+I-IX1-H 2 WHHHV o EFFICIENCY ARITHMETIC ADVANCED If iiornia >nal ty J92O EDITION CHADSEY-SMITH UNIVERSITY OF CALIFORNIA AT LOS ANGELES GIFT OF Tint . izL-':r EFFICIENCY ARITHMETIC ADVANCED BY CHARLES E. CHADSEY, PH. D. DEAN OF COLLEGE OF EDUCATION. UNIVERSITY OF ILLINOIS. URBANA. ILL. FOMERLY SUPERINTENDENT OF SCHOOLS. DETROIT. MICH. AND JAMES H. SMITH, A. M. INSTRUCTOR IN MATHEMATICS AND DIRECTOR OF PRINCIPALS' COURSE. STATE NORMAL SCHOOL. WHITEWATER, WIS., FORMERLY INSTRUCTOR IN MATHEMATICS. SCHOOL OF EDUCATION. UNIVERSITY OF CHICAGO. 1920 Edition ATKINSON, MENTZER & COMPANY CHICAGO NEW YORK BOSTON ATLANTA DALLAS COPYRIGHT, 1917-1920, BY ATKINSON, MENTZER & COMPANY All rights reserved n *> J -J PREFACE This book has been prepared in the belief that work in ithmetic in the seventh and eighth grades should emphasize ^f drill upon fundamentals and their application to living, vital ^v problems that the average child is almost sure to encounter in K'lis individual experiences. At the same time, it is recognized _ _ hat for the great majority using the books of this series certain topics will never receive consideration in the school training . unless presented in this volume. Great care has been taken to present these topics in a simple, clear manner which ought to make their meaning and significance intelligible even to the younger pupils. The problems of the book, almost without exception, are actual problems taken from the various lines of business represented. Business men from all sections of the country have contributed problems, furnished definite and accurate information upon which to base problems, and have criticized the work from the standpoint of practical efficiency and reliability. Acknowledgment is hereby made to these gentle- men for their invaluable assistance. The methods of presentation and explanation of topics new to the child have been carefully tested in the school room and their effectiveness is thereby assured. Simplicity, clearness, and the avoidance of unnecessary repetition we believe to be characteristic of this series, especially in the applications of percentage and practical measurements which so often unneces- sarily confuse the pupil. Many school systems are modifying their courses in mathe- mathics in order to permit elementary algebra to be commenced in the eighth grade. This volume permits, through its arrange- ment, a very simple omission of topics in Part I which will III 348558 IV PREFACE enable any teacher to cover the essential topics in less than the customary two years. The arrangement also enables those who prefer to postpone some of the topics found in Part I to combine the seventh- and eighth-grade topics in such a way as to give a more extended discussion of closely related subjects. The fact that there are in reality only a few mathematical principles involved in ordinary arithmetic is kept clearly in mind. Too often the pupil has been led to believe that each new topic has little in common with preceding topics and therefore fails to learn the greatest educational lesson that can be taught the application of a known principle to a new condition. The effort in this book is to keep the relationship between mathematical facts constantly before the pupil. Teachers of arithmetic must never forget that accuracy and reasonable rapidity in manipulation of numbers are one of the chief aims in this study. Pupils of the seventh and eighth grades need continued practice of this kind. Ample oppor- tunity for this drill is furnished, and from the beginning to the end of the course there should be recurrence to these exercises. While it is not possible, in the limited space, to make per- sonal acknowledgment to the large number of educators who have rendered assistance of great value in the preparation of this volume, the authors desire to express their indebted- ness especially to Miss Katherine L. McLaughlin of the Department of Public Instruction, Madison, Wisconsin, and to Mr. James C. Thomas of the publishers' editorial de- partment, for their invaluable criticisms and suggestions. Credit is also due to Mr. Charles L. Spain, Assistant Super- intendent of Schools, Detroit, Michigan, for valuable help relating to the "Speed and Accuracy" drills given through- out this series. CONTENTS PART I SEVENTH YEAR CHAPTER I. REVIEW OF THE FUNDAMENTALS 1-26 TRAINING FOR SPEED AND ACCURACY CHAPTER II. REVIEW OF FRACTIONS 27-48 THREE MEANINGS OF FRACTIONS, 27; REDUCTION OF FRACTIONS, 27; ADDITION AND SUBTRACTION OF FRACTIONS, 29; MULTIPLICATION AND DIVISION OF FRACTIONS, 33; REVIEW OF DECIMALS, 38; APPLIED REVIEW PROBLEMS IN FRACTIONS, 45. CHAPTER III. PERCENTAGE 49-88 EXPLAINING PER CENT, 49; THE DECIMAL POINT AND PERCENTAGE, 49; COMMON FRACTIONS AND THEIR EQUIVALENT PER CENTS, 50; EQUATIONS APPLIED TO PERCENTAGE, 52; DRILL PROBLEMS IN PERCENTAGE, 55; PROBLEMS COLLECTED BY PUPILS, 73; APPLIED PROBLEMS IN PERCENT- AGE, 75. CHAPTER IV. APPLICATIONS OF PERCENTAGE 89-128 BUSINESS TRANSACTIONS, 89; DISCOUNTS, 91; INTEREST, 95; PARTIAL PAYMENTS, 101; COMMISSION, 104; TAXES, 107; SPECIAL ASSESSMENTS, 110; CUSTOM DUTIES, 112; INTERNAL REVENUE, 115; INCOME TAXES, 116; INSURANCE, 118. CHAPTER V. BUSINESS FORMS AND ACCOUNTS 129-148 SALES SLIPS, 129; INVOICES, 131 ; MONTHLY STATEMENTS, 133; RECEIPTS, 134; CASH ACCOUNTS, 135; DAYBOOK OR JOURNAL, 137; PERSONAL AC- COUNTS, 138; INVENTORIES, 140; PAY ROLLS, 141; CASHIER'S MEMO- RANDUM, 142; AGENCIES FOR SHIPPING MERCHANDISE, 144-6. CHAPTER VI. PRACTICAL MEASUREMENTS 147-170 LINES AND ANGLES, 149; RECTANGLES, 151; BOY Scours APPLIED PROBLEMS, 154; PARALLELOGRAMS, 156; TRAPEZOIDS, 158; TRIANGLES, 159; AREA OF TRIANGLES, 160; CONSTRUCTIONS USED IN MEASUREMENTS, 163; APPLIED PROBLEMS, 165. V VI CONTENTS PART II EIGHTH YEAR CHAPTER I. REVIEW EXERCISES 171-198 TRAINING FOR EFFICIENCY, 171; CHECKING UP, 171; SPEED TESTS IN MULTIPLICATION, 175; SHORT METHODS IN MULTIPLICATION, 176; SPEED TESTS IN DIVISION, 180; SHORT METHODS IN DIVISION, 180; REVIEW OF FRACTIONS, 183; REVIEW OF DECIMALS, 185; REVIEW OF PERCENTAGE, 188. CHAPTER II. BANKS AND BANKING 199-230 BANK DEPOSITS, 200; CHECKS, 201; SAVINGS ACCOUNTS, 204; BANK DISCOUNT, 208; EXCHANGE, 209; FEDERAL RESERVE BANKS, 214; STOCKS AND BONDS, 216; SIGNATURES AND SEALS, 221; INVESTMENTS, 225. CHAPTER III. REMITTING MONEY 231-238 POSTAL MONEY ORDERS, 231; EXPRESS MONEY ORDERS, 232; BANK DRAFTS, 233; CHECKS, 234; EMERGENCY REMITTANCES, 236; TELEGRAPH- ING MONEY, 236; CABLING MONEY, 237; MONEY BY WIRELESS, 238. CHAPTER IV. PRACTICAL MEASUREMENTS 239-281 QUADRILATERALS, 239; TRIANGLES, 240; SQUARES AND SQUARE ROOTS, 241; RIGHT TRIANGLES, 246; EQUILATERAL TRIANGLES, 251; CIRCLES, 253; SHOP PROBLEMS, 255; HEXAGONS, 260; SOLIDS, 261; PRISMS, 262; CYLINDERS, 268; SILOS, 269; IRRIGATION, 270; GOOD ROADS, 272. CHAPTER V. EFFICIENCY IN THE HOME 282-293 BUILDING A HOME, 282; FURNISHING A HOME, 284; EXPENSES OF A HOME, 286; CAMPFIRE GIRLS, 287; THE FAMILY BUDGET, 288; EFFICIENCY IN BUSINESS, 290. CHAPTER VI. MEASURING INSTRUMENTS 294-312 THERMOMETER, 294; BAROMETER, 296; HYGROMETER, 297; WEATHER REPORTS, 298; ELECTRIC METER, 302; GAS METER, 304; STEAM GAUGE, 306; SURVEYOR'S CHAIN, 307; MEASUREMENT OF TIME, 308; STANDARD TIME, 309; INTERNATIONAL DATE LINE, 311. CHAPTER VII. GRAPHS 313-319 PICTORIAL GRAPHS, 313; LINE GRAPHS, 314; BAR GRAPHS, 316; DIS- TRIBUTION GRAPHS, 318; CIRCLE GRAPHS, 319. CHAPTER VIII. THE METRIC SYSTEM 320-329 WEIGHTS AND MEASURES, 320; LENGTHS, 321; SQUARE MEASURE, 322; VOLUME, 323; CAPACITY, 324; WEIGHT, 325; SUPPLEMENT, 332; INDEX, 345. ADVANCED ARITHMETIC PART I Training for Speed and Accuracy Several weeks before the opening of the regular baseball season, the players of the big leagues go south for a spring training trip. The players, with their lack of exercise during the winter's vacation, would not be in proper condition to go into the opening game of the season without this sort of preparation. You are just returning from a summer's vacation, during which you have lost some of your speed and accuracy in the various processes of arithmetic. It is therefore wise for you to take a preliminary training trip by reviewing the fundamental processes. When asked what the new workers in his firm needed most in arithmetic, the head of the school for training workers in one of the largest mercantile firms in the country replied: "Teach them to add, subtract, multiply and divide." He emphasized what all business men want speed and accuracy in those four fundamental processes. CHAPTER I REVIEW EXERCISES Exercise 1. Reading Numbers . In your studies and in reading the magazines and daily papers you are frequently called upon to read numbers. For convenience in reading, large numbers are pointed off into periods as in the following illustration: I I 1 1 I i i I 9 & 4* 2 B 3 3 6,069,000,000,000,000,000,000. The number above represents the estimated weight of the earth in tons. Read it. In the following table the diameter and average distance from the sun is given for each of the planets in our solar system. Read these distances. Name of Diameter Average distance from planet in miles the sun in miles 1. Mercury 2,962" 35,392,638 2. Venus 7,510 66,131,478 3. Earth 7,925 91,430,220 4. Mars 4,920 139,312,226 5. Jupiter 88,390 475,693,149 6. Saturn 77,904 872,134,583 7. Uranus 33,024 1,753,851,052 8. Neptune 36,620 2,746,271,232 A rapid review of this chapter should be given, followed by a systematic use of one or more of the standardized drill exercises at the beginning of each recitation period. REVIEW EXERCISES 3 Exercise 2. Writing Numbers Occasionally one is called upon to write difficult numbers, and he should be able to do so when the need arises. Write the following numbers : 1. Ten thousand ten. 2. One hundred fifty thousand fifteen. 3. Two million two hundred thousand. 4. Sixteen million sixteen thousand sixteen. 6. Twenty-eight million four hundred fifteen thousand. 6. Two billion one million two hundred thousand seventy. 7. Four trillion four hundred billion two million. 8. Sixteen billion sixty million fifteen thousand. 