,000 Erie 1st con. 4s . . 851 85f 85 85 -1 1,000 Illinois Central 4s . . 93i 93i 93i 93^ 11,000 Lehigh Valley con. 4^s 99f m 991 m -i 1,000 Louisville & Nashville gold 5s .... 108 110 110 110 + 2 2,000 Manhattan Ry.con.4s 92 92i 91| m -i 8,000 Missouri Pacific 4s . 59 57 56 56 -2 24,000 N.Y. Central & Hud- son River 4s 1934 . m 911 89i 90 • - H 35,000 Reading general 4s . m 95 94i 9H -i 1,000 Standard Gas 6s . . m 89f 89f 89 -f 4,000 Texas Pacific 1st 5s . 102 102i 102 lOU -1 62,000 Union Pacific 1st 4s . m m 97i 9()| -f 196,000 United Steel 5s . . 102ir 1021 102i 10l| -i 18,000 Wabash 1st 5s . . . 103^ 104 103i 102f -1 8,000 West Shore 4s . . 93i 94 93f 93i -i In the first column is shown the par value of the bonds sold; in the second, the name of the bonds and the interest they bear ; in the third, fourth, fifth, and sixth, respectively, the opening, highest, low^est, and closing prices of the day. In the last column, Net Cliamje, the net changes between the closing prices of the given day and the closing prices of the day preceding. Thus, on the day given, $8000 worth of Brooklyn Rapid Transit bonds bearing 5 % interest were sold. The opening price was $ 103 per $100 of par value ; the highest price, $103 ; the lowest price, $102.621 ; the closing price, $ 103 ; there was no change between the closing price of the day given and the day preceding. STOCKS AND BONDS 411 490. Example. What is the cost of $50,000 (par vakie) Chicago, Burlington & Quincy 4% bonds at the highest price quoted in the table (page 410) ? Solution. $100 of par value cost ifiOSf + .$0.12| brokerage, or $ecause of the lack of a common center for sellinsf such vSecurities. STOCKS AND BONDS 415 495. The principal ways in which stocks are bought and sold are as follows : stocks bought or sold are deliverable on the fol- lowing day unless otherwise specified ; this is called " regular " delivery. However, securities are not delivered on Saturdays nor on stock exchange holidays. Transactions may be for " cash," that is, deliverable on the day of sale ; " at 3 da.," that is, deliver- able on the third day following the sale ; "buyer's option," that is, deliverable at the option of the buyer at any time within the option period (from 4 to 60 da.) ; "seller's option," that is, deliverable at the option of the seller at any time within the option period. By far the largest part of the sales are "regular," On "cash," "regular," and " at 3 da." sales no interest is paid ; but on options over 3 da., interest at the legal rate on the selling price of the stock is paid by the buyer to the seller. To terminate an option of over 3 da., one day's notice is required. 496. A margin is a sum of money deposited with a broker to cover losses which he may sustain on behalf of his principal. Stocks and bonds are often bought and sold on a margin, as follows : June 8, A. M. Grey son deposited with Richard Roe & Co., his brokers, $ 4160, and instructed them to buy 400 shares of Atchison, Topeka and Santa Fe Railroad stock whenever they could do so at 104. On the same day the stock was bought in accordance with instructions. On June 14, pursuant to instructions, Richard Roe & Co. sold the stock at 107 J and sent A. M. Greyson the following statement and a check for $5322.56. M^^ ^7^^ New York, ■e-i'.^L>,4-r?'?7^ '^^^y? j>^ / e/:^ .19- /^^ -/yy'^Jl-^'M<~^ ^ ^ In account current with RICHARD ROE & CO. DATE AMOUNT DAYS INTEREST DATE AMOUNT DAYS INTEREST A- 7^ '/^DO-dA^a.^u^ oe OO c ^/ Co ^U^ r /4^ 1^ c^rvteyU..ay/^ OO OO C ^7 i^yoio OO */■/ Co ¥7oCo OO 4^/ Co M H H H By the above transactions A. M. Greyson has gained $1162.56. The amount of margins demanded by a broker depends upon the charac- ter of the stocks traded in. On stocks that have a good market 10% of the market value is usually demanded ; on stocks that have little or no market 416 PRACTICAL BUSINESS ARITHMETIC 20 % of the market value or more is often required. The broker, of course, pays for the stock in full. In order to do this he is frequently obliged to borrow money from a bank. This he may usually do by depositing (hypothecating) stock as security (see page 335). The speculators on the stock exchange may be divided into two classes : bulls and be^rs. A bull is a speculator who buys stocks in the expectation of selling them at a higher price. A bear is a speculator who sells stocks which he does not own, in the expectation that he can buy them at a lower price before the date on which they must be delivered. A bull who has bought is said to be long of stock ; a bear who has sold is said to have sold sliort, or to be slwrt of stock. A bull works for advancing prices ; a bear for declining prices. A bull, when selling at higher prices, is said to have realized his profits, or to have liquidated if he sells, whether the price he received is higher or lower than the price he paid. The term liquidate signifies the selling of securities held for long account and implies no dis- tinction between sales at a profit or sales at a loss. A bear, when he buys stock, is said to have covered, no matter whether he bought at a gain or at a loss. WRITTEN EXERCISE (All interest computations are at 6%) 1. On June 25 I purchased, through a broker, 300 shares of Amalgamated Copper at 67|- b. 3 (buyer's option any time within 3 da.). On June 28 the stock was dehvered and, pur- suant to my instructions, sold for 69| cash. Did I gain or lose, and how much ? 2. On April 15 my broker purchased for me 500 shares Delaware & Hudson at 1721 regular. On April 16 he sold the same at 174| cash. What was my gain ? 3. On Sept. 15 I bought, through a broker, 250 shares Read- ing (preferred) at 68| b. 30. On Sept. 25 my broker demanded the stock and, in accordance with my instructions, sold it for 70i regular. Did I gain or lose, and how much ? 4. On Dec. 1 D bought of me, through C, his broker, 2000 shares of Chicago, Milwaukee & St. Paul at 99^ s. 60 (seller's option any time within 60 da.). On Dec. 17 C, pursuant to my instructions, delivered the stock which he had purchased for me on the previous day at 96 regular. Did I gain or lose, and how much ? STOCKS AND BONDS 417 5. Jan. 15 I deposited S4080 with my broker and instructed him to buy 400 shares of Baltimore & Ohio whenever he could do so at 92 regular. On the same day he bought the stock as directed. On Feb. 27 I ordered him to sell, and he did so at 95 1 cash. What was my net gain ? 6. May 25 a speculator sent his broker a margin of $2000 with which to buy 100 shares Metropolitan Street Railway at 165 regular. The broker invested as directed. On May 27 the stock rose to 170| and the broker was authorized to sell. If he sold regular at this price, what was the speculator's gain ? the broker's commission? 7. What is the balance due on the following account current: New York,. lA^t f^ -j^^yf^ ^ T^.^^^^J^?-,^. yytr ^i ^/ ^./7 -*9- ^^^ -fyJr^^^.^.-^'^^ In account current with RICHARD ROE & C \o. DATE AMOUNT DAYS INTEREST DATE AMOUNT DAYS INTEREST 7^t ? p // m >? Tfta^ /O 2~S ?f ? ? ? CO // .'/ v PRODUCE EXCHANGES 497. Just as there are stock exchanges in many of the large cities to supply a regular market for the purchase and sale of securities, so there are produce exchanges (also called boards of trade, chambers of commerce, etc.) to supply a regulated market for the purchase and sale of farm crops. Produce exchanges are important accessories of commerce. They promote jiist and equitable principles of trade ; establish and maintain a uniformity in commercial usages ; and acquire, preserve, and disseminate valuable business information. The more important produce exchanges, by inspecting and grading all of the important food products, protect the public against fraud and adulterations. The cereals, for example, are 418 PRACTICAL BUSINESS ARITHMETIC inspected and graded according to their quality. There are usually four grades of wheat, six of corn, and four of barley, oats, and rye ; No. 1 wheat is the best quality, No. 4, the poorest, etc. The principal produce exchange in the United States is the Chicago Board of Trade. On the floors of this exchange are bought and sold a large part of the cereals and the meat products of the Mississippi Valley and the West. The association thus practically determines the price of these com- modities, not only for the United States, but for the world. Commodities are bought and sold on the exchanges for present or for future delivery. Contracts for present delivery are called cash contracts ; contracts for future delivery, futures. Speculative trading in grain and. cotton is usually in " futures." The established brokers' commissions on the Chicago Board of Trade are as follows : for grain, $7.50 per 5000 bu. ; for pork, -^ 12.50 per 250 bbl. ; for lard, $15 per 250 tierces ; for ribs, $12.50 per 50,000 lb. The lowest margins received are : Ope^. High. Low. Clos. wheat, 5 /^^ per bushel ; corn and oats. Wheat — July .. 87 89^ 87 88| 3;* per bushel; pork, $1 per barrel; ^Slg^^ig ^ «?j ^| lard, 1 2 per tierce ; ribs, ^f per pound. Com —July 68| 68§ 67f 68^ The margins demanded are some- cornlDec*' '"fi^ S^ ^^ 5?f times higher than the above figures. Oats— July . , . . 37| 37| sil 37| In the accompanying table is r=Dr::::Si S| ^f f^ shown the opening, highest, lowest, Pork— July ...2120 2135 2120 2135 and closing prices of provisions for Jr:^,ZfX::::To^ foil To^ fo'^ a certain day on the Chicago Board Lard— Sept. ... 10 17 10 25 10 17 10 25 of Trfldp Lard — Oct 10 22 10 27 10 22 10 27 Wr, T- Kibs- July ....1152 1160 1150 1160 " Wheat — July " signifies wheat Ribs — Sept 11 52 11 57 11 52 11 57 to be delivered in July ; " Wheat — ^^^ " ^«* 11 30 11 35 11 30 11 35 Sept." wheat to be delivered in September, etc. The usual time for future delivery is during the months of May, July, September, and December. In the following exercise it is assumed that all transactions are effected through a broker, who charges the usual commission. WRITTEN EXERCISE 1. What will it cost me to buy 5000 bu. September wheat at the opening price in the table ? 2. C bought 10,000 bu. July oats at 35/ per bushel and sold the same at the closing price in the table. What was his net gain ? 3. B bought 15,000 bu. July corn at the lowest price and sold the same at the highest price in the table. Did he gain or lose, and how much ? What per cent ? STOCKS AND BONDS 419 4. G bought 2250 tierces (765,000 lb.) of October lard at $ 7.26| and sold the same at the closing price in the table. Did he gain or lose, and how much ? 5. F bought 1500 bbl. of September pork at the opening price and sold the same at the closing price in the table. Did he gain or lose, and how much ? 6. D ordered his broker to sell 5000 bu. September corn and buy 5000 bu. December corn. If the broker sold at the highest price and bought at the lowest price in the table, what amount should he remit D ? 7. A broker bought on his own account 10,000 bu. of each, September wheat, December corn, and July oats, at the opening price, and sold the same at the closing price in the table. Did he gain or lose, and how much ? 8. H sold " short " 10,000 bu. September wheat at the highest price in the table. September wheat subsequently declined to 85J and he bought at this price to "cover his short." Did he gain or lose, and how much ? 9. June 27 I deposited with my broker a margin of f 200 for the purchase of 5000 bu. of September wheat at the lowest price in the table. On July 25 I ordered him to sell. He did so, receiving 89|^ per bushel. How much should he pay me in settlement ? 