9. Twenty-four billion sixty million sixty thousand. 10. Seventy million seventeen thousand six. 11. Twenty-nine billion six million twenty thousand. 12. Fifty million one hundred fifty thousand thirteen. 13. Forty billion one hundred seventy million. 14. Eight hundred thousand nine hundred sixty-four. 16. Twenty-four million twenty-six thousand two hundred. Exercise 3. Roman Notation It is customary to express chapters of books and often dates on important buildings in Roman numerals. Read the following numbers : 1. IV 6. XIX 11. XLIV 16. D 2. VI 7. XX 12. LXVI 17. M 3. XIV 8. XXII 13. XC 18. MDC 4. XVI 9. XXXIV 14. XCVII 19. MDCCCXCVII 6. XVIII 10. XL 16. C 20. MDCCCCXVII Express in Roman numerals: 1. 9 3. 29 6. 47 7. 72 9. 1492 2. 14 4. 33 6. 58 8. 96 10. 1918 4 SEVENTH YEAR EXERCISES FOR SPEED AND ACCURACY Addition, Subtraction, Multiplication, and Division To the Teacher: The following exercises have been standardized so that the same time limits should be used for each exercise. In the prepar- ation of this drill material, all of the fundamental facts were included, but special emphasis was placed upon the difficult facts by including them more frequently than the easy facts. The following time limits have been selected after a careful study of the achievements of pupils in the cities where extensive surveys have been made. The use of the three time limits provides an incentive for the rapid workers in a class as well as the slow ones. Grade Excellent Good Fair Seventh l| minutes 2 minutes 1\ minutes Eighth 1 minute 1^ minutes 2 minutes The best results can be obtained by giving one or two of these exercises at the beginning of each arithmetic recitation. Most of the exercises can be conveniently done by placing a sheet of paper under the examples in the book and writing the answers on this sheet of loose paper. Those exer- cises which cannot be conveniently done in this manner should be hekto- graphed or mimeographed. These exercises may be used in two ways: (1) All pupils may practice on each exercise together. The teacher should announce the three time limits in succession, each pupil indicating by E, G, or F the time in which he finished the exercise. After time is called, the pupils should exchange papers and check them as the teacher reads the correct answers. The teacher should keep individual records of the time limits made by each pupil, also noting the number of examples correctly worked by each pupil not finishing the exercise in one of the three time limits. (2) Start all of the pupils on the first exercise. As soon as a pupil finishes correctly all of the examples in this exercise in one of the three time limits, he should go on with the next exercise. Under this plan each pupil can progress at his own pace. Only the papers of those who have finished need be collected and checked, because those who did not finish must repeat the same exercise. Do not require a pupil to practice on the same exercise more than 3 or 4 times, but allow him to go on and attempt at a later date to complete the unfinished exercise. EXERCISES FOR SPEED AND ACCURACY Exercise 4. Addition 4 6 7 2 2 6 5 7 1 9 3 4 2 5 3 5 2 2 4 2 7 1 3 4 7 3 3 9 7 3 4 6 7 4 6 8 6 1 5 9 8 4 2 6 1 3 1 6 1 8 3 5 3 1 3 6 2 1 7 9 9 1 4 5 9 2 8 8 8 4 2 4 7 1 6 7 2 8 4 3 1 8 3 3 1 1 2 4 6 6 3 1 5 7 8 9 6 7 8 6 1 9 9 6 4 6 1 2 6 5 1 6 6 3 9 7 4 5 2 2 2 2 3 1 3 9 3 7 6 7 7 2 5 8 3 4 4 4 9 Exercise 5. Subtraction 19 36 31 27 44 19 69 63 22 38 43 66 7 9 8 3 6 4 2 7 7 4 5 6 67 32 62 88 24 79 41 30 66 60 36 61 9 3 6 8 5 6 7 3 3 7 7 2 43 99 44 28 76 70 64 28 41 38 64 86 6 8 3 9 2 4 8 3 4 6 9 6 Exercise 6. Multiplication 28 36 93 24 80 76 79 86 66 80 96 26 49 19 57 38 64 73 47 56 61 67 80 14 49 38 8768359427978 SEVENTH YEAR Exercise 7. Division 2)42 10 5)89 5 3)171 2)680 6 )474 5; 1325 9)7fi 16 4)37 2 2)196 8)472 7 )588 S 1552 9)46 18 7)25 9 6)888 3)207 6 390 4; 1348 Exercise 1. Addition 1 6 . 4 7 3 946 3 2 1 2 2 3 5 7 323 2 2 3 5 3 8 5 4 788 6 7 5 2 4 7 9 649 8 5 7 9 8 8 3 584 2 7 9 6 9 1 4 5 9 6 7 5 7 6 1 1 2 4 6 1 6 3 5 5 6 7 8 8 7 6 2 6 1 1 5 7 3 6 9 2 8 7 5 9 8 9 4 5 9 7 8 5 i Exercise 9. Subtraction 43 39 53 41 28 67 97 51 25 30 75 60 4 3 9 328 293 9 9 6 44 16 33 52 67 45 28 42 39 20 85 35 7 4 8 526 649 2 8 2 55 31 19 36 61 45 32 30 57 38 44 54 7 6 5 855 886 7 4 6 If these exercises are mimeographed, the order of the examples should be frequently changed to prevent memorizing the answers. EXERCISES FOR SPEED AND ACCURACY 7 Exercise 10. Multiplication 29 45 57 27 70 27 93 42 39 5 6 4 9 6 8 4 7 5 80 72 19 89 39 96 38 68 96 6 9 7 8 6 2 4 3 9 65 57 34 70 84 79 61 56 87 7 5 8 4 9 3 6 8 7 Exercise 11. Division 9)657 8)672 5)420 8)504 7)665 2)162 3)960 8)576 4)248 7)434 9)864 6)160 6)192 5)450 9)963 4)200 8)560 4)164 Exercise 12. Addition 9 4 3 4 2 2 9 4 6 8 2 9 4 3 3 2 1 9 9 8 2 7 1 3 8 5 6 1 6 2 4 9 6 7 4 3 9 7 3 7 8 8 3 6 9 9 8 3 1 5 9 6 9 3 7 6 4 7 2 1 3 5 6 5 8 7 8 4 6 6 5 5 9 9 4 6 5 8 5 6 6 2 7 9 5 3 7 1 7 5 7 2 7 3 3 4 6 3 5 9 3 6 3 6 SEVENTH YEAR Exercise 13. Subtraction 97 92 98 71 92 93 87 82 45 47 47 60 23 54 20 69 53 37 94 95 84 35 61 65 94 96 63 35 30 18 19 38 14 10 27 28 90 83 74 90 35 66 71 92 42 11 24 49 50 28 19 32 80 29 Exercise 14. Multiplication 489 908 578 629 942 905 6 8 5 3 7 4 529 920 388 493 438 308 9 2 7 5 3 9 476 847 736 321 175 9 4 8 6 7 Exercise 15. Division 7)5621 3)2856 2)1042 Exercise 16. Division 7)3157 4)3468 2)1888 6)5058 9)9487 3)2625 6)4320 8)2592 79)237 54)432 78)390 96)288 83)249 74)518 29)174 68)204 92)828 49)343 58)232 79)474 88)528' 63)504 91)455 EXERCISES FOR SPEED AND ACCURACY 9 Exercise 17. Addition 42 16 28 69 82 37 33 94 72 85 89 78 97 99 94 76 85 43 72 75 63 76 66 36 93 95 36 43 62 94 73 89 62 83 57 54 72 62 58 64 78 29 34 46 85 64 82 84 87 83 56 98 49 79 73 75 86 32 24 46 67 69 42 68 43 62 91 70 11 28 62 69 66 32 33 53 71 75 91 20 Exercise 18. Addition 84 36 67 29 33 65 78 41 92 43 76 47 69 33 59 85 49 84 79 88 78 83 66 36 18 99 39 24 73 64 68 43 96 47 46 98 73 77 68 76 76 42 88 89 96 78 44 76 Exercise 19. Subtraction 436 347 723 811 900 989 166 268 697 364 612 679 661 823 791 814 919 956 280 479 196 147 310 406 960 379 963 766 675 169 197 594 297 597 10 SEVENTH YEAR Exercise 20. Multiplication 2735 4981 9730 6573 5387 75849 9468 7509 5389 5628 7365 23685 9648 7 2489 4 1249 9 Exercise 21. Division 90)4140 30)2370 60)5760 40)3880 50)3950 80)5920 70)4760 20)1780 60)5940 40)3920 90)5130 Exercise 22. Division 70)6720 41)1435 32)1472 21)1953 22)1584 672 461 598 999 454 168 446 459 51)4233 Exercise 23. Addition 95673 97911 58437 55712 73327 78893 68223 81359 31)2418 776 957 873 891 967 838 563 288 EXERCISES FOR SPEED AND ACCURACY 11 Exercise 24. Addition 72 35 87 63 98 59 66 89 95 65 71 28 74 95 64 18 33 67 56 53 71 78 40 68 39 47 55 54 17 69 15 75 57 98 96 49 22 83 97 45 Exercise 25. Subtraction 8233 2678 9391 5373 6413 5742 9831 2765 3894 2052 7565 1486 9584 2885 9482 7073 9341 8510 8921 3968 3727 5949 7123 4476 Exercise 26. Multiplication 2156 6 7260 6 4368 8974 3 8 8950 7 5084 9 8394 6 8795 9386 4 3 1604 8 7235 8 4162* 7 4658 5 Exercise 27. Division 71)1704 52)3224 92)2300 61)5124 82)3444 91)7553 12 SEVENTH YEAR Exercise 28. Practice Problems 1 Not only does one need to know how to work examples rapidly in addition, subtraction, multiplication, and division, but he also needs to know how to apply these processes rapidly and accurately in solving problems. In completely solving any concrete problem the following steps are used : (1) Reading and interpreting the problem. (2) Selecting the principles and processes needed in its solution. (3) Performing the computations. (4) Checking the results. Be sure that you understand what is asked for and what facts are given which can be used in the solution of the problem. In selecting the principles or processes needed to solve the prob- lem, it will help if you picture the problem as a real problem and ask yourself what processes you would use in a similar real situ- ation. In checking the results, ask yourself whether the answer is reasonable, viewed from the conditions of the problem, as well as check the abstract computations. In the following exercise merely indicate the processes used in solving each problem: 1. A real estate dealer owns a farm of 142 acres worth $125 an acre; 5 city lots worth $1500 each, and a store valued at $8750. Find the value of all of his property. iThis list of problems is designed for drill in reasoning out the solutions of problems. The class period should be used in merely indicating the solutions of these problems. The pupils should be required to copy the indicated solutions, and then perform the computations and check the results for seat work or home work. This type of lesson gives the teacher an excellent opportunity to teach a pupil how to attack and solve a con- crete problem. PRACTICE PROBLEMS 13 Indicating the solution: 1 (142 X $125) + (5 X $1500) +$8750 = value of all of his property. 2. A farmer sold 5 jars of butter containing respectively 24 lb., 26 lb., 29 lb., 28 lb., and 31 Ib. Find the total num- ber of pounds that he sold. Indicating the solution: 24+26+29+28+31 = no. of lb. sold. 3. A boy bought a pony for $55. His expenses for the month amounted to $6. He sold the pony for $58. Did he gain or lose and how much? 4. The cost of drilling a well was 40^ per foot for drilling and 80 f* per foot for the iron tubing. If the well was drilled 150 ft. and 100 ft. of tubing was used, how much did it cost? 6. The distance from Chicago to St. Louis is 282 miles. What will a round-trip ticket cost at 3j per mile? 6. A man bought a lot for $1250. He built a house on it that cost $5275 and then sold the property for $7000. How much did he gain? 7. In 1917, the House of Representatives had a membership of 435. If the population of the United States was approxi- mately 100,000,000 at that time, what was the number of people to one representative? 8. A farmer exchanges 36 bushels of apples at $1 per bushel for coal at $8 per ton. How many tons does he receive? 9. Mr. Brown bought a house for $8000. He paid $2000 down and agreed to pay the balance in 8 equal yearly payments. How large was each payment? 10. A real estate man trades 40 front feet of city ground at $240 a front foot for a Western farm of 80 acres. How much is the farm worth per acr*? 1 Parentheses should be used to separate the various steps in the problem in order to eliminate the necessity for teaching the law of signs. 14 SEVENTH YEAR 11. If, as computed, the water area of the earth is approxi- mately 144,500,000 square miles and the total surface of the earth is approximately 196,907,000 square miles, how much more water surface than land is there? 12. If the flow of water through the Chicago Drainage Canal is 360,000 cubic feet per minute, how much water passes through it in 24 hours? 13. A building worth $400,000 was damaged to the amount of $75,000 by fire. The owners .received from an insurance company $60,000 damages. What was the net loss to the owners of the building? 14. A falling body drops 144 feet in three seconds and 256 feet in four seconds. How far does it drop in the fourth second? 15. The product of four numbers is 10,920; three of the num- bers are 7, 8 and 15. What is the fourth number? 16. A gallon contains 231 cubic inches. How many gallons are there in a cubic foot (1728 cubic in.)? 17. A man had $1275.45 on deposit in a bank. He gave checks for the following amounts: $110.00; $25.00; $222.50; $8.75 and $76.25. What was his balance in the bank after those checks had been cashed? 18. 15 acres of potatoes yielded 4125 bushels. What was the average yield per acre? 19. Mr. Jones bought 79 acres of land for $5530. How much did he pay per acre? 20. A speculator bought wheat in the fall of 1916 for $1.59 per bushel and sold it for $1.73 per bushel. How much did he make if he handled 500,000 bushels in the deal? 21. A man earns $1200 a year. His expenses per year are $975. In how many years can he save $1800 under those conditions? PRACTICAL PROBLEMS 15 22. Mrs. Klein bought 2 dozen eggs at 38 cents per dozen, 2 pounds of butter at 57 cents per pound and 10 pounds of sugar for $1.10. How much change should she receive from a ten-dollar bill? 23. A grocer bought 300 sacks of flour at $1.25 per sack and paid $12.00 freight on the whole amount. He is selling the flour at $1.50 per sack. How much profit does he make on each sack? 24. A man bought three houses. He paid $5500 for the first; $4565 for the second and $7750 for the third. He sold the three houses for $18,500. How much did he gain? 25. A farmer sold 1600 bushels of rutabagas at 35^ per 100 pounds (1 bu. of rutabagas weighs 52 lb.). How much did he receive for them? 26. A dealer bought 3726 bushels of wheat at $2.03 per bushel and sold it at $2.07 per bushel. How much did he make on the transaction? 27. A grocer bought a box containing 100 apples for $2.00. Ten of them spoiled. He sold the remainder at 5 cents each. How much did he gain on the box of apples? 28. John has 45 marbles. Harry and James each have 9 times as many as John. How many marbles do they all have? 29. If the daily pay of a railroad conductor is $4.80 for an 8-hour day, what is his salary for a year of 330 working days if his overtime amounts to 320 hours and is paid at one and a half times the regular rate? 30. A man's estate amounted to $15,630. His wife received $6000 and the rest was divided equally among his three children. How much did each receive? 31. 11,161,000 bales (500 pounds each) of cotton were raised in the U. S. in 1916. Find the production in pounds. 16 SEVENTH YEAR 32. A dairyman has several cows in his herd which are un- profitable. How much will he receive if he sells six of them weighing 1205, 1115, 1155, 1075, 1130, and 1145 pounds at $11.50 per cwt.? 33. The expenses for food in a student's boarding club of 38 members amounted to $110.84 for one week. What was the total cost per student if each pays 75 cents extra to cover hired help and other incidental expenses? 34. Mr. Warner has $8450 in cash with which he wishes to buy a farm. He reads an advertisement of a farm of 120 acres for sale at $175 an acre. The terms are j cash and the balance on time. If he buys the farm and pays f cash, how much will he have left to buy stock and farm implements? 35. Andrew bought 18 young hens for $27.00. He spent $5.75 in repairing the poultry .house on their lot. His total bill for feed was $35.65. His receipts for eggs were: October $3.16, November $5.15, December $8.04, January $10.78, Feb- ruary $12.84, March $9.23, April $8.91, May $7.96, June $6.50, July $5.94, August $5.39, and September $4.98. His hens were worth $1.25 each at the end of the year. Find his net profit for the yea.*. 36. Ellen pieced a quilt for her mother. The pattern which she selected makes a block 8 inches square. She made the quilt 2 yards wide, using 5 blocks and filling in the places between the blocks with plain strips. How wide was each of .the 4 plain strips? If she used 6 blocks in making the length and filled in with 5 plain blocks of the same size, how long was the quilt? 37. An agent bought 1000 bushels of corn at $1.18 a bushel and sold it at $1.27 a bushel. Find his gain. 38. A carpenter worked 2 days (10 hours each) and 6 hours. What did he receive at 65 cents an hour? PRACTICE PROBLEMS 17 39. Dorothy's mother asked her to figure up the milk bill for the month of January. They used 2 quarts per day and 5 extra quarts during the month. The milk cost 14 cents a quart. What was the amount of the bill? 40. A farmer had 16 ducks to sell. On November 1 they averaged 5^ pounds each and he was offered 31 cents a pound. On November 25 they averaged 6 pounds and he sold them for 34 cents a pound. What was his additional profit in the 24 days if the extra feed cost $2.38? 41. Fred raised 44 bushels of popcorn. He sold 9 bushels to a grocer and kept 1 bushel for his own use. He shelled the remainder and shipped it to the city, receiving 9 cents a pound. A bushel of shelled corn weighs 56 pounds. How much did he receive for the corn which he shipped to the city? 42. Ethel worked in a candy factory 8 hours per day and 1 hour overtime each of 24 days. She received 30 cents an hour for regular time and one and a half the regular rate for over- time. How much did she earn in the 24 days? 43. The girls in a high-school graduating class made a rule that their graduating outfits were not to cost more than $20.00. Martha bought 5 yards of material at $1.25 a yard; 3 yards of lace at 30 cents a yard ; 48 inches of ribbon at 30 cents a yard ; hooks and eyes 10 cents; thread 10 cents. She bought a pair of silk stockings for $2.00 and a pair of slippers for $6.50. The dressmaker charged her $4.00. How much less than the allow- ance did her outfit cost? 44. Given the weight of a load of wheat, the number of pounds in a bushel of wheat, and the price per bushel, how do you find what will be received for the load of wheat? 46. Given the weight of a jar full of butter, the weight of the jar, and the price per pound, how do you find the value of the butter? 18 SEVENTH YEAR Exercise 29. Addition 89 57 75 22 28 58 35 85 72 79 94 37 87 68 55 88 86 18 36 48 24 66 10 13 79 63 93 29 59 94 97 36 43 55 93 55 42 47 36 68 Exercise 30. Subtraction 56240 18017 51212 21538 57510 15691 57230 16583 84792 14916 85096 74830 94030 92508 94265 36279 95831 43630 53526 18037 Exercise 31. Multiplication 36 57 18 92 74 63 59 80 40 20 50 90 70 60 21 74 58 30 21 69 78 80 60 90 40 70 30 50 95 48 96 76 74 34 89 70 40 90 80 70 90 80 Exercise 32. Division 29)2014 48)1392 79)6557 EXERCISES FOR SPEED AND ACCURACY 19 Exercise 33. Addition 7 2 4 8 4 3 5 9 9 4 5 6 8 7 2 8 5 7 4 4 3 2 8 9 7 5 6 5 9 2 8 7 3 9 2 3 6 9 9 6 2 5 4 1 1 8 9 9 9 6 5 8 3 1 7 2 7 8 4 1 7 7 6 6 5 9 3 6 8 1 8 9 1 2 7 8 9 6 3 7 Exercise 34. Addition 24 97 92 79 18 17 99 68 73 54 64 51 79 37 76 65 95 65 39 78 87 99 92 55 96 42 88 79 83 72 92 61 53 87 26 61 56 96 24 38 Exercise 35. Multiolication 45 93 39 27 71 90 41 60 63 58 38 72 96 67 29 70 86 13 78 42 Exercise 36. Division 38)2014 99)4653 89)5162 20 SEVENTH YEAR Exercise 37. Addition 355 677 894 901 786 93344 61459 647 258 384 185 908 257 199 649 786 558 124 646 157 891 779 348 993 973 369 925 84287 27380 Exercise 38. Subtraction 73561 61345 92385 27887 46950 58605 82236 56959 62485 98489 24986 78092 91518 24729 99296 85208 Exercise 39. Multiplication 93 65 62 91 53 75 64 94 85 73 95 83 75 40 40 62 69 51 70 84 Exercise 40. Division 72)6552 42)3402 31)5913 62)4650 71)3763 92)2492 Exercise 41. Multiplication 76 94 86 82 21 61 92 80 13 60 26 35 58 14 69 54 74 91 91 37 Exercise 42. Division 58)5278 69)1104 28)2268 EXERCISES FOR SPEED AND ACCURACY 21 Exercise 43. Addition 7 3 4 2 7 3 8 9 7 5 3 7 6 6 3 9 2 6 3 2 5 2 4 8 6 1 6 2 8 9 8 6 6 6 9 9 9 6 4 3 7 3 9 4 8 5 4 4 7 6 4 8 6 4 5 8 1 3 5 9 9 7 5 7 5 3 9 6 6 1 3 9 8 1 7 7 7 9 6 3 Exercise 44. Subtraction 812130 315387 826364 117789 951349 386360 943147 684059 762325 164729 953276 154397 823427 385798 934399 169936 461 38 380 59 Exercise 45. Multiplication 257 62 502 17 418 64 936 49 Exercise 46. Division 8)7688 5)3755 9)7758 6)5802 2)1578 4)3740 7)6832 22 4)39320 7)62594 49)3136 SEVENTH YEAR Exercise 47. Addition 5467 8759 2856 4934 6976 8988 2678 7087 9893 3597 9568 6233 4065 9815 6086 6963 5417 4934 2849 9713 Exercise 48. Multiplication 795 317 714 873 391 809 85 27 45 36 91 39 Exercise 49. Division 6)15432 9)71505 3)29049 8)29960 Exercise 50. Division 88)1672 Exercise 51. Addition 2)17590 5)49315 59)4425 6989 3976 8698 4356 7519 5787 4699 5367 8878 7195 8749 3999 7964 1654 2425 9587 3580 1789 9283 7786 Exercise 52. Multiplication 529 386 542 578 468 851 67 89 47 19 52 87 EXERCISES FOR SPEED AND ACCURACY 23 EXERCISE 53. Addition 3 7 2 4 5 8 9 4 7 3 9 6 5 8 5 4 3 3 3 8 3 9 8 2 6 7 7 3 7 6 1 1 7 9 4 6 9 9 7 5 5 8 7 4 6 6 6 6 7 8 1 4 9 7 3 9 2 5 2 8 6 9 8 1 2 9 4 7 5 2 8 4 8 8 1 2 9 1 7 8 6 9 2 5629 964 8)778896 6)521844 68)1768 98)5978 Exercise 54. Multiplication 7216 378 Exercise 55. Division 5)394820 4)315744 Exercise 56. Division 39)3549 Exercise 57. Division 83)4897 9450 325 9)849384 7)689199 78)4446 67)5628 24 SEVENTH YEAH Exercise 58. Addition 783 816 238 696 739 893 584 464 681 359 