10. Aug. 5 I deposited with my broker $2500 as a margin for the purchase of 5000 bbl. of October pork at the closing price in the table. On Sept. 2 I ordered him to sell at $13,071 He did so and remitted me a check for the amount due. What w^as the amount of the check ? CHAPTER XXXIV LIFE INSURANCE 498. Life insurance companies, like fire insurance companies (page 278), are usually either stock companies or mutual com- panies. There are also assessment companies and fraternal beneficiary associa- tions. These usually depend upon monthly assessments or " calls " to pay death claims. They are required by law to hold but comparatively little, if anything, as a fund from which to pay losses. 499. Insurance rates are always a certain price per $1000 of insurance. They are payable annually, semiannually, or quarterly in advance. 500. The four leading kinds of policies are : ordinary life, limited life, endowment, and term. 501. An ordinary life policy, in consideration of premiums to be paid during the life of the insured, guarantees to pay at his death a stated sum of money. 502. A limited life policy, in consideration of premiums to be paid for a fixed number of years, guarantees to pay a stated sum of money at the death of the insured. It will be observed that in an ordinary life policy the premiums are pay- able during the life of the insured, while in a limited life policy they are payable for a fixed number of years, when the policy becomes paid up (no more premiums due). The premium is higher on the latter form of policy. 503. An endowment policy, in consideration of premiums paid for a fixed number of years, guarantees to pay a stated sum of money to the insured at a certain time or to the hene- jieiary (one in whose favor the insurance is effected) in case of prior death. 504. A term policy, in consideration of premiums paid for a fixed time, guarantees to pay a stated sum of money if the insured dies within the term of insurance. 420 LIFE INSURANCE 421 Thus, a person may insure his life for a limited number of years only. Since the company may never be called upon to pay the insurance, the premiums on these policies are low. 505. The reserve is that part of the premiums of a policy, with interest thereon, required by law to be set aside as a fund to be used in payment of the policy when it falls due. The legal rate of interest on reserve funds varies slightly in different states. The higher the rate of interest, the smaller tne i.^erve required. 506. The surplus of an insurance company is the excess of its assets (resources) over its liabilities. This fund, with certain restrictions, may be used for such purposes as the company deems best. After retaining a surplus large enough to pro- vide for contingencies, companies which issue policies on the mutual or participating plan divide the remainder of the surplus among such of its policyholders as are entitled to share in it. This is practically a return of an overcharge, but it is usually called the payment of a dividend. 507. Dividends may be used: (1) to reduce the next year's premium ; (2) to purchase additional insurance, payable when the policy matures ; (3) to shorten the time to run. Dividends may also be left with the company, with the distinct under- standing that there shall be no division of the same until the end of a certain period. As the policyholder receives no benefit unless he surrives the selected period, it will be seen that the return should be some- what larger. This plan is called semi-tontine, distribution period, accumu- lated surplus, deferred dividend, etc. 508. If a policy is discontinued, the insured may secure an equitable return for the reserve accumulated. The insured usually has several options in this matter : (1) he may take the cash value, or practically- all of the reserve value of the policy; (2) he may take a paid-up policy for such an amount as its reserve value will pur- chase ; (3) he may take extended insurance for the face of the policy for as many years and days as its reserve value will purchase. Annual Premium Rates for an Insurance of $1000 Age Ordinary Life 20-Paymknt Life 15-Year Endowment 20- Year Endowment 25 20.93 30.90 66.57 48.93 30 23.75 33.76 67.27 49.72 35 27.39 37.25 68.26 50.88 40 32.16 41.60 69.76 52.70 50 . 47.23 54.65 76.20 60.59 422 PRACTICAL BUSINESS ARITHMETIC ORAL EXERCISE 1. What kind of a policy is that on page 423 ? Who is the beneficiary ? the insured ? What is the annual premium ? 2. Should the beneficiary die in 1912, to whom would the policy be payable at the death of the insured in 1920 ? 3. Should the insured die after having paid one annual premium, how much would his heirs receive ? 4. If the surplus earnings (dividends) on the policy amount to $1200, at the end of 10 yr., how much cash (see page 424) would the insured receive should he surrender the policy ? 5. Should the insured decide to discontinue paying premiums after making five annual payments, how much paid-up in- surance, exclusive of the surplus, might he receive ? 6. How large a sum may the insured borrow on the policy after ten premiums have been paid ? 7. If the company secures interest in advance by deducting it from the amount of the loan, and the insured should borrow 14000 for one year at 5 %, what would be the amount of the check which he would receive from the company ? 8. Had the insured taken out the policy w^hen he was twenty-five years of age, what would be the annual saving, exclusive of interest, in the cost ? How much would he have saved in 15 yr. ? in 20 yr. ? 9. If the insured should discontinue paying premiums after 5 yr. and take extended insurance, how much would the beneficiary receive should the insured die in 1914? in 1919? 10. If the insured had taken a life policy (see rates, page 421) for the same amount, instead of an endowment policy, and died after having paid ten full premiums, how much less would his insurance have cost, exclusive of dividends and interest ? 11. If the insured should pay four full premiums on the policy, take extended insurance, and die 5 yr. later, how much would his beneficiary receive ? 12. If the insured discontinues making payments after seven annual premiums had been paid, how much would he get in cash at the end of 20 yr. from date of issue, if living ? LIFE INSURANCE 423 /C>,(P^J2. in Vw<0nSlClCri3.tl0n of the Application for this Policy, hereby made a part of this contract. The Penn Mutual Life Iqsurance Company of Philadelphia insures the life of tOtOat^ f^. ^ix6|?<>U " in the County of 'V^VOttl AGE SUM INSURED YEARLY PREMIUM ENDOWMENT IN Z-0 YEARS Rettilar (INED BY A.D. yE4. S.^«907 of UOCtt^^t^r in the Counjty of '^^lOttfO^ in the sum of T'€^J^ full years' premiums shall have been paid : '--' — ' — " This Policy shall participate annually in the surplus earnings of the Company in accord- ance with the regulations adopted by the Board of Trustees. The extended insurance, paid-up insurance, and loan or cash surrender value privileges, benefits, and conditions stated on the second page hereof form a part of this contract as fully as if recited at length over the signatures hereto affixed. In Witness Whereof, The Penn Mutual Life Insurance Company of Philadelphia has caused this Policy to be signed by its President, Secretai-y, and Actuary, attested by its Registrar, at its Home Office, in Philadelphia, Pennsylvania, the -^^^i4^^ day of v-^^^y 19 y /(Tc, Attest; -«-/iy Secretary egisttar ^S^I^U^^^^r\ President "-^e^tc^.j^itt^uuy^ Actuary 424 PKACTICAL BUSINESS AElTHxMETIG Table of Extension, Paid-up, and Loan or Cash Values, provided for by the Policy, if no indebtedness exists against it AT END OF YEAR TERM OF EXTENSION FOR THIS POLICY These' Values are for $1000 Insurance For this Policy multiply by /..U. PURE ENDOWMENT AT END OF EXTENSION PAID-UP INSURANCE ON SURRENDER LOAN OR CASH SURRENDER VALUES ^^ Years Days jU^ XJl 2U- U^ J^ ^^4^ Z^ ^r 5th A£. ^^ 2=JjL J-Le. 2=J^ Z^^ / J / ,^.3 2- 7^ /. ^ ^A/^ AA. 2-/ o 3 r^A X^'f ^ 8tli AJ=. ^rc ^3 c 3 C^ fo a£4- JJ^ ,^./f 4^^ 7- ^S-3 ^ J j-c ^ LCL ^^^ A^(P 4A/" -^^^^ S- Ucm. Jo ;6 'ajA^ ro(?o LLL / / / / ? r F F rooo ? ? ? / / / / // //» In solving problems 2-4 use ledger paper as above. If the student is not familiar with simj^le accounts, pages 41-47 should be reviewed. 2. Jan. 1, 1915, C. B. Johnson and B. H. Briggs engaged in a partnership business, each investing $3750. July 1, 1915, each partner withdrew 1 250. Jan. 1, 1916, their losses and gains were as follows : • Losses Gains Expense $104.75 Merchandise $628.45 Merchandise Discounts 24.20 Interest and Discount 133.50 Real Estate 250.60 Stocks and Bonds 190.50 What was the present worth of each partner Jan. 1, 1916? PARTITIVE PROPORTION AND PARTNERSHIP 431 3. A, B, and C were partners for a year. Each invested 89500 and during the continuance of the partnership each with- drew rj^lOOO. The losses and gains at closing were as follows : Losses Gains Merchandise Discounts $18.90 Merchandise $4375.80 Expense 650.00 Interest and Discount 90.14 What was the net capital of each at closing ? 4. O, P, and Q are partners sharing the gains and losses in equal proportions. O invested 18500, P $8200, and Q 'f 8450. During their first year the gains were as follows : merchandise, 16457.10; real estate, 1680.50 ; interest and discount, 129.90. If the cost of conducting the business was $1920.50, what was the present worth of each partner at the end of the year ? Gains and Losses Irregularly Divided 514. Sometimes the gains are divided according to certain arbitrary fractions which are not in proportion to the amount invested. In such cases the skill of a partner is frequently considered as being equal to a certain amount of capital. In some cases a certain amount is paid the heavier investor before other division of the gains or losses is made. In still other cases, a stated salary is paid to each partner before the gains or losses of the business are divided. This salary varies according to the ability of the several partners or according to the time each devotes to the business. WRITTEN EXERCISE 1. A and B entered into partnership, each investing $ 7500. Because of the greater experience of A he was to be credited with 81200 before any other division of the gains or losses. The gains or losses were then to be divided equally. During the first year the gains were as follows : merchandise, §4111.10 ; real estate, 1510. If the losses were i 622.80, what was the present worth of each at the end of the year ? 432 PRACTICAL BUSINESS ARITHMETIC 2. A and B entered into partnership, A investing 1 8000 and B 110,000. B doing no work, it was agreed that A should take $ 2000 from the gains before dividing, and that the net gain or loss should then be shared equally. The gains last year were 18900 and the losses ^1400. What was the net gain of each? 3. C, D, and E entered into partnership Jan. 1, each in- vesting 18500. The articles of agreement provided (1) that C should devote all his time to the business and D and E only a portion of. their time ; (2) that if losses occurred, they should be borne equally; (3) that if gains were realized, C should receive J and D and E each J. During the year the gains were as follows: Merchandise, $8217.10; Stocks and Bonds, 1612.50; Interest, .$492.92. If the expenses were $2,217.80, what was the present worth of each partner at the close of the year ? 4. F and G entered into partnership, F investing $5000 and G $7500. Because of the greater skill of F it was agreed that he should be credited with $ 1500 a year before other division of the gains or losses. Then if losses occurred, F was to bear | of them and G f ; but if gains were realized, they were to be divided equally. During the first year the gains of the firm were as follows : Merchandise, $3129.50 ; Real Estate, $250 ; Stocks and Bonds, $575 ; Interest, $130.50. If the cost of conducting the business was $938.48 (exclusive of F's salary), what was each partner's net capital at the close of the year ? 