377 769 575 471 579 736 237 548 828 284 756 864 599 169 623 798 773 Exercise 59. Multiplication 5629 7216 9450 964 378 325 Exercise 60. Division 94)7426 75)3675 46)3956 Exercise 61. Multiplication 4509 9486 2768 847 607 745 Exercise 62. Division 3)21642 7)42091 6)36318 8)55848 5)35215 9)61488 4)28260 Exercise 63. Division 6)54084 84)5712 63)3591 87)6003 EXERCISES FOR SPEED AND ACCURACY 25 Exercise 64. Addition 6745 3667 7354 7665 8643 5454 6070 5080 9270 8775 9150 7280 5984 5921 8777 6190 9382 9290 6870 9832 8680 9820 1390 8979 Exercise 65. Multiplication 8397 3014 5713 378 947 528 Exercise 66. Division 85)49895 97)81092 Exercise 67. Multiplication 7652 7381 8439 994 629 852 Exercise 68. Division 93)69657 76)63536 Exercise 69. Multiplication 83740 29561 7483 495 26 SEVENTH YEAR Exercise 70 Most stores now have cashiers to make change for their customers. This is much more economical be- cause the cashier by constant prac- tice becomes much more efficient than would be possible for the many clerks whose attention is mainly devoted to selling goods. The modern method of making change for a purchase is by addition. For example, if you sell goods to the amount of $1.73 and receive a five-dollar bill from the purchaser, instead of subtracting $1.73 from $5.00 you start with the amount $1.73 and take 2^, 25j and 3 one-dollar bills from the change drawer and say to the purchaser $1.73, $1.75, $2.00, $3.00, $4.00, $5.00. This method is not only quicker, but saves the purchaser the trouble of counting his change. Practice making change in this way for the following purchases. Amount of purchase 1. $. 0.12 2. $ 3.48 3. $ 1.06 4. $ 5.28 5. $ .08 6. $11.27 7. $12.39 8. $ 7.33 9. $ .65 10. $ 2.48 11. $ .42 12. $ .73 13. $ 1.62 Amount of money presented to the cashier A dollar bill Ten-dollar bill Two dollar bills Two five-dollar bills A dollar bill A ten- and a five-dollar bill Three five-dollar bills Ten-dollar bill Five-dollar bill Three dollar bills A half-dollar A dollar bill A two-dollar bill CHAPTER II REVIEW OF COMMON FRACTIONS Exercise 1. Three Meanings of a Fraction The fraction f may have any one of three meanings. (1) It may mean 3 of the 4 equal parts of a thing; (2) J of 3 equal things; or (3) 3 divided by 4. For example: an inch is divided into fourths, f of an inch may mean 3 of the 4 equal parts of an inch; f of 3 inches; or the quotient of 3 inches divided by 4. I 3 of the 4 equal parts of an inch. I I j of 3 inches. 1 13 inches-:- 4. The above diagram shows the three meanings of the fraction f . Work these three meanings out on your ruler. Exercise 2. Reduction to Lowest Terms The denominator 4 of the fraction indicates the size of the equal parts by showing into how many equal parts the whole has been divided. The numerator 3 shows the number of these equal parts which form the fraction. 1. Show the three meanings-that the fraction -j%- may have. 2. In the fraction -j% what is the denominator? What is the numerator? 3. This fraction shows that the whole has been divided into how many equal parts? 4. How many of these parts have been taken to form the fraction? 27 28 SEVENTH YEAR 6. Answer the same questions for the following fractions: 9 6 4 2 7. 15 12) > & 3> 8> T6' 6. Divide both the numerator and the denominator of the fraction 3% by 4. What is the result? 7. Compare the fraction f with the fraction j*%, using the above diagram. Show that the two fractions are equal by using your ruler. 8. Divide both terms of the fraction -fy by 3. Use your ruler to compare the result with -j^. 9. Divide both terms of the fraction ^ by 2. Compare the result with. -|. 10. Multiply both terms of the fraction f by 3. Use your ruler to compare the result with f . 11. Multiply both terms of the fraction % by 2. Compare the result with ^. Use other examples, if necessary, to make clear the following: PRINCIPLE: When the numerator and denominator of a frac- tion are both multiplied by or both divided by the same number, the value of the fraction is not changed. When the numerator and denominator of a fraction are both divided by the same number, the fraction is said to be reduced to lower terms. When both terms are multiplied by the same number, the fraction is said to be reduced to higher terms. REVIEW OF FRACTIONS 29 12. Change ^ to higher terms by multiplying both terms by 2; by 3; by 5. Reduction to higher terms is used in reducing fractions to a common denominator. 13. Which is shorter: To divide both terms of ^ by 5, and then both terms of the result by 3, or to reduce to lowest terms by dividing both terms of ^ by 15? Reduce to lowest terms: 1. f 7. if 13. if 19. U 25. |f 2 . A 8 . W 14 . |2 2Q ^ 26> || 3. f 9. 16. 21. if 27. 4. 10. a 16. 22. 28. . if . 5. 11. 17. ^ 23. if 29. 6. 12. 18. 24. 30. Exercise 3. Addition and Subtraction of Similar Fractions Similar fractions are fractions having the same denominator. 1. $3 +$4 are how many dollars? 2. 3 books+4 books are how many books? 3. 3 fourths+4 fourths are how many fourths? The form f+f- means the same as 3 fourths+4 fourths. Which is more quickly written? Which form occupies the least space? If we use the more convenient form f for 3 fourths, we must not forget that the denominator merely indicates the name or size of the equal parts. The numerator shows how many of these equal parts compose the fraction. In adding the frac- tions f+T, we are merely adding two numbers of fourths, making -J. How shall we proceed, then, in subtraction of similar fractions? 30 SEVENTH YEAR Add or subtract the following: -f- 1. + = 8. -- + = 15. 2. + = --- 16. 3- A-A= 10. |-|= 17. -+ = 4. i + f= 11. f + f = 18. f + i-i = 6. f + J = 12. J + f = 19. J - f - f = 6. | - f = 13. f - f = 20. +^- A = 7. f - f = 14. A+A= 21. f + f + f = Exercise 4. Addition and Subtraction of Dissimilar Fractions Dissimilar fractions are fractions not having the same denom- inators. Can you add $3 and 4 books together? You can not unless you say 3 things and 4 things are 7 things; or 3 articles +4 articles are 7 articles. Only like numbers can be added or subtracted. The term thing or article might be called the common denominator of the two numbers. Can we add f +f? What must be done before we can add them? What is the least common denominator of these two fractions? The following form will be found very convenient for adding dissimilar fractions : The advantages of writing the denominator once as in the form above are (1) it is shorter; (2) it indicates the common denominator more clearly and (3) shows that only the numer- ators are to be added. The expression Q^r- should be read 8 .[ 9 12 T 12' REVIEW OF FRACTIONS 31 Add or subtract as indicated i- 3- 4. After the pupils understand these problems, put the work on a time basis and give a drill exercise. 8 minutes is suggested as a suitable time limit for the average class. f + i = 7. 5 I + 58 38 SEVENTH YEAR Exercise 10. Review of Decimal Fractions A fraction, whose denominator is ten or some product of tens, is called a decimal. The value of a figure in a decimal is shown by its position with regard to the decimal point. In the above number how does the 1 in tenths place compare in value to the 1 in units place? How does the 1 in units place compare in value to the 1 in hundreds place? How does the 1 in units place compare in value with the 1 in tenths place? How does the 1 in units place compare in value with the 1 in thousandths place? Start at the 1 in hundred thousands place and go to the right. How do the values of the 1's change? Start at the 1 in millionths place and go to the left. How do the values of the 1's change? The number above is read one hundred eleven thousand, one hundred eleven, and one hundred eleven thousand one hundred eleven millionths. Read the following decimals : 1. .001 6. .375 11. .7584 16. .0875 2. 19.02 7. 3.1416 12. .5236 17. .00875 3. .0005 8. 1.4142 13. 1.732 18. .000875 4. 50.001 9. 2150.42 14.. 8.75 19. .005 6. .00125 10. .866 16. .875 20. .000005 REVIEW OF DECIMALS 39 How many decimal places are needed to write tenths; thousandths; hundredths; ten-thousandths; millionths; hun- dred-thousandths? Practice on this question until you can give the answers instantly, because it will help you in writing decimals. Write in figures : l 1. One hundredth. 2. Two hundred and five ten-thousandths. 3. Sixty-three thousandths. 4. Twenty-five hundredths. 6. Seven hundred fifteen thousandths. 6. Eighty-seven thousandths. 7. Nine hundred forty thousandths. 8. Sixty-three hundredths. 9. Sixty-seven thousandths. 10. Eight thousandths. 11. Five ten-thousandths. 12. One hundred twenty-five hundred-thousandths 13. Twenty-five millionths. 14. Twenty-five and five ten-thousandths. 16. One hundred and forty-three thousandths. 16. One hundred forty-three thousandths. 17. Four hundred one and four hundred one thousandths. 18. Three and twenty-five ten-thousandths. 19. Eight hundred and seven millionths. 1 In writing decimals, it is a good plan to have no erasers at the black- board and require the pupils to be sure of the number of places before they begin writing each decimal that you read to them. 40 SEVENTH YEAR Exercise 11. Addition and Subtraction of Decimals Decimals are added and subtracted in the same manner as whole numbers. The decimal points must be kept in a vertical line and the other figures in their proper columns. Add: 1. 2.7; .3; 37.1; 2.04; .0033; 16.125; 105.06. 2. 15.03; 325.075; 18.0025; 15.005; 87.08. 3. .0025; .009; .00125; .875; .05. 4. .425; 3.1416; 1.4142; 15.375; 8.8736; 5.75. 6. 45.375; 37.525; 29.65; 86.245; 18.0005; 57.075. 6. .0075; 5.0035; .2508; .025; 2.1754; .7856. 7. 3.006; 61.375; 25.025; 7.75; .0725; 15.7. 8. 25.5; 5.78; .375; 2.14; 37.45; 4.806; 8.6. 9. .625; .375; .875; .125; .75; .25; .075. 10. 4.5; 67.34; 8.054; .4862; 325.8; .755. Subtract: 1. 4.312 from 7.505. 6. 87.45 from 148.1. 2. 1.4142 from 3.1416. 7. 29.802 from 32. 3. 23.075 from 28.008. 8. .25 from 25.1. 4. 1.387 from 2.025. 9. 2.62 from 4.875. 6. 5.75 from 11.025. 10. 27.51 from 30. Note: Practice should be given in reading decimals as follows: 1.4142 read: one, point, four, one, four, two. Exercise 12. Multiplication of Decimals Express the decimal .05 as a common fraction. Also the decimal .5 as a common fraction. REVIEW OF DECIMALS 41 If we multiply Tih$-Xi%- without cancelling, what is the product? How do we express 1 qo6 as a decimal? Therefore: If we multiply .05 by .5, the product is .025. How does the number of decimal places in the product compare with the number of decimal places in both the multi- plicand and multiplier? PRINCIPLE: In multiplication of decimals as many places are pointed off in the product as there are decimal places in both multiplicand and multiplier. Multiply: 1. 25.5X4.025 9. 62.5X7.05 17. $250. X. 055 2. .005 X. 25 10. .21 X. 3 18. 275.5 X. 039 3. 3.75X3.78 11. S145.50X.375 19. $272.75 X .0275 4. 4.002X.32 12. $257.75X.06 20. 7.5X3.1416 6. .866X1.4 13. $1250.X.055 21. 2.54X2.54 6. 273.5X1.64 14. 2.72 X. 08 22. .5326X175.65 7. 352.X. 0175 16. .0385 X. 55 23. .0375 X. 0025 8. .0002 X. 0021 16. 6.45X3.83 24. 855. X. 0075 25. A cubic foot of water weighs approximately 62.5 pounds. Copper is 8.93 times as heavy as the same volume of water. How much will a cubic foot of copper weigh? 26. Gold is 19.3 times as heavy as the same volume of water. Find the weight of a cubic foot of gold. 27. How much heavier is a cubic foot of gold than a cubic foot of copper? 28. A gallon of water weighs 8.34 pounds. Kerosene is .8 as heavy as the same volume of water. What is the weight of a gallon of kerosene? 42 SEVENTH YEAR Exercise 13. Applied Problems U. S. Army Daily (Garrison) Ration per Man Beef, fresh 20. oz. Milk, evap. unsweetened. .0.5 oz. Flour 18. oz. Vinegari 0.64 oz. Baking powder 0.08 oz. Salt 0.64 oz. Beans 2.4 oz. Pepper, black 0.04 oz. Potatoes 20. oz. Cinnamon 0.014 oz. Prunes 1.28 oz. Lard 0.64 oz. Coffee, roasted and ground. 1.12 oz. Butter 0.5 oz. Sugar 3.2 oz. Syrup 1.28 oz. Flavoring extract, lemon. .0.014 oz. 1. Copy in column form and find the total weight, in pounds and ounces, of the seventeen items given in this table. 2. Find the total required for one week. For thirty days. 3. Find from local prices what the daily ration would cost for each soldier. Find the cost per day for a company of 195 men. 4. Does it cost the government as much to feed the soldiers as it would if they bought their supplies at your local stores? 7 hy? 6. How many ounces of beef, flour, and potatoes are required for each soldier per day? 6. How many ounces of beef, flour, and potatoes are required per day for a regiment of 1980 men? How many pounds? 7. It took 47 army engineers 14 days to build a bridge. What amount of rations did they require for that time? 8. Five Signal Service Corps men were stationed 21 days at Mt. View. How much sugar did they use during that time? 9. Find the amount of salt used by a regiment of 1980 men in a day? Express the result in pounds and ounces. 10. How much butter do 1980 soldiers use per day?. 1 Approximate reduction to ounces. The government standard gives vinegar 0.16 gill and syrup 0.32 gill. REVIEW OF DECIMALS 43 Exercise 14. Division of Decimals 1. Divide .025 by .05. Express as common fractions and divide. What is the quotient? Express this quotient as a decimal. Divide the following decimals by using common fractions: 2. .625-7-12.5. 3. .625^.125. Check your results secured by dividing with common frac- tions with the quotients expressed in the decimal form as shown below: .5 .05 5 .05) .02 5 12. 5) .6 25 .125). 625 25 625 625 Answer the following questions for each of the above -prob- lems: 4. How many decimal places are there in the divisor? 6. How many decimal places is the decimal point in the quotient to the right of the decimal point in the dividend? 6. Can you tell from the above problems how the quotient should be pointed off in the division of decimals? PRINCIPLE: In division of decimals, as many decimal places are pointed off in the quotient to the right of the decimal point in the dividend as there are decimal places in the divisor. Caution: Be sure that you place the figures of the quotient exactly where they belong or you will introduce an error in the result when you point off the decimal places in the quotient. Divide the following (carry out three decimal places if they do not come out even) : 44 SEVENTH YEAR 1. 30. by 7.5 6. 31.042 by 8.3 11. 26.52 by 3.4 2. 1.2 by .6 7. 8.2 by .0041 12. 20.5 by 8.2 3. 36. by 2.4 8. 46.875 by .375 13. 8.5 by 3.4 4. 51.165 by 37.9 9. .0003 by .5 14. 6.3 by .18 6. .008 by .04 10. .4 by .002 15. 3. by 8 Exercise 15. Changing a Common Fraction to a Decimal On page 23 it was shown that one meaning of a fraction is: the numerator divided by the denominator. This is the simplest method to use in reducing a common fraction to a decimal. Reduce f to a decimal. Divide 3 by 8. .375 8)3.000 Therefore: f = .375 Reduce the following fractions to decimals: 11. J 16. | 12. I 17. i 13. f 18. f 1 1 1. 2 6- 1 2-4 7-1 3- f i * 9. f . 1 10. i 19. 20. Exercise 16. Changing a Decimal to a Common Fraction Express the decimal .375 as a common fraction. Reduce this fraction to its lowest terms. Example: 1 3 7 5 Q=-^^= f . Reduce to common fractions: 1. .50 6. .6 11. .125 16. .05 2. .625 7. .875 12. .2 17. .075 3. .75 8. .03125 13. .33| 18. .025 4. .8 9. .0125 14. .66| 19. .02 5. .25 10. .0375 15. .16| 20. .35 APPLIED PROBLEMS IN FRACTIONS 45 Applied Problems Involving Fractions The following problems were supplied by one of the largest stores in the United States. They are practical problems, representing selections from actual sales slips, involving frac- tions. Many of the great commercial houses find it necessary to train their applicants in such problems as these in order to make them proficient in fractions. One young man graduated from a school for training em- ployees in a half-day. Why? Simply because he had mastered his arithmetic before applying for a position and so did not need the course of training. Exercise 17 Find the amount of the purchases in each of the following problems. (Data and prices for 1916) : 1. Mrs. H. A. Marshall purchased 9f yards broadcloth at $2.75 per yard. 2. Mrs. S. A. Thompson bought 1^ yards tulle at $2.75 per yard. 3. Miss Myrtle Hanlon purchased 1^ yards net at if yards lace at 30^; 1^ yards veiling at $1.75. 46 SEVENTH YEAR 4. Mrs. Harry Smith bought 2f yards lace at 65^; 2f yards edging at 3; 8| yards edging at 3^; 1^ yards edging at 15j 5. Mrs. C. P. Murray purchased if yards velour at $2.50; if yards velvet at $3.50. 6. Mrs. M. M. Spaulding bought 5f yards dress goods at $2.65; 4f yards dress goods at $3.55; 1\ yards dress goods at $6.00; 3 J yards dress goods at $5.35. 7. Mrs. E. F. Chatfield ordered 6f yards lace at 45 i; 1 ^ yards veiling at 95^; 1 \ yards fillet at 55^; f yard net at $1.95. 8. Mrs. R. F. Arnold purchased 5f yards edging at 12C 1 ; 2 \ yards silk at 85^; if yards cretonne at $1.50; f yard damask at 15^. 9. Mr. C. P. Chase purchased the following: 31 \ yards linoleum at $1.40; 81 f feet wood strips, laid, at 5f ?f; 6f yards cork carpet at $1.25; 2f dozen f-inch Daisy pads at 80^. 10. Mrs. R. H. Byron purchased \ dozen tassels at $9.00 per dozen; if yards braid at 60^; 1 \ yards guimpe at $1.75; 1^ yards trimming at 45)zf. 11. Mr. S. E. Brown bought if dozen stair pads at $2.00; 21^ yards china matting at 40ff; 6 yards Armstrong linoleum at $1.75. 12. Mr. H. H. Howard purchased if yards linoleum at 80?f; 1 Duchess rug at $7.50; 1 Bokhara rug at $35.00; 1 Smyrna rug at $7.00; 11 \ yards velvet stair carpet at $1.35. 13. Mrs. F. A. Cornell made the following purchases: 6f yards guimpe at 45f; f dozen tassels at $2.25; 4f yards fringe at $1.75. 14. Mrs. M. H. Gardner bought \ dozen tassels at 756; 3f yards trimming at $1.05; 5f yards braid at 50^; 1 j yards braid at $1.25. APPLIED PROBLEMS IN FRACTIONS 47 15. Mrs. J. C. Gibson gave the following order: 1^ yards fringe at 10^; 2 \ yards trimming at 25f; 3 J yards braid at 50^. 16. Mrs. E. S. Harding purchased 15^ yards cretonne at > f yard taffeta at $2.50; 1 velour remnant at $1.50. 17. Mrs. F. L. Black bought J yard braid at 75ff; 2j yards swansdown at $1.75; if yards trimming at 18^. 18. Mr. Frank Adams purchased ^ dozen rolls paper at 126 each; f yards oil cloth at 30^; if yards art paper at 25; ^ dozen Dutch Klenzer at 90p. 19. Mrs. Chas. Madison made the following purchases: f yards oil cloth at 65^; 17^ yards lace at 5^; ^ dozen bars Ivory Soap at 84); \ dozen cans Kitchen Klenzer at 50 j. 20. Mrs. M. C. Nelson bought 1\ yards net at $2.50; \\ yards muslin at $2.50; 16f yards net at 35ff; 1^ yards Sunfast at $2.25; \ pair portieres at $21.50. 21. Mrs. Harry Newell bought the following items: 7^ yards Sundour at $2.50; 4^ yards edging at 10^; 12^ yards muslin at 40^f. 22. Mrs. D. D. Penfield gave the following order: f dozen towels at $3.00; f yards damask at $1.50; \ dozen wash cloths at $1.00; \ dozen dusters at $1.75. 23. Mrs. C. H. Van Buren bought the following: f yards sheeting at 75^; \ dozen towels at $6.00; \ yard linen at 65^; \ yard linen at $1.25. 24. Mrs. C. P. Warren purchased as follows: \ dozen broom bags at $2.40; 3^ yards crash at 30^; 2^ yards huck at 55f; 3^ yards linen at 65^. 25. Mrs. Harry S. Perry purchased the following: \ pound candy at 40^ ; 2^ yards embroidery at 15^; 4f yards embroidery at 15^; if yards embroidery at 18^. 48 SEVENTH YEAR 26. Mrs. Wm. Penn bought the following: if yards silk at $2.00; 1 J yards silk crepe at $2.00; 1 f yards silk at $1.00; f yards silk net at $1.10. 27. Mrs. O. O. Morrison gave the following order: f yards silk at $1.75; 9 yards silk poplin at 500; if yards silk at $1.75; f yards crepe at $1.50; if yards silk at 750. 28. Mrs. S. S. Melrose bought as follows: 2f yards ribbon at 280; 2f yards ribbon at 290; if yards ribbon at 70; 4f yards ribbon at 140. 29. Mrs. Charles Mason purchased the following: 2 \ yards ribbon at 250; 3 \ yards ribbon at 180; if yards ribbon at 380; f yard ribbon at 380. 30. Mrs. Chas. P. Hulce ordered 2j yards trimming at 850; f yards trimming at $3.00; 2j yards braid at 500; 4f yards braid at 70; if yards cord at 80. 