5. J, K, and L entered into partnership, J investing $20,000, K $10,000, and L nothing. The articles of agreement provided (1) that the gains or losses should be shared as follows : J, |, K, ^, L, 2% ; (2) that the capital should be kept intact ; (3) that before any division of the profits was made, J should be credited with an annual salary of $ 1500. At the end of a year the resources were found to be $65,250 and the liabilities (not including J's salary), $16,750. What was each partner's share of the net gain ? After the net gain was credited, what, was the net capital of each partner ? PARTITIVE PROPORTION AND PARTNERSHIP 433 Gains and Losses Divided According to Investment 515. Sometimes the gains and losses are divided in propor- tion to the amount invested ; that is, according to the princi- ples of partitive proportion. 516. Example. A and B engaged in business, agreeing to share the gains or bear the losses in proportion to the amount of capital invested. A invested $2500 and B 13500. They gained $1800. What was the share of each? Solution. $2500 + $ 8500 = $ 6000, the total capital. Since the total capital is $6000 and A put in $2500, A's share is |fg§, or j%, and B's share is |§g§, or j'j. Therefore, A should receive j\ of $ 1800, or $ 750, and B should receive j7^ of $ 1800, or $ 1050. ORAL EXERCISE Find each maris gain or loss in each of the following problems : Investment Gain Investment Loss 1. A, $3000; B, 12000 1500 6. K,$2000; L,i4000 |120 2. C, $1000; D,$2000 $150 7. M,$1500; N,$2000 $700 3. E,$1200; F, $4800 $1200 8. O,$1000; P,$5000 $600 4. G,$1500; H, $4500 $1800 9. Q,$1500; R,$6000 $750 5. I, $1500; J, $7500 $1500 lo. S, $1750; T,$3500 $600 written exercise 1. A, B, and C invested $2000, $3000, and $5000, respec- tively, in a wholesale dry goods business. During the first year the net profits were $4155.80. What was the share of each ? 2. D, E, and F invested $2500, $3250, and $3500, respec- tively, in a manufacturing business. At the close of the first year their profits were found to be $3774.37. What was the share of each ? 3. G, H, and I formed a copartnership, G investing $3000, H, $2000, and I, $1500. During the first six months their net gain was $1829.10. How much was each man worth after his share of the net gain had been carried to his account ? 434 PEACTICAL BUSINESS AKITHMETIG 4. Copy and complete the following statement : C?^/^- C^r^r^^S'i.^C.'^d.'^^ '/j ^ .->v^..'i^ <i,.t-£.--7^l^ --;^'^.i*/T7^''€^?C-^ G.^^^/r^&^€.^d.d.c.c:j '^^^.d,^^ylJ-Mb^^-tAy <7^.^cA^-^U^^^^ ^zyusc SSf2- /or /JO? /Cj-r 2-oCj SXZJSO ???? nn ^roo n jsrz J?7 sj-g-z j-o /J Of A^lJTO J-Z2J'Sc? "^rQ o PARTITIVE PROPORTION AND PARTNERSHIP 435 Interest Allowed and Charged 517. The inequalities in investments and withdrawals are frequently adjusted by allowing and charging interest upon same. When interest is allowed on investments and charged on withdrawals, the gains and losses are usually divided equally. 518. Example. June 1, 1915, C. H. Dean and E. D. Snow formed a partnership, C. H. Dean investing $ 5000 and E. D. SnoAV $ 4000. They agreed that the gains and losses should be divided equally, but that, owing to the unequal investments, each partner should be allowed interest at 6 % on all sums invested and charged interest at the same rate on all sums withdrawn, said interest to be adjusted at the time of closing the books. The profits for the first six months were $ 1050. What was the net capital of each partner after the interest was adjusted and the net gain carried to his account ? c. H. Dean 1915 Dec. 1 Net Capital 5540 00 1915 June Dec. 1 1 1 Investment Interest i Net Gain Net Capital 5000 15 525 00 00 00 5540 00 5540 00 Dec. 1 5540 00 E. D. Sn OW 1915 Dec. 1 1 Interest Net Capital 15 4510 00 00 1915 June 1 1 Investment ^ Net Gain Net Capital 4000 525 00 00 4525 00 4525 4510 00 Dec. 1 00 Solution. $ 5000 in 6 mo. will earn $ 150 interest. $ 120 interest. 4000 in 6 mo. will earn ^150 + #120 -T- 2 = $135, the average interest earned. $150 — $135 = $15 ; that is, C. H. Dean's interest is $15 above the average. $135 - $120 = $ 15 ; that is, E. D. Snow's interest is $15 below the average. Therefore to adjust the interest on the investments, credit C. H. Dean's ac- count $ 15 and charge E. D. Snow's account $ 15. ^ of $ 1050 = $ 525, the net gain of each. Credit each account with the net gain ; then C. H. Dean's net capital is $5540 and E. D. Snow's net capital $4510. 436 PKACTICAL BUSINESS ARITHMETIC WRITTEN EXERCISE 1. Copy and complete the following statement of conditions; '3/,/^- ?hi//^i/^2.'C-u^'y^ ^/oooo » )t 10 3CC 1^33 /0S-O ro ? ' ' > Trryi/ /yior Cryzi^ 6,x Cz Zo/.s-ora ?n > jyzj- /Zfy^iZ / o/sc\ ? / ? f > yttja U CiyxiA^z 442 PRACTICAL BUSINESS ARITHMETIC 4. Jan. 1, 1916, C. H. Smith and W. W. Osgoodby formed a copartnership for the purpose of carrying on a real estate business. C. H. Smith invested §15,000 and W. W. Osgoodby $10,000. They agreed to share the gains and losses in pro- portion to the average net investment. July 1, 1915, C. H. Smith withdrew ilOOO and W. W. Osgoodby $750. On clos- ing the books at the end of the year the net gain was found to be $8685. What was each partner's present worth after his account was credited with his share of the net gain ? 5. Frank M. Congdon, E. H. Robinson, and O. B. Moulton are partners in a dry goods house under the firm name of E. H. Robinson & Co. On commencing business Aug. 1, 1916, Frank M. Congdon invested $17,500, E. H. Robinson $20,000, and O. B. Moulton $12,000. The articles of agreement pro- vided ; (1) that each partner should be allowed interest at 6% on investments and charged interest at the same rate on with- drawals; (2) that because of special skill and experience Frank M. Congdon should be credited $1500 before any other division of the gains and losses ; (3) that then the gains should be divided equally. Aug. 1, 1917, the results of the year's business were as follows : cost of merchandise purchased, $80,872; value of merchandise on hand, $1-1,280.95; sales of merchandise, $78,756; cost of real estate, $18,000; cost of permanent improvements on real estate, $1200; present esti- mated value of real estate, $ 25,000 ; notes in favor of the firm, $11,500; interest accrued on these notes, $112; cost and pres- ent value of horses and wagons, $ 1250 ; general expenses for the year (exclusive of the amount due Congdon), $1800 ; trav- eling expenses for the year, $1200; accounts owing the firm, $20,160.90; cash on hand, $19,033.10 ; mortgage on the firm's real estate, $12,000; interest accrued on the mortgage, $480; notes outstanding, $3500; accounts owed by the firm, $11,260. Show in proper statements the financial condition of the partners. CHAPTER XXXVI STORAGE SIMPLE STORAGE ORAL EXERCISE 1. I stored my piano in a warehouse from June 16 to Octo- ber 1 at il per month or fraction thereof. What sum must I pay in settlement ? 2. I rented a room in a storage warehouse from Sept. 1 to Dec. 18 at 16.50 per month or fraction thereof. What amount did I have to pay ? 3. What must I pay for tlie storage of 5000 bu. of wheat stored from Dec. 3 to Apr. 15 at 4^ per bushel per month or fraction thereof ? for the storage of 10,000 bu. of corn stored from Dec. 1 to Mar. 1 at 3|^ per bushel per month? 521. Storage is a charge made for storing goods in a ware- house. 522. The term of storage is the period of time for which a certain rate is charged. The term of storage is usually, though not invariably, 30 da. ; and in estimating charges, a part of a term is counted the same as a full term. 523. The rates of storage are sometimes fixed by an agree- ment between the contracting parties, sometimes by boards of trade, chambers of commerce, or associations of warehousemen, and sometimes by legislative enactment. 524. Simple storage is storage estimated at the time of the withdrawal of the goods from the warehouse. 443 444 PRACTICAL BUSINESS ARITHMETIC ORAL EXERCISE 1. Verify the following storage bill: yi ^^ ^a /SlA/ ^r ^ yf ^^^^ To Qiiincy Market Cold Storage and Warehouse Co., Dr. Main Office, 133 Commercial Street FOR STORAGE DATE RECEIVED MERCHANDISE ZJA A^i?/?-^^. TZta^zA ^^. ^ A^ JX- ^ 7^ /j^a ^ysr^ .^ /■-n? £^ % IMi diA 2. When were the eggs received for storage ? If there are 30 doz. in a case, how many dozen were received ? 3. Suppose the rate in the bill were 10^ per case per month or fraction thereof for the first 3 mo., and bf per case per month after the first 3 mo. What would this rate be for 4 mo. ? for 7 mo. ? for 9 mo. ? for 10 mo. ? for 11 mo. ? 4. Using the rate in the bill, find the storage on 150 cs. eggs stored from July 1 to Jan. 14 ; on 500 cs. eggs stored from July 3 to June 14; on 350 cs. eggs stored from June 14 to Mar. 4 ; on 12,000 doz. eggs stored from June 14 to Nov. 18. 5. The storage rate on poultry is ^ ^ per pound per month. Find the storage on 1000 lb. from Jan. 10 to Feb. 6 ; on 800 lb. from Jan. 10 to Feb. 18 ; on 1200 lb. from Jan. 10 to May 27 ; on 1600 lb. from Jan. 10 to July 3. 6. In a certain warehouse the rate of storage on cheese is 8 ^ per 100 lb., for each month or fraction thereof. At that rate find the storage on 1000 lb. cheese from May 3 to July 15 ; on 20,000 lb. from May 3 to Aug. 26 ; on 7500 lb. from May 3 to Sept. 12 ; on 10,000 lb. from May 3 to Oct. 6 ; on 5 T. from June 15 to Oct. 28 : on 10 T. from June 15 to Nov. 17. STORAGE 445 525. Example. The following memorandum of flour stored for you by the Central Storage Co. : received Nov. 1, 2000 bbl., and Nov. 16, 3000 bbl. ; delivered Nov. 8, 1000 bbl., and Dec. 5, 4000 bbl. If the rate of storage was b^ per barrel per month or fraction thereof, what was the bill to render ? 7 da. Solution Receipts and Deliveries Nov. 1, received 2000 bbl. Nov. 8, delivered 1000 bbl. , which were in storage 1000 bbl., balance in storage Nov. 16, received 3000 bbl. 4000 bbl., balance in storage Dec. 5, delivered 4000 bbl., 1000 of which were in storage 34 da 3000 of which were in storage 19 da. Total storage. Term Rate 'Storage 10; $50 100 150 $300 WRITTEN EXERCISE 1. In a certain warehouse the storage charges on flour are 3 ^ per barrel per month or fraction thereof. Nov. 1, I stored 500 bbl. ; Dec. 1, I withdrew 100 bbl. ; Jan. 1, I stored 600 bbl. ; Mar. 1, I withdrew 1000 bbl. What was the storage on the first withdrawal ? 400 bbl. of the second withdrawal was in storage for how many months ? What was the total storage due Mar. 1 ? 2. How much is due on the following account? Received from. Article ^~-:^^^^^/^^, SR.oofi -hkt. zy 1,^ r Jb. Weight J~A^C ^ ^ Sec finn ^/— ■ State -jLc^T^^ll' Jb. DELIVERIES AND CHARGES ^^^ 2^z^ ^ ji. ZjL ^L- 2a- ^fLj^ /J^Zj2± ^^ 'Ud- :/u /M2/Z^ Jl '^na^ d£. 446 PRACTICAL BUSINESS ARITHMETIC 3. The following is a memorandum of apples stored by you for T. B. Welch & Co. : received Nov. 28, 5000 bbl., Dec. 15, 1000 bbl., and Dec. 18, 3000 bbl.; delivered Dec. 28,2000 bbl., Feb. 1, 1000 bbl., and Feb. 10, 6000 bbl. Render a bill for the storage, charges being 5^ per barrel per month or fraction thereof. 4. Copy and complete the following bill : \IL^£^A^£^L^ J- z^<^ /^Srw^^:z^;^^^-4-^4^ To EASTERN COLD STORAGE CO., Dr. 28 to 44 North Street FOR STORAGE ?^ //g/7 /' JO/7/?^ vjT^/ ^2E^^ Lm. 'y.fi^OTf fc -A Uy>7J .. ? dZ A Tr? / ., /./gW ft?^ AVERAGE STORAGE 526. When there are frequent receipts and deliveries of goods, it is customary for some warehouses to average the time and charge a certain rate per month of thirty days. The process is called average storage. 527. Example. The following is a memorandum of the re- ceipts and deliveries of flour stored by the Eastern Storage Co. for A. M. Briggs & Co. : received Apr. 10, 2000 bbl., and Apr. 30, 3000 bbl.; delivered May 8, 1000 bbl., and June 9, 4000 bbl. The storage charge being 41 ^ per barrel per term of 30 da. average storage, what was the amount of the bill to render ? Solution. The solution of this problem is clearly shown in the following statement of account : STORAGE 447 Account of Flour Received and Delivered by EASTERN STORAGE CO. For A. M. BRIGGS & CO. Time m Quantity in Date Receipts Deliveries Balance Storage Storage for 1 da. 19- Apr. 10 2000 bbl. 2000 bbl. 20 da. 40000 bbl. 30 3000 bbl. 5000 bbl. 8 da. 40000 bbl. May 8 1000 bbl. 4000 bbl. 32 da. 128000 bbl. June 9 4000 bbl. 0000 bbl. 00 da. 00000 bbl. 5000 bbl. 5000 bbl. 30)208000 bbl. Average storage for 1 mo. = 6933^ bbl. 69331 bbl. dit4k\f — $312, the amount of the bill to render. WRITTEN EXERCISE 1. The Quincy Storage and Warehouse Co. received and delivered on account of Boynton Travers & Co. sundry barrels of apples as follows : received Dec. 1, 1915, 1000 bbl., Dec. 26, 2000 bbl.; delivered Feb. 1, 500 bbl.. Mar. 1, 1000 bbl.. Mar. 15, 1100 bbl.. Mar. 31, 400 bbl. If the charges were 6^ per barrel per term of 30 da. average storage, what was the amount of the bill to render? 2. The Central Storage Warehouse Co. received and delivered on account of A. S. Osborn & Co. sundry bushels of wheat as follows : received Oct. 1, 17,600 bu., Nov. 15, 3600 bu., Dec. 18, 4200 bu., Dec. 27, 4320 bu.; delivered Oct. 31, 10,000 bu., Dec. 4, 10,720 bu., Dec. 19, 4000 bu., Dec. 28, 5000 bu. If the charges were T| ^ per bushel per term of 30 da. average storage, what was the amount of the bill to render ? 3. Metropolitan Storage Co. received and delivered on ac- count of Chas. B. Sherman sundry barrels of flour as follows : received Nov. 15, 1915, 1800 bbl., Nov. 30, 1000 bbl., Dec. 18, 600 bbl., Jan. 30, 3000 bbl. ; delivered Dec. 1, 1000 bbl., Dec. 31, 1900 bbl., Jan. 31, 600 bbl., Feb. 5, 600 bbl., Apr. 30, 2300 bbl. If the charges were 5J^per barrel per term of 30 da. average storage, what was the amount of the bill to render ? 448 PRACTICAL BUSINESS ARITHMETIC WRITTEN REVIEW EXERCISES 1. I bought wheat at $0.80 per bushel and put it in storage. If the storage charges were 2%, for how much must I sell the wheat to realize a gain of $0.12 per bushel, and make allowance of 6 % for incidentals ? 2. A produce dealer bought 150 T. cabbage-at $ 5.50 per ton.- He paid 90 ^ per ton for storage and then sold the cabbage at a clear profit of 25%. How much did he receive per ton and what was his gain ? 3. Nov. 1 a speculator bought 5000 bbl. apples at $2.25 per barrel and put them in storage. Feb. 1 he withdrew them from the storage warehouse. He had them sorted and repacked, when he found that he had only 4600 bbl. of sound apples. These he sold at $3.50 per barrel. If the storage charges were 5^ per barrel per month or fraction thereof, and the charges for repacking were $500, did he gain or lose, and how much ? what per cent ? 4. Dec. 15, 1915, A. L. Farley bought 1000 bbl. flour at $4 and placed it with the Union Warehouse Co. for storage. Jan. 15 he bought 3000 bbl. flour at $4.15 and placed it with the same warehouse company for storage. On Feb. 15 he with- drew 2000 bbl. from storage and sold it at $5.85, on Mar. 25 he withdrew 1000 bbl. and sold it at $ 5.62^, on Apr. 1 he with- drew 1000 bbl. and sold it at $ 5. 87 J. If the storage charges were 5^ per barrel per month or fraction thereof, and cartage and incidentals cost $ 100, did he gain or lose, and how much ? APPENDIX A ADDING MACHINES Machines or mechanical devices for performing arithmetical calculations are now commonly used in business offices ; in banks, factories, insurance offices, and wholesale and retail houses they may be regarded as indispensable. A machine will list and add figures in one fifth or one sixth of the time in which the work can be done by a person using a pen or a pencil, and with an accuracy that a person cannot equal. The operations of subtraction, multi- plication, division, and trade discount may be as readily per- formed as those in addition. The machine writes figures as rapidly as a typewriter, and as legibly ; figures are recorded by simply touching the keys. The figures written down are added automatically, and at any time, by the mere operation of a handle, will be recorded without the possibility of an error, the absolutely correct total. When an item is incorrectly put into the keyboard, it may, before pulling the handle, be corrected. Machines are of different sizes, and some machines have paper carriages simi- lar to the carriage on a typewriter ; on these carriages, if desired, results are printed and carbon copies made. Ma- chines may be furnished with an electric drive, thus avoiding the handle pull. 449 450 PKACTICAL BUSINESS AEITHMETIC Machines can be equipped for adding dollars and cents ; feet and inches • dozens and gross ; hours and minutes ; tons and hundred weights ; pounds and bushels; grains and penny- weights; English pounds, shil- lings, and pence, or any other kind of foreign money ; dates and amounts ; or any kind of figures. Machines may be equipped with the unlimited split device for dividing the keyboard into two or more sections, for listing and adding two or more sets of figures at one operation. Thus they may also be equipped with devices for automatically listing and adding across the sheet or form in two or more columns. There is a duplex adding machine with two sets of wheels, to accumulate two separate totals at the same time. With a ma- chine of this type, totals of groups of items may be secured and a grand total of the group totals accumulated at the same time. Adding-subtracting machines add debits, subtract credits, and automatically compute the difference and print it. There are special "^^^ adding machines for handling monthly statements and for ledger posting and cost accounting ; a pay-roll machine that, with one operation, prints the employees' numbers and the amount of pay on the pay-roll sheet and pay envelopes. The following are some of the uses of these machines in offices : proving daily postings ; daily ledger balance ; daily cash balance ; daily reca- pitulation of sales (as cash, credit, C.O.D., etc.] checking invoices and freight bills; figuring discounts; computing commissions; summary of day's receipts and disbursements; figuring estimates; making out pay envelopes; analysis of outstanding accounts ; analy- sis of accounts payable ; balancing petty cash account; footing ledger accounts before taking the trial balance ; taking off the trial-balance figures (debits and credits) ; reconciling caslibook balance with bank balance, listing the number and the amount of each outstanding check ; making monthly statements giv- ing month, date, total of debits, total of credits, balance and special terms ; compiling statements of cost of production ; footing inventories and calculating extensions ; posting customers' Jedger. The cuts show various types of calculating machines. APPENDIX B TABLES OF MEASURES MEASURES OF CAPACITY Liquid Measure Dry Measure 4 gills = 1 pint 2 pints = 1 quart 2 pints = 1 quart 8 quarts = 1 peck 4 quarts = 1 gallon 4 pecks = 1 bushel = 231 cubic inches = 215D.42 cubic inches Barrels and hogsheads vary in size ; but in estimating the capacity of tanks and cisterns 31.5 gal. are considered a barrel, and 2 bbl., or 63 gal., a hogshead. A heaped bushel, used for measuring apples, corn in the ear, etc., equals 2747.71 cu. in. A dry quart equals 67.2 cu. in., and a liquid quart 57.75 cu. in. MEASURES OF WEIGHT Avoirdupois Weight Troy Weight 16* ounces = 1 pound 24 grains = 1 pennyweight 100 pounds = 1 hundredweight 20 pennyweights = 1 ounce 2000 pounds = 1 ton 12 ounces = 1 pound Apothecaries' Weight Comparative Weights 20 grains = 1 scruple 1 lb. troy or apothecaries' = 5760 gr. 3 scruples = 1 dram 1 oz. troy or apothecaries' = 480 gr. 8 drams = 1 ounce 1 lb. avoirdupois = 7000 gr. 12 ounces = 1 pound 1 oz. avoirdupois = 437^ gr. The ton of 2000 lb. is sometimes called a short ton. There is a ton of 2240 lb., called a long ton, used in all customhouse business and in some wholesale trans- actions in mining products. In weighing diamonds, pearls, and other jewels, the unit generally employed is the carat, equal to 3.2 troy grains. The term " carat" is also used to express the number of parts in 24 that are pure gold. Thus, gold that is 14 carats fine is II pure gold and \% alloy. Miscellaneous Weights 1 keg of nails =100 pounds 1 barrel of salt = 280 pounds 1 cental of grain = 100 pounds 1 barrel of flour =196 pounds 1 quintal of fish = 100 pounds 1 barrel of pork or beef = 200 pounds A cubic foot of water contains about 7i gal. and weighs 62 1 lb., avoirdupois. 451 452 PRACTICAL BUSINESS ARITHMETIC MEASURES OF EXTENSION Long Measure 12 inches = 1 foot 3 feet = 1 yard 5| yards, or 16 1 feet = 1 rod 320 rods, or 5280 feet = 1 mile Surveyors* Long Measure 7.92 inches = 1 link 25 links = 1 rod 4 rods, or 100 links = 1 chain 80 chains = 1 mile City lots are usually measured by feet and decimal fractions of a foot ; farms, by rods or chains. Miscellaneous Long Measures 4 inches = 1 hand 6 feet = 1 fathom 120 fathoms • = 1 cable length 1.15 miles, nearly, = 1 knot, or 1 nautical or geographical mile Square Measure 144 square inches = 1 square foot 9 square feet = 1 square yard 30| square yards = 1 square rod 160 square rods = 1 acre 640 acres = 1 square mile The hand is used in measuring the height of horses at the shoulder. The fathom and cable length are used by sailors for measuring depths at sea. The knot is used by sailors in measuring distances at sea. Tliree knots are frequently called a league. Surveyors* Square Measure 625 square links = 1 square rod 16 square rods = 1 square chain 10 square chains = 1 acre 640 acres = 1 square mile 36 square miles = 1 township Cubic Measure 1728 cubic inches = 1 cubic foot 27 cubic feet = 1 cubic yard 128 cubic feet = 1 cord 1 cubic yard = 1 load (of earth, etc.) 24 1 cubic feet = 1 perch The square rod is sometimes called a perch. The word rood is sometimes used to mean 40 sq. rd. or \ A. In the government surveys, 1 sq. mi. is called a section. The perch of stone or masonry varies in different parts of the country ; but it is usually considered as 1 rd. long, 1 ft. high, and li ft. thick, or 24f cu. ft. Angular Measure 60 seconds = 1 minute 60 minutes = 1 degree 90 degrees = 1 right angle 360 degrees = 1 circumference Angular (also called circular) measure is used principally in surveying, navi- gation, and geography for measuring arcs of angles, for reckoning latitude and longitude, for determining locations of places and vessels, and for computing difference of time. A minute of the earth's circumference is equal to a geographieal mile. A degree of the earth's circumference at the equator is therefore equal to about 69 statute miles. TABLES OF MEASURES 453 MEASURES OF TIME 60 seconds = 1 minute 12 months = 1 year 60 minutes = 1 hour 360 days = 1 commercial year 24 hours = 1 day 365 days = 1 common year 7 days = 1 week 366 days = 1 leap year 30 days = 1 commercial month 100 years = 1 century September, April, June, and November have 30 da. each ; all of the other months have 31 da. each, except February, which has 28 da. in a common year and 29 da. in a leap year. Centennial years that are divisible by 400 and other years that are divisible by 4 are leap years. In running trains across such a broad stretch of country as the United States, it is highly important to have a uniform time over considerable territory. Rec- ognizing this, in 1883, the railroad companies of the United States and Canada adopted for their own convenience a system of standard time. This System divides the United States into four time belts, each covering approximately 15'' of longitude, 7^° of which are east and 7^° west of the governing meridian. The .region of eastern time lies approximately 7|° each side of the 75th meridian, and the time throughout this belt is the same as the local time of the 75th merid- ian. Similarly, the regions of central, mountain, and Pacific time lie approxi- mately 7|° each side of the 90th, 105th, and 120th meridians, respectively, and the time throughout each belt is determined by the local time of the governing meridian of that belt. There is just one hour's difference between adjacent time belts. Thus, when it is 11 o'clock a.m. by eastern time, it is 10 o'clock a.m. by central time, 9 o'clock a.m. by mountain time, and 8 o'clock a.m. by Pacific time. Since railroad companies change the time at important stations and termini, regardless of the longitude of such stations and termini, the boundaries of the time belts are quite irregular. MEASURES OF VALUE United States Money English Money 10 mills = 1 cent 4 farthings = 1 penny 10 cents = 1 dime 12 pence = 1 shilling 10 dimes = 1 dollar 20 shillings — 1 pound sterling 10 dollars = 1 eagle = $4.8665 The term " eagle " is seldom used in business. The mill is not a coin, but the name is frequently used in some calculations. In Canada the units of money are the same as in the United States. 