31. Miss T. E. Bennett made the following purchases: if yards edging at 70; 2f yards lace at 40; \\ yards lace at 600; \\ yards lace at 25^. 32. Mrs. Harold P. Platt bought the following: \ yard dress goods at $3.10; f yards dress goods at 65j; \ yard dress goods at $3.25; \ yard dress goods at $3.50. 33. Mrs. C. F. Prince ordered the following: \\ yards silver lace at $4.65; lOf yards lace at $2.95; 2f| yards lace at $3.50; 12j yards lace at $1.50; f yards veiling at 500. 34. Miss S. A. Roberts bought \\ yards braid at $1.65; 4 yards braid at 15^; 4f yards braid at 3^; 85 yards braid at 10^; if yards braid at $1.50. 35. Mrs. C. F. Sheldon purchased 16 \ yards net at 500; 3f yards muslin at 550; 44f yards net at $1.00; 2f yards net at $1.25; 2f yards Sundour at $1.25. CHAPTER III PERCENTAGE Exercise 1 * The expression per cent jneans hundredths- To say that 4 per cent of a certain cow's milk is butter fat means that -j-g-o" of the milk is butter fat. The sign % is usually used in place of the words per cent. The fraction twenty-five hundredths may be expressed in three ways: (1) as a common fraction, -Y&O> (2) as a decimal, .25; (3) as a per cent, 25%. The name hundredths is expressed in the first case by the denominator 100; in the second case by means of the decimal point and the two decimal places; and in the third case by the sign %. It is customary to omit the decimal point after whole numbers. The decimal point is placed in the expression 25.% to make clear the process of changing from decimals to per cent. How has the decimal point been moved in changing from the decimal 0.25 to the expression 25.%? A decimal, then, may be changed to a per cent by moving the decimal point two places to the right and attaching the % sign. Change the following decimals to per cents: 1. .25 6. .125 11. .75 16. .3 2. .35 7. .875 12. .005 17. .025 3. .01 8. .5 13. .00125 18. .0075 4. .2 9. .625 14. 2.5 19. .85 5. .16f 10. .375 15. 3.75 20. .20 49 50 SEVENTH YEAR We have already shown that 25.% = .25. In changing from % to a decimal, how is the decimal point moved? Change the following per cents to decimals: 1. 20% 6. 25% 11. 250% 16. 50% 2. 33j% 7. .25% 12. 625% 17. 37j% 3. 375% 8. 75% 13. 10% jo O/ 4. 12|% 9 62~^ 14. 66}% t a 1 5.0/ 4 / 5 1 2 T' 10. 40% 15. 60% 20. 3.9% Exercise 2 How do you change a common fraction to a decimal? Change the following fractions to decimals and then to per cents as follows: -^=.05 = 5%. i. i 6. i 7 2. | 7. 1 8 3. } ** 8. A 1 Q b * 5 ' 9. 3 8 M.'*5" 10. 5 8 11. i 12. 13. 3. 4 2. 5 "- 1 4 5 16. 17. 18. 19. -> 15. f 20. 5~0 From the results that you have secured in the above exercise, fill out a table similar to the form shown below. Learn all the % equivalents of the common fractions, for you will need this information in the following exercise. Common Fractions and Their Equivalent Per Cents i=?% i=?% 1=?% !=?% i=?% i=?% !=?% !=?% Have the teacher check this table before' you learn it so that you will not learn any incorrect equivalents. PERCENTAGE 51 Exercise 3 Find 12j% of 64. 12 \% = what common fraction? If we know that 12^% = ^, which is easier, to take .12^X64 or | of 64? Find the following per cents by using fractional equivalents: 1. 33j% of 120 13. 75% of 320 2. 87 \% of 160 14. 66f % of 300 3. 25% of 60 15. 16f % of 96 4. 20% of 45 16. 83^% of 36 6. 37j% of 200 17. 2% of 150 6. 50% of 1640 18. 80% of 60 7. 12 \% of 400 19. 60% of 450 8. ll% of 81 20. 25% of 820 9. 62 \% of 72 21. 14f % of 70 10. 40% of 75 22. 37 i% of 16 11. 10% of 150 23. 33 J% of 63 12. 6|% of 30 24. 50% of 84 Since per cents may be expressed in equivalent decimals, it is often convenient to multiply by a decimal if the fractional equivalent is large. Find the following per cents, using decimal multipliers: 26. 17% of 153 31. 6% of 43 26. 23% of 90 32. 7% of 55 27. 52% of 83 33. 11% of 85 28. 37% of 135 34. 15% of 124 29. 29% of 105 36. 21% of 34 30. 16% of 38 36. .5% of 96 37. Find 5j% of $2000. 38. Which is larger, 17% of $35 or 15% of $39? 52 SEVENTH YEAR Exercise 4 Choose the most convenient equivalent and find the following per cents: 1. 25% of 1240 16. 21% of 825 2. 8% of 412 17. 40% of 150 3. 12% of 217 18. 50% of 842 4. 20% of 315 19. 16% of 124 5. 12 \% of 720 20. 87 J% of 128 6. 16f % of 96 21. 2% of 500 7. 22% of 121 22. 7% of 125 8. 5% of 132 23. 60% of $80 9. 5% of 120 24. 33j% of $360 10. 80% of 250 25. ll% of $450 11. 13% of 138 26. 75% of $480 12. 37i% of 88 27. 17% of $312 13. 66f % of 75 28. 6% of $450 14. 15% of 200 29. 5j% of $110 15. 62j% of 160 30. If % of EQUATIONS Exercise 5 1. What is the product of 9X15? 9 and 15 are called the factors of the product, 135. 2. If the two factors are given, what process is used in finding the product? 3. If 8 times a certain number = 128, what is the number? 4. If 5 times a certain number =55, what is the number? 6. If the product of two factors =48 and one of the factors is 6, what is the other factor? PERCENTAGE THE EQUATION 53 6. If the product of two factors is 91 and one of the factors is 13, what is the other factor? 7. If the product of two factors and one of the factors are given, what process is used to find the other factor? Show how the preceding problems illustrate the principles: 1. Factor X factor = product. 2. Product -r- one factor = the other factor. The letter X is often used to stand for the unknown product or the unknown factor. It is shorter and is not confusing if you remember that it always stands for the unknown number. Such expressions as 9X15 = X and 8XX=128 are called equations because the expressions on the left and right sides of the equality sign are equal. Any equation can be represented by a balance as shown in the illustration above, putting the expressions on the scale pans and thus showing their equality. The value of X in the equation 9 X 15 = X can be found by multiplying the two factors 9 and 15. The value X in the equation 8XX=128 is found by dividing the product 128 by the factor 8, giving the other factor X = 16. Find the values of X in the following equations: 1. 7XX=35 3. .06X300 = X 2. X=9X25 4. .25XX = 50 54 SEVENTH YEAR 6. XX15 = 75 9. 40 = XX500 6. X= 12X20 10. 6%X$150 = 7. 12XX = 240 11. 25%XX= 8. 240 = XX20 12. $16 = X%X$200 Exercise 6 Percentage problems may be easily solved by stating them in the form of an equation and then solving by the principles: 1. Factor Xf actor = product. 2. Product 4- one factor = the other factor. Remember that, in multiplying or dividing, per cents must be expressed either as decimals or as common fractions. 1. What is 6% of $200? This problem may easily be changed into an equation. X may stand for what, which merely stands for the unknown number. 7s may be replaced by the equality sign ( = ) and the word of may be replaced by the sign X. The equation is: X=6%X$200. 6% and $200 are both factors of the unknown product X. The principle Factor Xj 'actor = product applies to this equation. Before we multiply, it will be necessary to change 6% to a decimal or a common fraction because the multiplier must be an abstract number. 6% = .06. Therefore : 6% X$200 = .06 X$200 = $12.00. 2. What is 25% of $80? Equation: X=25%X$80. 25% =i Then25%X$80=|x$80 = $20. State the equations for the following problems and then solve them : 3. What is 5% of $300? 8. What is 15% of $25? 4. What is 10% of $120? 9. What is 60% of $350? 6. What is 33 J% of $90? 10. What is 8% of $110? 6. What is 50% of 22 pounds? 11. What is 16f % of 48 hogs? 7. What is 20% of 84 miles? 12. What is 12^% of 24 cents? PERCENTAGE THE EQUATION 55 Exercise 7 1. A boy bought a motorcycle for $70 and sold it at a gain of 20%. How much did he gain? This problem can be changed into the simple form of the preceding exer- cise. The question is: How much did he gain? The problem states that he gained 20%. Since gain is always figured on the cost, he gained 20% of $70. In short form the problem really means: What is 20% of $70? Equation: X=20%X$70. X = .20X$70 = $14.00, the gain. Remember that the number of per cent must be changed to a decimal or a common fraction before multiplying, because the multiplier must be an abstract number. 2. A merchant sold a suit costing $15 at a profit of 40%. What was his profit on the suit? By studying this problem as we did problem 1, we see that it can be put in the shortened form: What is 40% of $15? Equation: X = 40%X$15. 40%=f . Then X=f X$15 = $6.00, the profit. 3. A firm recently announced an increase of 15% in the salaries of all of its employees. How much increase would a man receive whose salary had been $100 per month? 4. On a loan of $250 for a year, I receive 6% of that sum for the use of the money. How much do I receive for the use of the money? 6. A real estate dealer sold a lot costing $1500 at a gain of 33j%. What was his gain? Exercises 6 to 13 have been arranged according to the three types of percentage problems for the convenience of the teacher who prefers to use a different method from the one developed in the text. 56 SEVENTH YEAR 6. A farmer planted 40% of his farm of 240 acres in corn. How many acres did he plant in corn? 7. A ranch owner had 648 cattle and marketed 12|% of them. How many cattle did he market? 8. An agent sold an automobile costing him $1200 at a profit of 33^%. Find the amount of his profit. 9. My neighbor sold a cow costing him $75 at a gain of 20%. Find the amount of his profit. 10. I have a balance of $150 on deposit in the bank. If I give a tailor a check for 20% of this amount to pay for a suit of clothes, how much does my suit cost me? 11. A grocer sells eggs costing 36 cents per dozen at a profit of 25%. How much profit does he make on each dozen of eggs? 12. A farmer takes a can containing 100 pounds of milk to a creamery. A test is made of the milk and it shows that the milk contains 3.9% of butter fat. How many pounds of butter fat are there in the can of milk? 13. A family pays 30% of their income of $1200 for rent. How much do they pay for rent? 14. At what price must a horse costing $125 be sold to gain for its owner 20%? 