1 far. = |Q^ ; \d. = 2,^-^^ ; Is. = '2.^\f. French Money German Money 100 centimes = 1 franc = $0,193 100 pfennigs = 1 mark = $0,238 MISCELLANEOUS MEASURES Counting by 12 Counting Sheets of Paper 12 things = 1 dozen 24 sheets = 1 quire 12 dozen = 1 gross 20 quires = 1 ream 12 gross = 1 great gross = 480 sheets 454 PEACTICAL BUSINESS ARITHMETIC BUSINESS ABBREVIATIONS A . . . acre Mar. . . . March Apr. . April Mdse. . . merchandise Aug. . August Messrs. . . Messieurs, Gentlemen ; bbl. . barrel; barrels Sirs bdl. . . bundle; bundles mi. . . . mile; miles bg. . bag; bags min. . . . minute; minutes bkt. . basket; baskets mo. . . . month; months bl. . . bale; bales Mr. . . . Mister bu. . bushel; bushels Mrs. . . . JMistress bx. . . box; boxes N.' . . . north cd. . . cord; cords No. . . . number ch. . . chain ; chains Nov. . . . November c.i.f. . . carriage and insurance free Oct. . . . October Co. . company; county oz. . . ounce; ounces C.O.D . . collect on delivery p. . . . . page Coll. . collection pc. . . . j)iece; pieces Cr. . creditor; credit per. . . . by the ; by cs. . . case ; cases per cent. . per centum, by the hun- ct. . cent ; cents ; centime dred cu. ft. . cubic foot ; cubic feet pk. . . . peck ; pecks cu. in. . cubic inch ; cubic inches pkg. . . . package ; packages cu. yd . . cubic yard ; cubic yards pp. . . . pages cwt. . . hundredweight pr. . . . pair; pairs d. . . . pence pt. . . . pint ; pints da. . . day; days pwt. . . . pennyweight; penny- Dec. . . December weights doz. . . dozen; dozens qr. . . . quire; quires Dr. . . debtor ; debit ; doctor qt. . . . quart; quarts E. . . . east rd. . . . rod ; rods ea. . . each rm. . . . ream ; reams e.g. . . exempli gratia, for ex- Km. (or VI.) Reichsmark, Mark ample s. . . . . shilling; shillings etc. . . et ccetera, and so forth S. . . . . South far. . . farthing; farthings sec. . . . second; seconds Feb. . . February sq. ch. . . square chain; square f.o.b. . . free on board chains fr. . . franc ; f i-ancs sq. ft. . . square foot ; square feet ft. . . foot; feet sq. mi. . . square mile; square gal. . . gallon; gallons miles gi- • • gill; gills sq. rd. . . square rod ; square rods gr. . . grain ; grains sq. yd. . . square yard; square gro. . . gross yards hhd. . . hogshead; hogsheads T. . . . . ton hf. ch t. . half chest ; half chests tb. . . . tub; tubs hr. . . hour ; hours Tp. . . . township ; townships i.e. . . id est, that is viz. . . videlicet, namely ; to wit in. . . inch; inches via . . by way of Jan. . . January wk. . . . week; weeks kg. . . keg ; kegs wt. . . . weight; weigh 1. . . . link ; links yd. . . . yard; yards lb. . . pound; pounds yr- • . . year ; years. BUSINESS SYMBOLS AND ABBREVIATIONS 455 BUSINESS SYMBOLS «/c account ■=. equal; equals 13 one and three «A account sales foot; feet; fourths + addition minutes ^ per; by or ~~ aggregation C hundred % per cent ; & and II inch ; inches ; seconds hundredth ; . . . • . and so on X multiplication hundredths @ at; to # number, if written £ pounds sterling '/o care of before a figure; •/ since f cent; cents pounds, if written — subtraction V check mai'k after a figure therefore o degree 11 one and one fourth M thousand ^ division 12 one and two fourths ; V6 5 shillings 6 pence ; 1 dollar; dollars one and one hall five sixths INDEX Abbreviations, 454 Above par, 398 Abstract number, 50 Account, 41 Account current, 415, 417 Account purchase, 271, 275 Account sales, 271, 392 Acute angle, 201 Acute-angled triangle, 202 Adding machines, 449 Addition, 10, 94, 125, 194 Ad valorem duty, 291, 295 Agent, 270 Aliquot parts, 158 Altitude, 204 Amount, 232, 328 Angle, 201 Angular measure, 452 Apothecaries' weight, 451 Arabic numerals, 3 Arc, 202 Areas, 204 Assessment, 397, 400 At a discount, 366, 398 At par, 366 At a premium, 366, 398 Average, 85 Average clause, 284 Average date of payment, 385 Average investment, 438 Average storage, 446 Average term of credit, 385 Avoirdupois weight, 451 Bank discount, 326, 327 Bank drafts, 358, 360 Bank loans, 334 Bank money order, 355 Bankers' bills of exchange, 375, 377 Bankers' daily balances, 346 Banker's sixty-day method of interest, 303 Banking, 300 Base, 204, 232, 236 Base line, 205 Bear, 416 Below par, 398 Bill of lading, 366 Bills, 39, 40, 59, 63, 106, 107, 134, 152, 165, 166, 170, 171, 172, 173, 174, 175, 176, 183, 187, 199, 248, 253, 254, 268, 269, 297, 298 Bills and accounts, 170 Bills of exchange, 375, 378, 379 Bins, 226 Blank indorsement, 315 Blanket policy, 278 Board foot, 220 Bonds, 405, 406 Bond table, 409 Brick work, 225 Broker, 270 Brokerage, 270 Bull, 416 Bullion, 9 Buying bonds, 410 Buying on commission, 274 Buying by the hundred, 105 Buying by the thousand, 105 Buying by the ton, 108 Buying stocks, 402 Cable length, 452 Calculation table, 229 Cancellation, 115 Capacity, 226 Capital, 429 Capital stock, 396 Capitation tax, 286 Carpeting, 215 Cash account, 41 Cash balance, 393 Cashier's check, 361 Certificate of deposit, 361 Change memorandum, 181 Charter, 396 Checking results, 20, 32, 52, 57, 58, 69, 87, 88, 89 Checks, 5, 358, 362, 383, 400 Circle, 202 Circumference, 202 Cisterns, 224 Clearing house, 358, 359 Code, 356 457 458 PKACnCAL KUSIXESS AKITHHETIC 2?i VlMdfi!m^m^W7,4m,^;l DiviaoB, Mi, 71, im, lOf, 1», 197 U$ UoauKmUuf Ulk U rxAaa^^ Ti^ DnfM^ »«V ^V7, S«, aM, a« ]>n«rcc;,SS7 Datki^2Sri ,4» ctfaco(Nnl«,aM Eirca ■iMiln; lU Exact n«ef«l,n7 976 4» r«l» Fac«,Sl$ Fae*o«; ^^ lU r«tffa|tt9;4iil Factoffii;, 114 FadbMii, 4^ FedMal IflttMae Tax, 2S7 FmbJ jftMiti^ 1» iktf MMuwrnu^ httmeem HaAtm^ t» Timtim^ the f^fAm m Xam, 9U1 rm Ifmm, 1^, 1^ Tinm wjiUf^ 99Bi , in JhuA ^ftMef^ itm 9i»^9» FlMifliii^ 214 191 Dmibtatym *4 nUM «4 ^nu^kmiiffi^ 9t§ r;iW F/.eal4ate,a» th!9nMm^9f» li0ft^mmtf^9fm tfmmittir^Wt Ffa«tt«wl nfttetiMW, 14^ IKD£X 459 G;Mn auftd km^ SGS lisHm^ foods for < GiunixrlossfACcllliigiptketSAi Loaf MtMWMk ^tt GmiOiie Mipnswttttiotts, \U^ 15S. :Ml, M»k^r, US Gi«itosft coautton dirisor« llf xtftlwd, 483 M««s«.ir«$ oil ^Mn^^iV'^A liKxvnt*^ biMKJL 4iili^ MMrts;, Ml IiKxMmis mmI ait«slttM«it«, 411 Mtelxfe jgO MML 371 ImKiv^ettMBla, 114.313 MiMi mot oI ^itJaii^ii^ HI luli«rtiNK« %ftx« H^ MhBuifcimwM imhmmOUEI ItvsttmmM, ITT MIsniluMOiK ^iMriA^ 4S1 lti$^xrjiiKv ml«\ Hl^ 411 Ittlw^i utwiWv^ Ii^ti^r. il^ M<%M %«M^ 1^ 31. 31 31 Int<^itv<$<> 3Q0 ]tm) m>l«\ 31<1 311 Jv^ul iK>l«, 31<^ SSS MMl«i^4l rua«nl mifiM^llI KiAfil«%i,llPr T.i(^|eIiI. 31 l.ANft»t e^^ntiM^n nmM^ 113 VkMHims 3. «ci l^ttxr ^vr «Kt>ri<^ 1X1, lil l^iHifi^ IK 3llv 3K «S^ 33^ 3a lir omltl^ 391 >C^iMk«it«lliM^ 3, «l 460 PRACTICAL BUSINESS ARITHMETIC Obtuse angle, 201 Obtuse-angled triangle, 202 Odd number, 113 One-fourth pitch, 210 One-half pitch, 210 Open policy, 278 Orders of units, 3 Ordinary life policy, 420 Ordinary policy, 278 Paid-up policy, 421 Painting, 213 Papering, 216 Par value, 398 Parcel post, 77 Parenthesis, 31 Partial payments, 338 Partitive proportion, 426 Partners, 429 Partnership, 429 Pay rolls, 86, 181, 182, 185 Payee, 315, 327 Pay-roll memorandum, 182 Per cent, 92, 231 Per cents of decrease, 238 Per cents of increase, 237 Percentage, 231 Perch, 225, 452 Perimeter, 202 Periodic interest, 319 Periods, 4 Perpendicular lines, 201 Personal accounts, 42 Pitch of roof, 210 Place value, 3 Plane surface, 201 Plastering, 212 Policy, 278 Poll tax, 286 Port of delivery, 291 Port of entry, 291 Postal money order, 354 Postal savings bank, 352 Postal service, 77 Power, 51 Practical measurements, 201 Preferred stock, 397 Premium, 278 Present worth, 41 Prime number, 113 Principal, 270, 300 Principal meridian, 206 Problems in interest, 318 Proceeds, 328 Promissory notes, 9, 314, 316, 335, 336, 341 Properties of 9, 87 • Properties of 11, 88 Property insurance, 277- Property tax, 286 Proprietary account, 43 Public lands, 205 Qualified indorsement, 316 Quotient, 66 Radical sign, '206 Radius, 202 Ranges, 205 Rate, 232, 300 Rate of exchange, 355, 360, 366, 376 Reading decimals, 92 Rectangle, 201 Rectangular solids, 218 Reduction, 121, 122, 123, 124, 192, 193 Reference method of interest, 313 Registered bond, 407 Remainder, 66 Repeaters, 264 Reserve, 421 Resource, 41 Review of the common tables, 191 Review tests, 30, 49, 65, 112, 157, 245, 255, 276, 337 Right angle, 201 Right-angled triangle, 202 Roman numerals, 6 Rood, 452 Savings bank, 349 Savings-bank accounts, 349 Scalene triangle, 202 Scrip, 399 Section, 205 Selling on commission, 272 Selling^by the hundred, 105 Selling by the thousand, 105 Selling by the ton, 108 Separatrix, 3 Share, 396 Shipment, 271 Shipping invoice, 273 Short methods, 55, 71, 126, 136 Sight draft, 364 Similar fractions, 124 Simple accounts, 385 Simple interest, 301 Simple storage, 443 Sinking fund, 323 Six per cent method of interest, 311 Sixteen to one, 136 INDEX 461 Solids, 218 Solution of problems, 146 Specific duty, 291 Square, 201, 209 Square measure, 452 Square root, 206 Standard time, 453 Statements, 4^, 179, 180 Statutory weights of the bushel, 200 Stock broker, 398 Stock certificates, 396," 397, 398 Stock company, 396 Stock exchanges, 414 Stock insurance company, 278 Stockholder, 396 Stocks and bonds, 396 Stone work, 225 Storage, 443 Stricken bushel, 226 Subtraction, 31, 96, 126, 194 Surface, 201 Surplus, 421 Surveyors' long measure, 452 Surveyors' square measure, 452 Table of aliquot parts, 160 Table of bond quotations, 410 Table of common measures, 451 Table of compound interest, 321, 323 Table of foreign coins, 293 Table of important per cents, 232 Table of insurance rates, 281, 421 Table of simple interest, 314 Table of stock quotations, 402 Table of time, 330 Table of twelfths, 266 Tables of metric measures, 371 Tare, 38 Tariff, 291 Tariff, or rate, book, 281 Tax rate, 287 Tax table, 290 Taxes, 286 Telegram, 356 Telegraphic money order, 356 Telegraphic rates, 357 Term of discount, 328 Term of storage, 443 Term policy, 420 Terms of a fraction, 120 Tests of divisibility, 114 Time note, 315 Time sheets, 86, 181, 182, 185 Time slip, 185 Township, 205 Trade discount, 246 Traveler's check, 381, 382 Triangle, 202 Troy weight, 451 Underwriter, 278 Unit, 7 Unit fraction, 120 United States coins, 8 United States method of partial pay- ment, 338 United States money, 8, 9, 453 Valued policy, 278 Values of foreign coins, 293 Vinculum, 31 Warehousing, 293 Warehouse entry, 294 Weigh tickets, 108 Wood, 220 ■"i 1.3 r ni, ' / 60.^^ O ^-Zy- .25 V / 2. y ■' J^ -. 1 2,^ j^ 63 ill '::v3'- ^ 33^ 3 as ff It, ^'^~ .-0. ^ V4- ^^y -''».,.-' ^'t ,;,. «? ,.„;..., ■I J I - y I 4^ 61 X ^rX. .-iif OGk - r4 - "^ ' -i^. . ^^^ -1 -JL f^ ^ '" ^^* .,| "i,.^; ^ 7^ 1 '-'' JIS £1111 -to , ^ JO(tXi-^ % 00>^, ^^ .6*2/ ANSWERS TO PRACTICAL BUSINESS ARITHMETIC ,1 BT \r) JOHN H. MOOEE r AND \^^ GEOEGE W. MINEK ^ REVISED EDITION GINN AND COMPANY BOSTON • NEW YORK • CHICAGO • LONDON COPYRIGHT, 1906, 1915, BY GINN AND COMPANY a A ^ A •- ANSWERS Page 4 1. 6,006,005. 4. 321,000,006. 7. 27.125. 2. 753,000,000,000. 5. $3,000,004.05. 8. 62,000.425. 3. 4,000,125. 6. 10,000,001,103. 9. $3,420,001.15. Page 7 1. XIX ; LXXXVIII ; XCIX ; 4. MCDXCII, or MCCCCXCII ; CXXIV ; MCMVII ; MCMX. MDCXX ; MDCCLXXVI. 2.985,100. 6.5,217,210,271.43; 3. 5,217,210,000.016. 5,217,207,540.004. Page 19 1. 19,857. 2. 16,665. 3. 11,028. 4. 30,316. 6. 24,396. 6. 9884. Page 20 7. 45,842. 8. 25,895. 9. 25,317. 10. 17,599. 11. 29,839. 12. 17,007. Page 21 1. $1956.92. 2. $16,326.51. Page 22 1. $37,358,013.62. 3. $43,557,265.17. 6. $9,264,451.21. 2. $36,243,941.97. 4. $857,538.97. 6. $11,603,633.30. Page 23 7. $6,312,125.73. 8. $12,284,421.92. 9. $19,813,964.89. Page 25 1. 52. 4. 335. 7. 622. 10. 3221. 13. $347.45. 2. 67. 5. 572. 8. 488. 11. 4541. 14. $732.48. 3. 66. 6. 493. 9. 512. 12. $357.39. RE 815.3 1 2 PRACTICAL BUSINESS ARITHMETIC Page 26 1. 212,400. 2. 74,784. 3. Vertical totals: pine, $21,071.54 ; oak, $27,018.17 ; maple, $1794.21 ; spruce, $1951.01; walnut, $2741.56; cherry, $1623.73. Horizontal totals: Monday, $19,389.77; Tuesday, $9582.54; Wednesday, $10,620.78; Thursday, $4351.68; Friday, $6454.51; Saturday, $5800.94. Check, $56,200.22. Page 27 4. Horizontal totals: $77,591.59; $156,846.01; $70,092.38; $4233.37; $74,992.38; $102,960.37; $17,848.77; $14,610.08; $5160.14; $238,854.56; $18,660.82; $10,869.85; $114,162.44; $18,604; $2143.31. Vertical totals : $172,481.07; $229,044.01; $206,739.21; $101,314.96; $218,050.82. Check, $927,630.07. 6. Horizontal totals: J. E. Snow, $1192.67; W. B. Moore, $370.74; T. B. Welch, $820.24 ; E. H. Ross, $1015.60 ; Minnie Davis, $972.35 ; Ada Benton, $547.25; Elmer S. Frey, $3031.28; Joseph White, $372.37; Margaret Dix, $304.55; F. O. Beck, $714.16; L. O. Avery, $1821.49; B. W. Snyder, $848.11; Ella Harding, $218.07 ; Carrie Simpson, $222.53 ; W. F. Baldwin, $827.65; E. O. Burrill, $772.05. Vertical totals: Mon- day, $1859.95; Tuesday, $2647.98; Wednesday, $2931.92; Thursday, $1997.10; Friday, $2447.18 ; Saturday, $2166.98. Check, $14,051.11. 6. a. $13,785.29. b. $13,422.46. c. $13,365.10. d. $14,320.43. Page 29 1. 52,187,258,800. 4. 47,498,388,917. 7. 47,480,394,697. 2. 52,163,267,812. 6. 39,769,350,892. 8. 45,296,432,916. 3. 55,583,217,175. 6. 51,571,866,229. 9. 46,907,836,534. Page 30 1. 428,977 ; 422,257. 3. Check, 12,496. 2. 379,703 ; 445,056. 4. Check, 11,079. Page 32 1. $60,766.18. BE ANSWERS 3 Page 33 2. (a) 1904, $1,460,827,271 ; 1905, f 1,518,561,666 ; 1906, |1, 743,864,500; 1907, $1,880,851,078; 1908, |1,860,772,714 ; 1909, $1,663,011,104; 1910, $1,744,984,720 ; 1911, $2,049,320,199 ; 1912, $2,204,322,409 ; 1913, $2,465,- 884,149. (6) 1904, $469,736,293 ; 1905, $401,048,595 ; 1906, $517,302,054 ; 1907, $446,429,653; 1908, $666,430,922; 1909, $351,090,880; 1910, $188,037,290; 1911, $522,094,094 ; 1912, $551,057,475 ; 1913, $652,905,915. (c) $18,592,399,810 ; $13,826,266,639. (d) $4,766,133,171. Page 34 1. $317. 2. $343. 3. $274. 4. $488. Page 35 5. $282. 6. $361. 7. Column amounts : $209.15; $208.16; $216.46. Line amounts: $720.42; $506.18; $661.42; $508.28. Check total, $2396.30. 8. a, $721.12 ; 6, $857.12 ; c, $717.75 ; d, $818.42 ; e, $419.37 ;/, $374.20 ; g, $3953.88 ; h, $41.51 ; i, $4.39 ; j, $3907.98. Page 38 1. a, $1051 ; &, $942 ; c, $842 ; d, $918 ; e, $417 ; /, $830 ; g, $736 ; h, $878 ; i, $833 ; i, $655 ; k, $934 ; I, $9050 ; m, $1942 ; n, $1928 ; o, $9036. 2. a, $1021 ; 6, $894 ; c, $871 ; d, $723 ; e, $591 ; /, $738 ; g, $759 ; h, $697 ; i, $591 ; j, $922 ; fc, $1011 ; I, $7347 ; m, $2047 ; n, $3518 ; o, $8818. Page 39 1. $628.71. Page 40 2. $710.89. 3. 2163 lb. 4. 672 lb. 6. 3091 lb. Page 44 1. $1485.25, balance. 3. $205.55, loss ; $255.55, loss. 2. $72.06, gain. 4. $575.32, liability. Page 45 5. $575.32, balance. 6. $7219.65, present worth. 1. Gain on mdse., $270.60 ; cost of expense, $478.60 ; loss on expense, $78.60. 2. Total resources, $7212 ; amount owed C. H. Jones, $430.60; present worth, $5866.40. EE PRACTICAL BUSINESS ARITHMETIC 3. $4463.17. 4. $6189.25, present worth. Page 46 5. $728.35, net gain. 6. $3664.21, net gain. 7. $1346.50. Page 47 Face of paper, total $2672.92 ; 2. Face of paper, total $2339.82 ; Discount, total $19.84 ; ' Discount, total $20.73; Collection and Exchange, Collection and Exchange, total $2.18; total $1.58; Proceeds, total $2650.90, check. Proceeds, total $2317.51, check. 3. Face of paper, total $2118.31; Discount, total $13.90; ' Collection and Exchange, total $1.79; Proceeds, total $2102.62, check. Page 1st Balance, total $4353 ; Checks, total $4737; Deposits, total $2975 ; 2d Balance, total $2591, check. 1st Balance, total $3331 ; Checks, total $3420 ; Deposits, total $2240 ; 2d Balance, total $2151, check. 48 3. 4. 1st Balance, total $3405 ; Checks, total $3684 ; Deposits, total $2347; 2d Balance, total $2068, check. 1st Balance, total $3509 ; Checks, total $3684 ; Deposits, total $2233 ; 2d Balance, total $2058, check. 1st column, total 41,290; 2d column, total 50,750; 3d column, total 42,004 ; check, 134,044. 3. $4463.17. Page 49 2. 1st Balance, total $3541 ; Checks, total $2476 ; Deposits, total $2100 ; 2d Balance, total $3165, check. 4. $3664.21. 6. $1346.50. 1. Check, 53,985. Page 53 Check, 255,717. 3. Check, $3186.60. 4. Check, 26,460. 5. Check, 911,204. 6. Check, $1320.80. Page 54 7. $471.90. 8. $557.25, gain. 9. $5.42. 10. $1867.48. 11. $182.13. 12. $1535.58. ANSWERS 5 Page 57 1. $21,638.98. Page 58 1. $2213.87. 2. $3141.40. Page 59 3. $90.15. Page 60 1. $156. 2. $184.37. Page 62 1. $1300.75. 5. $254.20. 9. $92.56. 12. $225.75. 2. $228.48. 6. $125.28. 10. $87.55. 13. $443.88. 3. $219.30. 7. $475.60. 11. $110.70. 14. $191.58. 4. $333.90. 8. $223.48. 1. 79,112. 2. 258,633. 3. 208,936. 4. 312,912. Page 63 1. a. 2484. b. 2664. c. 2682. d. 8508. e. 8514. 3. $35,918, gain. 2. a. 3312. b. 3652. c. 3576. d. 11,344. e. 11,352. 4. $665.56. Page 64 1. 1st Balance, total $1409.95 ; 2. 1st Balance, total $833.87 ; Checks, total $2369.11 ; Checks, total $915.84 ; Deposits, total $1933.54 ; Deposits, total $654.81 ; 2d Balance, total $974.38, 2d Balance, total $572.84, check. check. Page 65 1. $674.76. 3. 8206, check. 6. 5456, check. 7. $35,918. 2. $1160.22. 4. 15,360, check. 6. 33,225, check. Page 69 1. $123.75. 2. 6500. 3. 950. Page 70 4. $4559.50. 6. 450 T. 8. 2000 bbl. 10. $686. 6.3106. 7. $8290.65. 9. 100 shares. 11. 16- bu.; $657,564,300. 12. Total yield, 1,668,460,000 bu. ; total valuation, $1,028,239,000. RE 6 PRACTICAL BUSINESS ARITHMETIC Page 74 1. $10,010; 115,525. 3. $11,446.70. 5. 37+ bu. ; $443,939,481. 2. 82g«gmo. 4. $733.20. Page 75 6. (a) 1,601,754; (6) 665. 7. (a) 1,578,172; (6) 641. 8. 1910, $3,654,243.54 ; 1911, $3,742,305.63. 9. 1910, $2.22- ; 1911, $2.31-. * 10. $715,921,352.50. Page 76 1. 108. 3. 80. 5. 294. 7. 615. 9. 395. 2. 85. 4. 80. 6. 187. 8. 311. Page 81 (The small figure above the amount indicates the price-list number.) 1. $4749.80; $4397.20; $4862.60; $5242.90; $59n.45. 2. $4793.05; $4392.45; $5046.30; $5416.10; $6033.30. Page 82 3. $5419.35; $4980.70; $5522.65; $5910.70; $65^78. , 4. $5177.55; $4742.05; $5196.35; $5752.30; $6310.16. Page 83 6. $6219.60; $5776.35; $6518.10; $6760.50; $7780.15. 12 3 4 5 6. $7071.35; $6510; $7095.30; $7614.90; $8455.85. Page 84 7. $6232.80; $5850.15; $6304.15; $6641.85; $7332.25. 12 3 4 5 8. $5798.30; $5494.60; $5847.20; $6294.95; $7233.80. Page 85 1. 16 in. 2. $2.35. 3. $15,132. RE ANSWERS Page 86 4. 16 yr. 5. 742 pupils. 6. $0.70. 7. 63001b.; 631b. 8. Total amount, $153 ; average daily wages, $2.55. 4. 24,877,125. Page 90 6. $738.71. 6. $3099.60. 7. $70,287.28. Page 93 1. .5; .50; .500. 2. 900.0011; .0911; 500.002. 3. .000174; 174,000,000.000007; 7,000,000.000174. 4. 7000.0075 ; .0000257 ; 200.000046 ; .000246. Page 94 6 .4010097 ; 4,010,000.0000097 ; .000500 ; .00000005. 6. 606.05001 ; 606.00051 ; 56.000000Q128. 7. 17,000.001876; 17,000.1876; 21.16. Page 95 9555.284126. 3. 96.3982201. 4. 40,091.710245 1. 255.6735. 6. 2668.4189928. 6. Line totals : $13,299.39 ; $2897.30 ; $5997.21 ; $10,280.58 ; $8359.91 $17,856.91; $16,173.09; $21,845.56; $8905.13; $10,015.09; $17,708.81 $8521.80; $23,641.05; $13,323.26; $11,306.09; $14,185.56; $9044.06 $74,812.27; $7399.48; $16,290.70. Column totals: $119,263.52; $135, 004.95; $27,693.42; $29,901.36. Check, $311,863.25. 7. 5545.288766. 4.3578. 16.2155. .110745. Page 96 1177.46. 7. .000196. 3.7325. 8. 7.50279. 10.9999729. 9. 85.794. 10. 254.012. 11. 421.60071. 12. -03472^. 13. $2942.36, gain, Page 97 14. $1697.93, gain. 15. $2537.83, gain. 16. $272.52, loss ; $3176.91, present worth, Page 100 1. 474.392. 3. 474.392. 5. .189084. 7. 78,461. 9. 311.09078. 2. 474.392. 4. 3217.1 6. .00474392. 8. 3103.2. 10. $159^375. 11. $4500. 12. 355,333,000 bu. ; $328,327,692, total valuation. 8 PRACTICAL BUSINESS ARITHMETIC Page 102 1. 127,000. 4. .26. 7. .4. 10. 146,600. 13. .025. 2. 24. 5. 720. 8. .05. 11. 2500. 14. .00000002. 3. .0002. 6. 5000. 9. 910,800. 12. .00006. 16. 100,000,000. Page 103 16. 18,090,999.100800909. 19. 444,044,016.444. 22. .1 17. 1,000,044.009. 20. 2.277525. 23! fO.50. 18. 5,550,511.1055. 21. 1,055,556.5001. 24. 200; $40. Page 104 26. 557,012,903 bu.; $172,674,000, total valuation. Page 105 1. $2.48. 3. $3.84. 6. $11.36. 7. $34.30. 2. $3.93. 4. $1.85. 6. $3.90. 8. $27.28. Page 106 1- $70. 3. $578.76. 5. $8959.58. 7. $227.17. 2- $6.08. 4. $130.08. 6. $233.68. 8. $6648. Page 107 t 1. $14.64. 2. $14.94. 3. $3. Page 108 1. $13.28; $12.91. 2. $10.99; $10.18. Page 109 3. $51.90. 6. $423.68. 7. $123.92. 9. $1398.97. 4. $6.45. 6. $157.35. 8. $334.12. 1. 653.3136. 2. 248.076. 3. 150 da. 4. $6.72. Page 110 6. 13,612.5. 9. 400 cd. 13. A, $2800 ; B, $3300 ; 6- $1305. 10. $193.29. C, $2300. 7- $6. 11. $50.50, gain. 14. $222.35. 8- $4.50. 12. ^. 16. $2346.05. ANSWERS 9 Page 111 16. $173.66. 18. $429.79. 20. $2.06. 17. $4.781 . 19. 40 A. 21. $56,299.99, gain. 22. (a) 353.4975 ; 158.2824; 227.5579; 139.187; 111.2937; 164.901. (6) 381.217; 74.1416; 516.1397; 146.0072; 37.214. Check, 1154.7195. Page 112 1. 3010.2525. 4. 5060.61. 7. 3630.336. 2. 24,388.8. 6. 333.693. 8. 3633.333. 3. 30,045.6. 6. 1605.6. 9. 5556.0505. Page 114 1. 2*, 7. 6. 32, 5, 7. 11. 2, 52, 13. 16. 22, 3, 52, 23. 2. 2, 32, 7. 7. 28, 112. 12. 2, 3, 127. 17. 2*, 3, 43. 3. 25, 32. 8. 13, 53. 13. 2, 3^, 151. 18. 28, 52, 37. 4. 2, 3, 131. 9. 2, 32, 61. 14. 2^, 3*, 5. 6. 28, 72. 10. 28, 3, 17. 15. 5, 641. Page 115 1. 16. 2. 88. 3. 6. 4. 12,288. Page 116 5. $375. 7. 600 bu. 9. $30.87. 6. 80 da. 8. 180 men. 10. 1200 rm. Page 117 1. 48. 2. 2. 3. 4. 4. 14. 7. 600 bu. 8. 180 men. Page 117 2. 2. 3. 4. Page 118 5. 240. 7. 7875. 6. 858,390. 8. 54,720. 1. 840. 3. 288. 5. 240. 7. 7875. 9. 330. 2. 504. 4. 2944. Page 122 1. \h ^% \h T^. \h tV 3. ^^^mi.; £H; f lb. ; ^,, mi 2. ^% cu. ft. ; j\ A. ; ^ T. 4. ^^ mi. ; ^^ly ^i- 5 ^% 5. IfT.; I^T.; fg-A.; |^A.; ^^sq.mi.; |f g sq. mi. ; f 1 mi mi, BE 10 PRACTICAL BUSINESS ARITHMETIC Page 123 ' 1. ^F- 4. 2.D0fl._ 7. l^//i. 10. i8|AA. 2. -|^- 5. Hi''- 8. A|oiL. 11. 5J7_^5X. 3. J^O. 6. -LV^^- 9- ^11-- 12. 2^/^. 1. 2|^mi. 4. lOf A. 7. 1531 lb. 2. 12tVA. 6. 41 IT. • 8. 51 cu .ft. 3. 4i|| r. 6. 3^A'oT. 9. 14 1 sq. mi. Page 124 1. II, if, U- 6.ff8 ^HlHhjVo- 11- bV^, II &, ^Vo, \%% 2. f §, l§, A- 7. if, f i II, l|. 12. rh, II, ^\, l|. 3. ^1, f -1, t\, T«l^ . 8- IIS ,A%,tVo,t¥o- 13. 31f 1, 7^0 4. M, i%. %h n . 9- 7^4 ,t\\,t\VtI4- 14. 