15. If a suit marked at $25 is reduced 20% in price, what is the reduced price mark? 16. A man bought 4 suburban lots for $700 each. On two of them he made a gain of 25% when he sold them and on the others he lost 10%. What was his loss or gain on the four lots? The last three problems in this exercise may be more conveniently solved by using the method shown in the next exercise. PERCENTAGE. THE EQUATION 57 17. How much yearly interest will be received from a Victory Loan Bond at 4f % interest? 18. A certain city has a population of 10,500. 60% of the inhabitants are native born, 18% of German descent, 10% of Irish descent, 7% of Italian descent, and the remainder of other nationalities. How many of each group are there in this city? 19. An automobile agent bought 12 cars and sold 83^% of them during the first month. How many did he sell during that month? How many did he have left out of the 12 cars? 20. Elizabeth saw an advertisement of a special sale on girls' coats. All coats were to be reduced 20% of the former prices. How much would she have to pay for a coat formerly marked $28.50? 21. A dry-goods dealer bought a supply of coats at $15 each. He marked tham at an advance of 80%. What was the marked price of the coats? 22. A seventh-grade basket ball team won 75% of the games played. If this team played 8 games, how many games did they win? How many games did they lose? 23. A city had a population of 13,080 in 1910. The popula- tion in 1920 showed an increase of 65%. What was the popu- lation of this city in 1920? 24. Real estate owners estimate that an apartment or a house must rent for 10% of its value in order to pay for repairs, insur- ance, taxes, and a fair profit on the investment. What should be the monthly rent on a house costing $6000 at that rate? 26. A school superintendent received a salary of $3600 for a term of 10 months. He received an increase of 25% in his salary. What was his new salary per month? 26. Roy's spelling paper was marked 85%. If there were 40 words in the test, how many did he have correct? How many did he have wrong? 58 SEVENTH YEAR 27. A merchant sells an overcoat for $45.00. His profit was 40% of the selling price. Find the profit. 28. Mrs. Downer rents a house valued at $5250 for a year at 8% of its valuation. Find the monthly rent. 29. A coal dealer raised the price of a certain grade of coal 15%. What was the new price on coal formerly selling at $8.00 per ton? 30. A cow produced 262 pounds of milk in a week which aver- aged 3.8% butter fat. How many pounds of butter fat were there in her milk that week ' 31. Mrs. Griffin receives a yearly income of 8% on an invest- ment of $3750. How much is her monthly income from that investment? 32. What should be the monthly rent on a house valued at $4500 to yield a return of 10% on the value of the property? 33. A school had an enrollment of 252 in 1919. In 1920 the enrollment increased 25%. What was the enrollment in 1920? 34. A merchant bought a bill of goods amounting to $3875.40. He was given a reduction of 2% for paying cash for the goods. What was the amount of the reduction? What was the net amount of his bill? 35. A regiment consisting of 2360 men had 35% of its men killed or wounded in a battle. How many men were left unhurt out of the regiment? 36. A farmer owed $7250 on his farm. He paid off 8% of this amount. How much did he then owe on the farm? 37. In a city grade school enrolling 1840 pupils, 45% were boys. How many girls were there in this school? 38. Frank sold a pair of roller skates, costing $3, for 83-g-% of their cost. Find the selling price. PERCENTAGE THE EQUATION 59 Exercise 8 1. What will be the result if 200 is increased 12% of itself? 200 is already 100% of itself. If it is increased 12%, the result will be 112% of 200. Equation: X = 112%X200. X = 1.12X200 =224.00, the new result. 2. What will be the result if $125 is decreased 20%? $125 = 100% of itself. 100% -20% (decrease) =80%. The new result will be only 80% of $125. X = 80%X$125. X=fX$125 = $100. What will be the result if 3. 300 is increased 30%? 13. $30 is decreased 33j%? 4. $500 is increased 6%? 14. $250 is decreased 20%? 5. 180 Ib. is increased 10%? 15. 360 is decreased 10%? 6. $240 is increased 16 %? 16. $75 is decreased 20%? 7. 80 is increased 20%? 17. 40 is decreased 40%? 8. 36 is increased 33 J%? 18. 240 bu. is decreased 12 J%? 9. 160 Ib. is increased 12 J%? 19. 140 Ib. is decreased 10%? 10. 20 bu. is increased 25%? 20. $120 is decreased 16 %? 11. $500 is increased 8%? 21. $80 is decreased 37 J%? 12. 32 is increased 25%? 22. 8 bu. is decreased 50%? 23. If a suit of clothes marked at $30 is reduced 16 % in price, what is the reduced price mark? 24. A certain brand of shoes, retailing at $5 per pair, advanced 20% in price in a year. What was the increased price of a pair of these shoes? 25. A man paying a rental of $408 per year finds that his rent is to be increased 12% on account of improvements on the property. What is his new rent per year? 60 SEVENTH YEAR 26. If $1640 worth of groceries have advanced 25% in price since they were purchased, what is their new valuation? 27. A man has $14,000 invested in a lumber business and $26,000 in an artificial stone enterprise. In the lumber business, he loses 8% of his investment. What amount must he gain on the other investment to yield him a profit of 10% on both investments? Exercise 9 1. 24 is what % of 30? This type of problem may easily be changed into the equation form: 24=X%X30. In this equation we have the product (24) given and also one of the factors (30). The other factor is unknown. This equation involves the principle: Product-;- one f actor = the other factor. .8 or 80% 30)24.0 24.0 Therefore: 24 = 80% of 30. 2. 16 is what % of 24? Equation: 16=X%X24. The unknown factor X% =the product 16 -5- the factor 24. Since a fraction may stand for an indicated division, we may indicate this division in the form of the fraction, -|-f . Then X%=f = f or66f%. Therefore: 16 is 66f % of 24. 3. 6 is ?% of 18? 9. $80 is ?% of $120? 4. 20 is ?% of 25? 10. 24 bu. is ?% of 40 bu.? 6. 15 is ?% of 18? 11. 48 is ?% of 64? 6. 25 is ?% of 40? 12. $120 is ?% of $2400? 7. 48 is ?% of 80? 13. $16 is ?% of $200? 8. 27 is ?% of 36? 14. 20'bu. is ?% of 24 bu.? PERCENTAGE PRACTICE PROBLEMS 61 15. 80 is ?% of 160? 22. $400 is ?% of $1200? 16. 81 is ?% of 90? 23. $63 is ?% of $1260? 17. 21 is ?% of 63? 24. $7 is ?% of $140? 18. 24 is ?% of 240? 26. $15 is ?% of $300? 19. 16 is ?% of 96? 26. $12 is ?% of $240? 20. 75 is ?% of 125? 27. 320 acres is ?% of 480 acres? 21. $60 is ?% of $75? 28. 10 gallons is ?% of 80 gallons? Work of this type is valuable in giving experience in solving equations before attempting to solve concrete problems in which such equations are involved. Exercise 10 1. A newsboy bought 50 Sunday papers and sold 48 of them. What per cent of his papers did he sell? Since he sold 48 out of 50, the question is: 48 is what % of 50? Equation: 48=X%X50. PRINCIPLE : Product -=- one factor = the other factor. Then X% =48 -i- 50 = .96 or 96%. 2. A farmer bought a carload of steers averaging 930 Ib. When the farmer sold them, they averaged 1240 Ib. What was the per cent of increase in their weight? 1240 Ib. -930 Ib. =310 Ib., the increase. 310 Ib. is what % of 930 Ib.? 3. If the farmer bought the steers for $9.75 per hundred and sold them for $12.85 per hundred, what was his per cent of gain in the selling price per hundred over the buying price? 4. If a grocer buys eggs at 36 cents per dozen and sells them at 39 cents per dozen, what is his per cent of profit? 6. During the season of 1916, the Boston American League ball team won 91 games out of a total of 154. What per cent of its games did Boston win? 62 SEVENTH YEAR 6. During the same season, Brooklyn in the National League won 94 games out of 154. Find the per cent of games won by Brooklyn. 7. In the World's Series between Boston and Brooklyn, Boston won 4 out of the 5 games played. What per cent of games did Boston win in this series? 8. A lumber firm increased its capital from $30,000 to $45,000. What was the per cent of increase in its capital? 9. A laboratory test showed that a white potato, weighing 16 oz., contained 10 oz. of water. What is the per cent of water in potatoes as shown by this test? 10. The same kind of a test on a sweet potato, weighing 15 oz., showed that it contained 8.25 oz. of water. What per cent of water is there in a sweet potato? 11. If the per cent of refuse is the same in both white and sweet potatoes, which of these vegetables contains the more nutritive material? 12. If sweet potatoes are selling at 4 cents per pound and white potatoes at 2 cents per pound, which is more economical, considering the amount of nutritive material in each? 13. What per cent of profit must be made on the sale of goods costing $50,000 to cover an expense of $7500 and a net gain of the same amount? 14. A certain grade of canned peas advanced in price from 12 cents to 15 cents per can. Find the per cent of increase. 16. An owner of a bungalow costing $3000 rents it for $25 per month. His expenses are $60 for repairs, taxes and insur- ance. Find the per cent of profit each year on his investment. 16. A farmer applied fertilizer to a field yielding an average of 48 bushels of corn per acre and secured 66 bushels per acre. Find the per cent of increase due to the fertilizer. PERCENTAGE. THE EQUATION 63 17. A teacher bought a set of reference books for $24.70 and sold them two years later for $15.00. What per cent did they depreciate in value in the two years? 18. Erma bought a pair of stockings marked 75 cents for 60 cents at a clearance sale. What was the per cent of reduction from the regular price? 19. The seventh and eighth grades of a village school had a good attendance contest. There were 20 pupils in the seventh grade and 25 in the eighth grade. The attendance for the first week was: 7th Grade 8th Grade Monday 20 24 Tuesday 20 23 Wednesday 19 25 Thursday 18 25 Friday 20 25 What was the average per cent of attendance for the five days in each grade? Which grade won in the contest that week? 20. Fred selected 8 ears of Golden Bantam sweet corn for seed. He took 10 grains from each ear and tested them. Out of the total number tested only 4 failed to grow. What was the per cent of grains that germinated? 