134^io, 1123^00. 5. It, II, M, u • lO- II, II, II, II- 15. 6126 II,178H. Page 126 1. 'tV. 4. 31] i- 7. 185/^. 10. 242 1 13. $374.40 2. If. 5. 24^^o- 8. 37|. 11. 2181|§. 14. $583.38 3. 19|. 6. 32H- 9. 221i|. 12. 1153 iV Page 129 1. 29,332/(.. 4. 38,3171. 7. 102,857| 10. 90,288^9_ 2. 19,657. 5. 37,807 8. 99,313f . 11. 58,893^1 3. 21,337/^. 6. 49,097 Page 9. 97,868f . 131 12. 42,3601. 1. 271. 4. 138ii. 7. 160||. 10. t\' 2. 631. 5. 124M- 8. 2028 iV- 11. 2M- 3. 122^. 6. 228VV. Page 9. 2V- 133 12. U- 1. 61i. 7. 83J. 13. 560. 19. 2016|. 2. 53^. 8. 17f. 14. 51. 20. 2187^. 3. 14tV. 9. 70*. 15. 25. 21. 2160. 4. 67A- 10. 28}i. 16. 357. 22. 31981. 5. 28|. 11. 20f. 17. 15lf. 23. 3173f. 6. 2it. 12. 33|>. 18. 750. 24. 448. 1. P70.51. 2. 1215.97 Bl ANSWERS 11 Page 134 3. !|55.68. 4. $97.34. Page 135 \. ^^^. 3.1121. 6.266. 7. $169. 9. $62.50; 2. If. 4. 326|. 6. 66. 8. |2.72, gain. $218.75. Page 136 10. $62.50; $203.13. 11. 23.22 gr. pure gold, 2.58 gr. alloy; 116.1 gr. pure gold, 12.9 gr. alloy. 12. 19.29 gr. nickel, 57.87 gr. copper. 13. 412.8 gr.; 371.^2 gr. 1. 18,042|. 3. 15,679^V- ^' 8455^2. 2. 19,178-11. 4. 20,827^. 6. 934911. Page 137 1. $5268.75. Page 138 1. $503.50. 2. $2602.50. Page 141 1. \^%. 4. 1171. 7. 1^. 10. 4|. 13. 1^\. 16. 119^\. 2. 60. 6. 26|. 8. 7-,L. 11. 35|. 14. 2^^- ^'^' H- 3. 152. 6. 77^. 9. l^,. 12. 68t\. 15. 34§. 18. 12||f. 1. 211§. 3. 69-i§|. 5. 24tV^. 7. 96. 9. 6t^\V 2. 16|il. 4. 30|. 6. 36|t|. 8. 27^-^7. Page 143 1. Cost, $100 ; asking price, $140 ; 4. First cost, $32; marked price, $48. selling price, $126. 5. $6300. 2. Bonds, $1440 ; bank stock, $900. 6. Oats, 3300 bu. ; wheat, 1100 bu.; 3. $18,672. rye, 1650 bu.; $3313.75. Page 144 1. 9,000,000 ; 7,200,000. 3. 76,800,000 ; 12,800,000. 2. 3,136,000 ; 224,000. 4. | ; ^ ; 31,443,324. 5. 1,907,210. RE 12 PRACTICAL BUSINESS ARETHMETIC Page 145 1- I- «• U- 9- ^Uu- 13. 260f^. 2. tV- 6. 1§. 10. T^^^. 14. 126^^. 3- ^hs- 7. ^7^. 11. 181^. 16. 175^^. 4- i'^- 8. i- 12. 171^^. 16. 1725a_. 1. .875. 4. .4375. 7. .035416. 10. 5.5833+. 2. .3125. 6. .028125. 8. .28. 11. 21.625. 3. .5625. 6. .6875. 9. .00078125. 12. 165.85. Page 148 2. $29.82. 4. 219f da. 6. 250 bu.; 585 bu. ; 1295 bu. 3. 51 men. 6. 10 wk. Page 149 1. 121.77. 2. $154.22. 3. $1.70. 4. $6.25. 6. S^^f. 6. 3/2 da. Page 150 7. $105. 9. $4.31. 11. 262 da. 13. $8599.22. 16. $8.50. 8. $3.59. 10. $222.75. 12. $97.50. 14. $259.15. 16. $1542.63. 17. $1.52 ; $2032.65. 18. A, $50; B, $77.50 ; C, $132 ; D, $160. Page 151 19. $566.29, gain. 20. $51.81, gain. 21. $179.31. 22. $43.87, gain. 23. ^ ; 50% ; 60f ; A, $356.13 ; B, $710.63 ; C, $312.62 ; D, $730.37. 24. $621.63. Page 152 26. $1136.23. 26. $36.09. 27. $14.44. 28. $4.69. 29. $31.50. Page 156 1. $1.64-. 3. If; ^1. 6. $2.25. . 7. | ; $5. 9. $22.20. 2. $1.68. 4. II; ^\. 6. $2.80. 8. $33.60. Page 157 1. A, $21.60; B, $32.40; C, $27. 3. $48. 5. ^. 2. $21,756.69; $25,382.81. 4. $150. 6. $56; f 7. 6|; 4^\; 7^ ; 2^ ; 14| ; 3^; 2^V 5 H '^ ^^'2 5 3^1 ; 4-,^ 8. f ; $135. 9. A, 1 $1530.45; B, ^, $1020.30; C, ^, $510.15. ANSWERS 13 Page 160 1. $210. 2. $292.75. Page 163 1. 14897.90. 2. 1410.92. 3. |5705.11. 3. $680.25. 1. $19,631.33. 2. $54,934.83 ; $2856.25. Page 165 3. $204.69. 4. $537.59. Page 166 6. b. $426.74. 4. $2125.76. 6. $2487.46. 6. a. $198.69. 1. 760 yd. 2. 816 yd. 3. 3660 yd. 4. 2252 yd. Page 167 5. 6916 yd. 6. 5163 bu. 7. 7370 bu. 8. 2040 bu. 9. 6426 bu. 10. 16,323 bu. Page 169 (The small figures indicate the price-list number.) 12 3 4 $59.72; $62.33; $57.84; $201.30; $211.72 $95.74 ; $100.92 $212.20 ; $204.05 $56.63 ; $191.36 $87.97 ; $197.64 6. $145.91 6. $201.54 $195; $97.06 ; $201.52 $155.42 $198.14 1. $103.75. $163.09; $166.58 $204.09; $202.67 Page 176 2. $441.84. 5 $64.97 ; $215.96 $108.06 $218.74 $173.06 $214.41 $67.14. $229.22. $112.03. $227.20. $183.24. $224.89. 3. $333.75. Page 177 4. $51.87. 5. $450.30. 6. $922.32. 7. $882.33. 8. $155.77. 9. $547.12. Page 178 10. $1353.45. 12. $260.56. 14. $52.81. 11. $4329.50. 13. $305.92. 15. $56.3?. RB 1. $573.50. Page 180 2. $1254.20. 16. $515.68. 17. $203.25. 3. $65. 1 14 PRACTICAL BUSINESS ARITHMETIC Page 182 1. $149.81 : 11 pennies, 3 nickels, 8 dimes, 7 quarters, 8 halves, 4 I's, 12 2's, 7 6's, and 8 lO's. Page 183 2. $227.20. 3. 20 pennies, 4 nickels, 8 dimes, 6 quarters, 7 halves, 4 I's, 16 2's, 7 5's, 9 lO's, and 3 20's. 1. $2690.76. Page 184 2. $804.71. 3. $5631.88. Page 185 4. $155.95 : 15 pennies, 5 nickels, 3 dimes, 5 quarters, 4 halves, 7 I's, 5 5's, 6 lO's, and 3 20's. Page 187 1. $3.12. 2. $3.87. 3. $88.65. Page 188 4. $30.25. 6. $19.56 ; $13.61 ; $25.31 ; $21.48. 5. $35.87; $29.87. 7. $52.58; $53.49; $75.68; $95.84; $115.72; $125.37. Page 192 1. 1386 in. 3. 335s. 5. 57.75 ft. 7. 522,720 sq. ft. 2. 48-1 pk. 4. 41,814 in. 6. 48,000 oz. 8. 20,608 cu. ft. 1. 3520 ft. 3. 32,397f sq. ft. 6. 1980 ft. 2. 96cu.ft. 4. 31iin. 6. 300 sec. Page 193 1. 232 rd. 4 yd. 7. 33 sq. yd. 5 sq. ft. 72 sq. in. 2. 131gal. 3qt.,orl6bu. Ipk. 7qt. 8. 13 T. 19 cwt. 3. 4 hr. 9. 76 rd. 2 yd. 4. 1 sq. yd. 4 sq. f 1. 128 sq. in. 10. 400 cd. 6. 204 bu. 11. 3 cu. yd. 3 cu. ft. 6. 20 mi. 60 rd. * 12. 17431b. 12 oz. 1. /^ft.; /^yd. 2. £5375. 3. .818 rd. 4. £527. 5. 5.3605 T.; 6.875 T.; 12.145 T.; 14.62 T.; 14.195 T. 6. $5.47; $6.78; $2.16; $4.25; $10.13; $101.84. ANSWERS 15 Page 195 1. £1180 88. 6. 2 mo. 16 da. 9. 30f cd. 2. £2134 9s. 6. 1 mo. 10. $20,512.50. 3. 582 T. 489 lb. 7. 6 mo. 15 da. 11. £1198 14s., gain ; 4. 3087 T. 990 lb. 8. 6 mo. 16 da. $5833.47, gain. Page 196 1. 237 da. 3. 232 da. 6. 254 da. 7. 94 da. 2. 201 da. 4. 254 da. 6. 133 da. 8. 163 da. 9. 2 yr. 7 mo. 18 da.; lyr.3mo.27da.; 5 yr. 8 mo. 25 da.; 17yr.9mo.21da. Page 198 1. $12.86; $13.38. 3. 500 mi. 6. $43,666.25. 2. $67,671.87. 4. $2, gain. Page 199 7. £93 Is. 6d.; $452,95. 9. $28.83; $17.52. 10. £45 19s. 3d.; $223.68. Page 200 11. $23.96. 1. $268.09. 2. $216.41. 3. $642.49. Page 202 2. $17.22. Page 203 3. 36 ft.; 131.9472. 4. $7.92. 6. 4800 poles. Page 205 1. 1114.308 sq. yd. 2. 54.45 ft. ; $5445. 3. 4500 tiles. 4. 8946 sq. ft. Page 206 3. $288,000. 4. $2000. Page 208 1. 18. 5. 24. 9. 95. 13. ^. 2. 22. 6. 32. 10. 58. 14. {|. 3. 26. 7. 85. 11. 8.4. 16. ||. 4. 27. 8. 63. 12. 12.26. 16. |f |. RE 16 PRACTICAL BUSINESS ARITHMETIC Page 209 1. 30 rd. 2. 120 rd. - 3. 50 ft. 4. |190. 6. $28. Page 211 2. 33,750 shingles. Page 212 3. 17,500 shingles. 1. |205.20. 2. f21.71. Page 213 3. $101.70. 1. |24. 2. $7.61. 3. $122.67 4. $146.67 ; $149.11. Page 214 1. $19.22. 3. 1231 sq. ft. hard wood ; 1154 sq. ft. spruce. 6. $42.90. 2. $118.13. 4. $79.26. 6. $312.94. Page 216 1. 20 yd. 2. 181yd. 3. $22.92. 4. 30 yd. 5. 23^ yd. Page 218 1. $7.60. 2. 8 rolls. 3. $3.44. Page 219 1. 140/^cu. yd. 2. 135 on. ft. 3. $8050. Page 220 1. llicd. 2. 40 ft. 3. 600 ft. ' 4. 4 ft. Page 223 1. 21331ft. 3. 2560 ft. 5. 1600 ft. 7. $36.78. 2. 390 ft. 4. 3733^ ft. 6. 3600 ft. 8. $332.05. Page 224 1. $26.76. 2. $39.79. 3. $29.45. 1. 3240 gal.; 3231.58 gal. 3. 900 gal.; 897.66 gal. 2. 2120.58 gal.; 2115.07 gal. 4. 26,507.25 gal. ; 26,438.4 gal. ANSWERS 17 Page 225 1. 132.12, or about 133 perches. 2. 67.88, or about 68 perches. 3. (a) 109.63, or about 110 cu. yd. (6) 102.22, or about 102 cu. yd. Page 226 1. 45,738 bricks. 2. |712.80. 3. (a) 203,500 bricks ; (&) 198,550 bricks. Page 227 1. 460.8 bu. 3. 4 ft. 5.\ in. 5. 42.18 bu. 7. 33.08 bu. 2. 42 bu. 4. 462.8 bu. 6. 362.88 bu. Page 230 (Problem 1 includes problems 1-12 on pages 189, 190.) 1. $507.31. 4. $426.13. 7. |545.96. 10. $515.06. 2. $700.15. 6. $414.98. 8. $430.51. 11. $637.58. 3. $641.86. 6. $1107.98. 9. $694.76. 12. $339.99. Page 234 1. $656. 3. $3. 5. $4050. 2. A, $453.60 ; B, $750 ; C, $2250. 4. $2847, gain. 6. $2503.91. Page 235 1. 16%. 2. 80%. 3. 4%. 4. 21%. 6. Smith, 58% ; Brown, 42%. 6. 11%. Page 236 1. $4000.^ 2. $60,803. 3. $20,625. 4. $359,100. ' 6. 2275 students. Page 237 1. $0.95. 2. $6. 3. $147.63. Page 238 1.12,444. 2. $0.64. 3. $125. 4. 212 papers. 5. 43bbl. Page 239 1. $155.02. 2. $23,477.20; $14,086.32. 3. 3^%; 3200%. 4. $2494.17. Page 240 6.33^%. T. 4^%. 9. $1491. 11. 1900% ; 96%. 6. 54% ; 46%. 8. $4000. 10. 88.8%. BE 18 PRACTICAL BUSINESS ARITHMETIC Page 241 12. $2400. 14. A, 175,000; B, 150,000; C, 125,000 13. 764%. A, 38|%; B, 331%; C, 27^%. 15. United States, 450,000,000 T. ; 48.6% Great Britain, 250,000,000 T. ; 27% Germany, 175,000,000 T.; 19% France, 50,000,000 T.; 5.4% Other countries. 200,000,000 T. ; 1,125,000,000 T. Page 242 16. 25.2%. 17. 22|% 18. Corn, 24.1% decrease ; wheat, 3.1% increase ; oats, 20.8% decrease ; barley, 21.5% decrease ; rye, 2.8% decrease ; buckwheat, 26.3% decrease. Page 243 20. Total, 27,323,055 ; men, 22,489,425 ; women, 4,833,630 ; Per Cent Total Men Women N. Atlantic 30.3 29.1 35.9 S. Atlantic 13.1 12.3 16. N. Central 33.7 35.1 27.2 S. Central 16.8 16.9 16.9 Western Totals, 6.1 100% 6.6 100% 4. 100% Jl. 26.3% ; 20.8% ; 79.2% ; 380%. Page 245 1. 16,000%. 2. $2250. 3. 14.8%. 4. $606.14; $11.71. 6. $196.52. 6. 1st mo. $2400 3d mo. $3600 ; 7. 121.3%. 8. $1800. Page 248 ; 2d mo. $3000 ; 4th mo. $3240. 1. 2. $2268. 3. $3000. $1872. 4. $1710. 5. 2916. 6. $1760. 7. 100 yd. 9. $244. 8. $135.72. Page 249 10. The second; $1. 11. $432, gain. 12. a. $307.67. 6. $51. c. $888.25. Page 250 1. 73%. 3. $550. 5. $540. 2. A single discount of 65% ; 13%. 4. 5^%. 6. $1687.50. ^,. RE 'lO ANSWERS 19 Page 252 1. |288. 2. 156.25. 3. !|675.90. 4. |1200. 6. |1083.46. Page 253 1. 184.38 2. $720, gain. 3. fl323. 4. |3199.39. Page 254 6. $3020.87; f3083.16 ; $3103.41; $3167.40. 7. $41.61. 6. £340 63. 3d.; $1656.13. 8. $400.55. Page 255 1. 331%. 3. 22f%. 5. 33JL%. 7. $270. 9. $107.53. 2. 25%. 4. 28f%. 6. $800. 8. $341.89. Page 257 1. $49.27. 3. $2.50, loss. 6. $136.50 ; $796.50. 2. $3470.83. 4. $190 ; $3990. Page 258 1. 140%. 3. 100%. 6. $300, gain ; 33^%.- 2. 140%. 4. $230, gain ; 33^%. 6. 25%. Page 259 1. $72. 2. $85. . 3. $18.60. Page 260 4. $1600, loss. 5. $6451.50. 6. $14. 7. $120. 1. 20%. 2. 12i%, gain. 3. $3800. 4. $8467.20. / Page 261 6. $17,404.80. . 7. $990. 9. $16. 11. $216 ; 32%. 6. $6072 ; 30.67%. 8. $162, gain. 10. $675. 12. $5.73. Page 263 2. $16,300. 8. 26%. 4. $81.43. 5. $1620. 6. 6^% ; $110.03. Page 265 J eAb^^ ^ hAJ^ ^^ pAa ^^ y^ ^^ rj-.ii + 'r.wy ' t. r e r.ao ux in.mE r. 8 n rl.un ^ eu.ns ,,1'- ,. ri. h + r^j_n l_^iii_^. 8.^-^^^^-^. 11.-^. 14. p. r e 'ew.hd 'ep.ay -L ^ T3-u# !i^ 9 i-tl^. 12. ^. to. Tl. 3#, 1^ Z.AHL 6.^. 9. i-tl^. 12 '"-' .a m RE 20 PRACTICAL BUSINESS ARITHMETIC Page 267 1. $625. 2. !|40. 3. fO.50. 4. f4.80. 6. fO.60. Page 268 6. Bookcases, $14.40 ; chiffoniers, |21. 60. ^- ^^^^TTT' pencils,—-—; cards, ^. 0. ht f.ht .fa Page 269 2. $2.35. 3. 12^%. 4. $0.41. Page 273 2. $2842. 4. $3880.82, proceeds. 6. $430.50. 3. $1293.60. 5. $1142.32. 7. $235.20. Page 274 8. $225. 9. $366.69, proceeds ; $6.69, gain. 10. $1649.80, net proceeds. 1. $3.75; $2730. 2. $200; $81,450. 3. $1037.50. 4. $262.50. 6. $6971. Page 275 6. $7563.75. 7. $243.75 ; $173,243.75. 8. $834.75. 9. 2% ; $5319. Fack of Debt 1. $457.75 2. $259.00 3. $175.50 4. $325.45 6. $182.40 6. $255.50 7. $112.75 8. $282.00 9. $258.00 10. $424.00 11. $455.95 12. $132.00 13. $2375. Page 276 Rate of Agent Principal Commission Received Received 2% $9.16 $448.59 1% $2.59 $256.41 3% $6.27 $170.23 2% $6.51 $318.94 5% $9.12 $173.28 4% $10.22 $245.28 4% $4.51 $108.24 H% $4.23 $277.77 mo $6.45 $251.55 Hlo $14.84 $409.16 2% $9.12 $446.83 5% $6.60 $125.40 14. 4%. 15. $357.50. ANSWERS 21 Page 282 1. $210. 2. $31.25; $78.13. 3. $32. 4. $168 ; $4218.75. Page 283 6. A, $3000 ; B, $2500 ; $90 ; $75. 7. $252. 6. $8071.65. 8. $5600; $1600. 9. $55.33 ; A, $2000 ; B, $2400 ; C, $1600. 10. ^tna, $10,366.67 ; Continental, $3887.50 ; Ger. Am., $5183.33. Page 284 11. $50.90, less. 12. In full : B, $1500 ; D, $7000. Page 285 1. A, $5400 ; B, $5100. 3. $556.25 ; $2443.75. 2. $2540; $38.10. 4. $25,856.60; $387.86. 6. $180 ; $138.88 ; $9258.88. Page 288 1. $63.60. 4. $65. 7. $780,000. 2. $44.73. 6. $82.40. 8. $575,000. 3. $52.06 6. $240,000 Page 1. 289 9. $0.012 ; $94.90. 10. $16.50. 12. B, $479.50 ; C ;, $876. 14. $9; $19. 11. $0,017. 13. $0,006. Page 290 1. $46.22. 9. $641.70. 17. $103.32. 25. $356.93. 2. $22.32. 10. $1534.50. 18. $140.90. 26. $488.44. 3. $19.53. 11. $1827.45. 19. $54.48. 27. $1596.81. 4. $86.12. 12. $406.41. 20. $88.29. 28. $1465.31. 5. $157.69. 13. $372. 21. $178.47. 29. $394.51. 6. $245.52. 14. $517.08. 22. $163.44. 30. $1671.95. 7. $273.42. 15. $1333.43. 23. $122.11. 31. $187.86. 8. $342.24. 16. $1670.28. Page 24. $136.20. 295 32. $394.61. 1. $3062.60. 2. $365.80. 3. $6568. 90. 4. 34;*-. RE 22 PRACTICAL BUSINESS ARITHMETIC 1. $24.50. 2. $170.45. 3. $170.45. 4. $434.35. 6. $1200. Page 6. $404. 7. $9.50. 8. $537.60. 9. $28,486.80. 296 10. $542.70. 11. $200. 12. $965. 13. $2142. 14. $119. 16. $1509.90. 16. $2380. 17. $3319.75. 1. $2.70+. Page 297 2. $365.36. 3. £136 16s. lOd. Page 298 4. $657.46; $229.95. 6. 72^- 6. 8%+ ; 1. $5.58. 4. $4.20. 2. $2.45. 5. $7.20. 3. $4.52. 6. $5.52. Page 299 7. a. $40.80. 6. $96.15. Page 302 7. $4.35. 10. $10.07. 8. $13.41. 11. $1.19. 9. $11.20. 12. $3.65. 13. $4.70. 16. $2.68. 14. $5.45. 17. $6.90. 16. $1.26. 18. $4.44. 1. $88.13 2. $21.53 3. -$17.11 4. $65.10 Page 303 $34.27; $39.17; $29.38. $6.73; $14.80; $9.42; $10.77. $4.89; $9.78; $12.22; $2.44; $24.44. $86.81; $13.02; $39.06; $78.12; $69.44; $60.76; $26.04. Page 304 1. $399.35. 2. $338. 1. $11.20. Page 305 3. $195.42. Page 306 2. $19.53. 4. $449.96. 3. $41.62. 1. $120. 2. $318. 3. $304. Page 307 4. $79. 7. $560.03. 6. $742.05. 8. $1875.20. 6. $336.09. 9. $41. 10. $0.21. 11. $29.82. 12. $28.27. BE ANSWERS 23 1. $6.30. 2. $10.83. 3. $3.68. 4. $0.63. 6. $1.77. 1. $80.25. 6. 7. 8. 9. 10. $8.25. $2.15. $3.22. $4. $0.08. Page 308 2. $250.53. Page 309 11. $6.75. 12. $5. 13. $14.40. 14. $2.10. 16. $4.20. 3. $113.71. 16. $7.35. 17. $1.48. 18. $0.84. 19. $0.73. 20. $2.52. 1. $1.62. 2. $44.12. 1. $5.8Y. 2. $8. 3. $103.87. 4. $23.29. Page 313 5. $191.59. 6. $95.08. Page 314 7. $48.26. 8. $98.23. 3. $262.50. 4. $467.50. 5. $2.84. 6. $4.83. 9. $266.22. 10. $142.83. 7. $82.87. 8. $159.50. Page 316 4. $1301.04; $735.17; $1836.13. 1. $14.97. 2. $5.13. 3. $7.59. 4. $9.22. 5. $5.37. 6. $2.56. 7. $10.20. 8. $11.97. Page 317 9. $690.41. 10. $1849.32. 11. $92.81. 12. $129.45. 13. $37.97 14. $66.24 16. $10.76 $56.96. $22.08. $16.14. 16. $130.41; $86.94. J Page 319 1. Time offer .'^-'; 3. Cash offer. ^^ - 6. $1777.78. 2. Time offer./, ^ 4. $5.60, gain. 6. $77.16. 7. $1200. 1. $394.40. 2. $144.21. Page 320 3. $43.20. 4. $1943.73. 6. $1892.40. 1. $802.94. 1. $1624.88. 2. $670.60. Page 321 2. $156.12. Page 322 3. $5542.82. 4. $2139.38. 3. $811.82. 6. $1876.94. 6. $3732.25. 24 PRACTICAL BUSINESS ARITHMETIC Page 324 1. $624,317.55. 2. $38,937.24. 3. $6996.81. 4. $1000. 1. $11.94. 2. $76. 3. $1065.60. 4. $994.70. Page 325 6. $248.27. 6. 15%. 7. 36%. 8. $8.75. 9. $19,978. Page 329^ 1. Apriri6; 46 da. 4. April ^ ; 21 da. 7. April 11 ; 27 da. 2. Feb. 261 a^a. 6. June 29 ; 47 da. 8. July 30 ; 57 da. 3. May 1^ ; 7i da. 6. April 8 ; 58 da. 9. June 18 ; 89 da. •? ' Page 331 1. $4.90; $1045.55. 3. $1.95; $298.05. 2. $1.84; $243.69. 4. $2.07; $458.73. Page 332 6. $3.19; $793.21. 7. $1004.85. 9. $669.60. 6. $877.24. 8. $1249.18. 10. $670.66. Page 333 11. No. 20, July 25 ; 38 da. ; $12.67 ; $1987.33. No. 21, Aug. 1 ; 45 da. ; $26.25 ; $3470.25. No. 22, June 30 ; 13 da. ; $3.25 ; $1496.75. No. 23, July 14 • 27 da. ; $4.05 ; $896.55. No. 24, July 15 ; 28 da. ; $1.77 ; $376.75. 12. $427 3.39. 13. $254.59. Page 334 14. $973.74. Page 335 1. $4925. 2. $1188. Page 336 3. $12,032.50. 4. $15,083.13. 1. $2000 ; $2010.10. 2. $4000. Page 337 1. 2. 3. Face (Totals) $2100.85 $1584.84 $2227.82 Discount Coll. & Exch. (Totals) (Totals) $17.55 $1.87 $13.54 $1.59 $19.05 $1.85 Proceeds $2081.43 $1569.71 $2206.92 ANSWEKS 25 Page 340 1. $525. 3. $419.85. 2. $1979.17; $1038.55; $562.89. 4. a, $235.31; 6, $472.11; c. $3802.33. Page 344 1. $233.85 ; $1.46 more by the United States rule. 3. $5086.87. 2. $515.36. 4. $313.13. Page 345 6. $317.91; $4.79 more by the United States rule. 6. $6054.45. 7. $219.94. Page 348 1. $2112.22. 2. $5.78; $4050.53. 3. $1816.48. Page 351 1. $308.85; $932.61. 2. $813.50, balance, July 1, 1915. 3. $783.57, balance, Jan. 1, 1916. Page 353 1. $84.28 ; $85.12. 3. $73.44. 6. $50 ; $50.22. 2. $72 ; $72.48. 4. $97.52. Page 357 1. $75.30. 2. $134.49. 3. $1292.95. Page 362 1. $3962.71 ; $680.14 ; $768.92. 2. $250 ; $1 per $1000. Page 363 3. $850. 5. $712.65. 4. $1.70, collection; $2906.70, proceeds. 6. No answer can be given here. > Page 365 ^ 1. $497.83. 2. $3484.25. 3. $1149.13. Page 366 4. $6321.66. Page 368 1. 3^1^% discount ; $17,113.42; $12,923.29; $127,099.31. 2. $178.05; $477.80 26 PRACTICAL BUSINESS ARITHMETIC Page 369 3. $16,841.45. 5. $373.94. 4. $6789.69. 6. $43.38, total charges ; $42,907.87, total proceeds. Page 370 1. £25.3; £150.75; £200.525; £300.6375. 2. $124.10; $586.17. 3. $65.45; $357.18; $60.80; $139.93; $562.20; £256 17s. 2d. 6476.68 fr.; 5252.1 M. 4. $20,992,790. Page 373 1. $14,062.50. 3. 54steres; 14 ^^^ cd. 5. $284, gain. 7. $2.27. 2. $114.24. 4. $1.38. 6. .97 mi. 8. 2 hr. Page 374 1. 246.91 guilders. 2. £10 5s. 4d. 3. $50. 4. $25. Page 377 1. a, $487.50 ; 6, $5850 ; c, $8775 ; d, $64.60 ; e, $96.90 ; /, $484.50 ; g, $47.69 ; h, $38.15 ; i, $476.88 ; j, $1430.63 ; k, $953.75 ; I, $2861.25. 2. a, $485.50 ; 6, $5826 ; c, $8739 ; d, $64 ; e, $96 ; /, $480 ; g, $47.44 ; A, $37.95 ; i, $474.38 ; j, $1423.13 ; k, $948.75 ; Z, $2846.25. 1. $2661.93. 2. $24,275. 3. £4900. Page 378 4. $867.38. 5. $20,190. 6. $198. 7. £4825. 8. £120. Page 379 9. $322.86. 10. $23,359.03. 11. $23,365.06. 12. £4776 15s. Page 380 13. $2064.19. Page 382 1. $244.93. Page 383 2. $4902.21. 1. £1078 8s. 9d. 2. $3524.46. 3. $7127.27. 4. $5054.42. RE ANSWERS 27 Page 387 1. March 13, 1916. 4. June 18, 1916. 7. Nov. 3, 1916. 2. April 16, 1916. 5. May 16, 1916. 8. Dec. 29, 1916. 3. Sept. 18, 1916. 6. Feb. 28, 1917. 9. Dec. 11, 1916. 10. July 12, 1916. Page 391 1. Jan. 4, 1916. 3. April 12, 1916. 6. April 6, 1916. 2. Dec. 24, 1915. 4. May 10, 1916. Page 392 1. July 11. 2. July 31. Page 394 1. $201.86. 2. $2082.34. Page 395 3. $1089.26. 4. $1302.02. 5. $741.47. 6. $1054.31. Page 400 1. $2000. 3. $2200. 6. $50,000 ; $2375. 7. $48,750 ; $1300. 2. $3375. 4. 4|%. 6. 2% ; $300. Page 401 8. $25,000,000 ; $18,750,000. 11. 4% ; $31,900. 9. 8% ; $1000. 12. $30,000 ; $3750 ; $3000. 10. 9% ; $9000. 13. $6,500,000 ; $13,500,000. Page 402 14. $18,575 ; $105,000 ; $62,175. Page 403 1. $475,000. 3. $312,812.50. 6. $290,312.50. 2. $273,125. 4. $200,937.50. 6. $268,437.50. Page 404 7. $376,2.50. 9. $.304,500. 11. $349,.562.50. 13. $340,812.50. 8. $458,937.50. 10. $471,187.50. 12. $493,062.50. 14. $416,937.50. 1. $1000, loss. 10. $2812.50, loss. 19. $1125, gain. 2. $1812.50, gain. 11. $1375, gain. 20. $11,625, gain. 3. $5750, loss. 12. $1500, gain. 21. $1750, gain. 4. $875, gain. 13. $2250, gain. 22. $3750, gain. 5. $3625, loss. 14. $2750, gain. 23. $2375, gain. 6. $1625, gain. 15. $250, loss. 24. $250, loss. 7. $1000, gain. 16. $250, gain. 26. 59^. 8. $3312.50, gain. 17. $875, gain. 9. $1625, gain. 18. $5000, gain. 28 PRACTICAL BUSINESS ARITHMETIC Page 405 26. 200. 27. $8,689.06, loss. 28. $249,875. Page 411 1. $26,906.25. 3. $83,646.25. . 5. $45,238.75. 2. $612.50. 4. $253,750; $5087.50; June 1, 1925; $22.50. Page 413 1. $10,822.22. 4. $14,245.42. 7. $6010.83. 2. $19,860.56. 6. $6370. 8. $9876.26 3. $3867.92. 6. $12,640. 9. $11,251.67. Page 416 1. $600, gain. 2. $812.50. 3. $440.26, gain. 4. $6529.33, gain. Page 417 6. $762.64. 6. $482.67 ; $25. 7. $2956.25. Page 418 1. $4357.50. 2. $207.50. 3. $123.76, gain ; 1.1+ %. Page 419 4. $6482.81, gain. 6. $478.75. 8. $345, gain. 10. $16,417.67. 6. $75, loss. 7. $116, loss. 9. $284.38. Page 425 1. $4403.20. 3. $599.80,' 20-yr. endowment. 6. $708.45. 7. $2602. 2. $3324. 4. $2267.13. 6. $11,001.61. Page 427 1. G, $12,220 ; H, $24,440 ; 3. $9000, share of each son ; I, $6110. $12,000, share of each daughter. 2. F, $2280 ; D, $1140 ; E, $570. 4. A, $7000 ; B, $4200 ; C, $6300. Page 430 1. $1392.25, net gain of each; $6392.25, Boyd's present worth; $6392.25, Allen's present worth. 2. $3786.46. 3. $9765.68. ^^^^ ^^"^ 4. $10,249, O's present worth ; $9949, P's present worth ; $10,199, Q's present worth. 1. $10,099.16, A's present worth ; $8899.16, B's present worth. RE 3 I's present ANSWERS 29 Page 432 2. |4750, A's net gain ; $2750, B's net gain. 3. $12,052.36, C's present , worth ; $10,276.18, D's present worth; $10,276.18, E's present worth. 4. $7323.26, F's net capital ; $8323.26, G's net capital. 5. $31,700, J's net capital; $14,250, K's net capital ; $2550, L's net capital. Page 433 1. $831.16, A's share ; $1246.74, B's share ; $2077.90, C's share. $1020.10, D's share ; $1326.13, E's share ; $1428.14, F's share. $3844.20, G's present worth ; $2562.80, H's present worth ; $1922.10, resent worth. Page 434 4. $1308, gain on merchandise ; $800, Robinson's | of net gain ; $400, Bressee's ^ of net gain ; $4800, present worth of the firm ; $3200, Robin- son's present worth ; $1600, Bressee's present worth. Page 436 1. $17,209.50, present worth of the firm ; $10,150, Brown's net invest- ment ; $4850, Hart's net investment ; $15,000, net investment of the firm ; $2209.50, net gain of the firm ; $11,254.75, Brown's present worth ; $5954.75, Hart's present worth. Page 437 2. $43,461.10, total resources; $12,400, total liabilities; $31,061.10, present worth of the firm ; $12,060, Burgess's net investment ; $9940, Clapp's net investment; $9061.10, net gain of the firm; $16,590.56, Burgess's present worth ; $14,470.55, Clapp's present worth. 3. $15,100.55, total resources; $3258.25, total liabilities; $11,842.30, present worth of the firm ; $10,219.75, Linden's net investment ; $6057.70, firm's net loss; $7680.25, Greene's net investment; $17,900, firm's net investment ; $7190.90, Linden's present worth ; $4651.40, Greene's pres- ent worth. 4. $1044.04, net gain of each ; $42,551.33, total resources ; $12,028.25, total liabilities ; $30,523.08, present worth of the firm ; $15,560.99, West- fall's present worth ; $14,962.09, Manning's present worth. Page 439 1. $5345.08, R's present worth ; $4364.92, C's present worth. 2. $28,700, E's present worth ; $22,190, F's present worth. RE 30 PRACTICAL BUSINESS ARITHMETIC Page 440 1. $43,586.12, total resources; f8460, total liabilities; |35,126.12, pres- ent worth of the firm ; |19,302.50, Cutter's net investment ; $17,447.50, Woodward's net investment ; $1623.88, net loss of the firm ; $18,490.56, Cutter's present worth ; $16,635.56, Woodward's present worth. 2. $1194, Curtis's net gain ; $796, Barton's net gain ;. $9490, present worth of the firm ; $5694, Curtis's present worth ; $3796, Barton's present worth. Page 441 3. $11,000.88, cost of sales ; $2908.21, Palmer's ^ of net gain ; $2908.21, Mills's i of net gain ; $2908.20, Newbury's ^ of net gain ; $78,874.62, total resources; $10,150, total liabilities; $68,724.62, present worth of the firm. Page 442 4. $19,220, Smith's present worth ; $12,715, Osgoodby's present worth. 5. $14,596.95, net gain ; $5865.65, Congdon's net gain ; $4365.65, Robinson's net gain ; $4365.65, Moulton's net gain ; $91,336.95, total resources ; $27,240, total liabilities ; $64,096.95, present worth of the firm ; $23,425.65, Congdon's present worth ; $24,575.65, Robinson's present worth ; $16,095.65, Moulton's present worth. Page 445 1. $3; 4 mo. ; $87. 2. $36. 3. $950. Page 446 Page 447 4. $270. 1. $466.80. 2. $511.37. 3. $582.63. Page 448 1. $0,995+. 2. $8; $240. 3. $3600, gain ; 28.8%. 4. $6200, gain. r /^ 5jl8fi^ UNIVERSITY OF CALIFORNIA LIBRARY