21. In a spelling test Ruth spelled 38 words correctly out of a list of 40 words. If the teacher graded in per cent grades, what should have been her grade (scoring all the words equally)? 22. In a seventh grade spelling test of 50 words, Helen re- ceived the highest grade. She spelled 48 words correctly. What per cent of the list did she have right? 23. Many cities have school 200 days in a year. What per cent of a year (365 days) is the school term? What per cent is used for vacations? 64 SEVENTH YEAR 24. A high school of 85 pupils was given a half-holiday on the Friday following the end of the month if the attendance was 97% or more. During one month of 20 school days there were 82 half-days of absence. What was the per cent of attendance? Was the school entitled to a half -holiday? 25. A girl bought a dress priced at $25 for $20 at a clearance sale. What was the per cent of reduction? 26. A bushel of corn on the cob weighs 70 pounds. A bushel of shelled corn weighs 56 pounds. The weight of the cobs in a bushel of ear corn is what per cent of the total weight of a bushel of corn on the cob? 27. Mrs. Keith set an incubator with 144 eggs. 118 eggs hatched. What per cent of the eggs hatched? 28. Donald has 45 hens and gets an average of 30 eggs a day during the spring. What is the average per cent of his hens laying each day? 29. In one section of a seventh grade there are 12 girls and 9 boys. What per cent of the class are boys? What per cent of the class are girls? 30. Compute the per cents of boys and girls for your class this year. 31. A landlord rented a house for $45 per month for a year. His expenses for taxes, insurance, and repairs amounted to $180. If the house was worth $6000, what per cent of the value of the house was his net income? 32. The population of Syracuse in 1910 was 137,249. In 1920 the population was 171,647. Find the per cent of increase for the ten years. 33. A city railway company reported a net profit of $2.86 for each $50 share. What was the per cent of profit? PERCENTAGE FRACTIONAL EQUIVALENTS 65 Exercise 11 1. 24 is 75% of what number? Equation: 24 = 75%XX. X, the unknown factor, = 24 -f- .75 = 32. Care must be taken in this type of problem to reduce the per cent to a decimal or a common fraction before dividing. 2. 16 is 25% of what number? Equation: 16 = 25%XX. In this problem, we see that 16 =25% or j of the number. The number = 4 times 16, or 64. Fractional equivalents are much shorter in solving some equations than decimals. Practice using both in solving equations and then choose the more convenient method for each equation. 3. 18 is 12j% of ? 12. $15 is 5% of ? 4. 21 is 75% of ? 13. $21 is 6% of ? 6. 48 is 80% of ? 14. $14 is 4% of ? 6. 40 is 62 \% of ? 16. $12.80 is 8% of ? 7. 8 is 16f % of ? 16. 11 Ib. is 4% of ? 8. 64 is 50% of ? 17. 9 is 2 J% of ? 9. 12 is 25% of ? 18. 12 is 3% of ? 10. 63 is 87 J% of ? 19. 245 is 20% of ? 11. 9 is 16j% of ? 20. 81 is 37j% of ? Exercise 12 1. If a man sells a house for $2760, which is 92% of what he paid for it, what was the original purchase price? In short form this problem means: $2760 is 92% of ? (cost). Equation: $2760 = 92%XX. Find the value of X. 66 SEVENTH YEAR 2. I wrote a check for an insurance premium for $52.24 and found that it would take out 42% of the money I had on deposit in the bank. How much money did I have on deposit? 3. After losing 18% of his investment in a gold mine, a man has $6192.60 left. How much did he have invested in the mine? 4. A farmer sold a cow for $84, thereby gaining 20%. How much did the cow cost? Suggestions: The cost of the cow = 100% of the cost. If the farmer gained 20%, he sold the cow for how many % of the cost? 6. The present enrollment of a school of 486 pupils is 20% more than its last year's enrollment. What was the last year's enrollment? 6. The circulation of a certain newspaper is now 39,875. This is an increase of 10% over that of last year. What was last year's circulation? 7. If a railway line has been extended 18% of its original length and is now 554.6 miles long, what was its original length? 8. If I add to my bank deposit $1*20, which is 60% of what I already have on deposit, what was my balance before making the deposit? 9. I paid $5 for a pair of shoes. This was 16 % of what I paid for a suit. How much did I pay for the suit? 10. A bank distributes dividends amounting to $4800. This sum is 12% of its capital stock. Find its capital stock. 11. A banker gained 8% on an investment. If his profits were $202, what was the amount of his investment? 12. A boy gained 6 Ib. during his summer vacation. This was 6 j% of his weight at the beginning of the vacation. How much did he weigh at the close of the vacation? PERCENTAGE. THE EQUATION 67 Practice Exercises in Percentage These exercises have been devised to give practice on the various processes involved in percentage. If the pupils fail to do each exercise in the time limit, they should be drilled on the facts in a different arrangement until they can reach the stand- ard time. Hektograph or mimeograph this material for written practice work. Demand 100% accuracy for each exercise. Time Limits for Written Work Excellent 1 min. Good 1^ min. Fair 2 min. Exercise A Change the following decimals to per cents: 18 916 1724 2632 ? % 5.04 = ? % ' % .425 = ? % ' % -6 = ? % ' % 1.54 = ? % ' % .043 = ? % ' % 3.8 = ? % ' % 1.05 = ? % ' % .039 = ? % Exercise B 2228 .75 = ? 9i o .725 = ?% .45 .06 = ? % , .71 = ?% 1.20 .625 = ? <% , .675 = ?% .425 A = ?<% > .35 = ?% .07 .035 = ? % , .005 = ?% .375 .33! = 1 % , .025 = ?% .66 f 2.52 == ? % , .054 = ?% 1.38 .225 = ? % , .03 = ?% .7 Change to per cents: 17 814 1621 i 8 = ?% 3 4 = ?% 1 =?% -i- = ? % 2 ^ = ?% TV = ? % i a = ?% 5 8 = ?% A ^ ? O/ } = ?% ^ = ?% 1 ? <7 :5 s = ?% |^ = ?% * = ?% (i = ?% 1 = ?% = ?% -f = ?% j^j- = ? % = ?% If = ? % 68 SEVENTH YEAR Exercise C Change to common fractions: 17 814 1621 2228 60 % = ? 10 % = ? 30 % = ? 62j% = ? 75 % = ? 6f % = ? 12j% = ? 125 % = ? 28-f% = ? 66f % = ? 6}% = ? 37j% = ? 5 % = ? 40 % = ? 16|% = ? 150 % = ? 33j% = ? 87i% = ? lli% = ? H-f-% = ? 25 % = ? 70 % = ? 83f % = ? 175 % = ? 90 % = ? 20 % = ? 50 % = ? 80 % = ? Exercise D Change to decimals: 17 814 1521 2228 32 % = ? 10 % = ? 80 % = ? lj% = ? 50 % = ? lj% = ? 105.5% = ? 40 % = ? 125 % = ? 33i% = ? 4.1% = ? 7.5% = ? 3.9% = ? 275 % = ? 250 % = ? lf% = ? 4f % = ? 2 % = ? 21 % = ? 42 % = ? 25 % = ? 87j% = ? 175 % = ? .25% = ? 62j% = ? 6 % = ? 5.25% = ? 4.9% = ? Exercise E 1. 6%X$375 = -5 > 3. 11%X$600 = ? 6. 8%X $85 = ? 2. 7%X $50 = ! 4. 3.5<; %X$400 = ? 6. 15%X$160 = ? 7. 4.1%X2001b. = ? Exercise F 1. 21%X$300 = ? 3. 9%X$250 = ? 5. 5%X3601b. = ? 2. 3%X $85 = ? 4. 18%X$230 = ? 6. 32%X$300 =? 7. 3.9%X2751b. = ? In hektographing or mimeographing such exercises as E to M, leave space enough under each example to perform the solution. PRACTICE EXERCISES IN PERCENTAGE 69 Exercise G 1. 37|%X480 = ? 3. 83j%X 54 = ? 5. 12j%X808 = ? 2. 14f%X210 = ? 4. 75 %X640 = ? 6. 60 %X420 = ? 7. 25%X808 = ? 8. 66f%X312 = ? Exercise H 1. 62j%X840 = ? 3. 40 %X520 = ? 6. 6j%X 80 = ? 2. 16|%X984 = ? 4. 11|%X639 = ? 6. 70 %X190 = ? 7. 33|%X975 = ? 8. 125%X240 = ? Exercise I Find the value of x in each equation : 1. 25 = x% X40 4. 64 = z%X96 2. 12 = 3% X x 6. 120 = 75% X x 3. x = 12^% X 64 6. z = 6% X $250 Exercise J Find the value of x in each equation : 1. 400 = 8% X x 4. 32 = x% X 80 2. a: = 33^% X 876 5. x = 37j% X 48 3. 320 = x% X 400 6. 96 = 25% X * Exercise K State equations for the following and solve each: 1. What is 60% of $65? 2. $24 is what per cent of $40? 3. 15 cents is 37^% of what amount? 4. What is 83 J % of $84? Exercise L State equations for the following and solve each: 1. What is 62 J% of $720? 2. $120 is what per cent of $2400? 3. $640 is 40% of what amount? 4. What is 6j% of $800? 70 SEVENTH YEAR Have the pupils solve the following list of percentage problems as a speed exercise. Use the following time limits for this exercise : Excellent 4 minutes. Good 6 minutes. Fair 8 minutes. Exercise M 1. A merchant sold a suit costing $30 at a profit of 40%. What was his profit on the suit? 2. A newsboy buys papers at 2 cents each and sells them at 3 cents each. What is his per cent of gain? 3. A merchant's expenses for operating his store amount to 16f % of his yearly sales. If he sells $36,630 worth of goods during 1920, what were his expenses for operating his store that year? 4. A boy spent 33^% of what he had on deposit in a bank for a bicycle. If the bicycle cost $42, what did he have on deposit before he bought the bicycle? 6. A variety store buys a certain toy for 6 cents each and sells it for 10 cents. Find its per cent of profit on this toy. 6. A city had a population of approximately 6000 in 1910. The 1920 census showed that it had gained 25% in the ten years. Find its population in 1920. 7. An overcoat, marked $48, was sold on a special sale at a reduction of 33f %. What was the selling price? 8. What is the per cent of profit on an article bought for 4 cents and sold for 10 cents? 9. A real estate firm rents a house costing $4800 so that it yields a return of 10% on the investment. What monthly rent does it charge for this house? 10. A bookkeeper working on a salary of $120 per month had his salary increased 12^%. What was the yearly increase in his salary? Encourage pupils to work every problem mentally that they possibly can and merely set down the final answer. This practice should be fol- lowed in every exercise in this book as well as in speed exercises. PERCENTAGE REVIEW PROBLEMS 71 REVIEW PROBLEMS IN PERCENTAGE 1 Exercise 13 1. Mr. Brown lost 15% on an investment of $1800. What was his loss? 2. A "boy who weighs 77 Ib. has gained 10% since his last birthday. What was his weight then? 3. An owner of a farm worth $175 an acre wishes to get a return of 4|% on his investment. What rent must he charge? 4. If you have 12 problems to solve for home work and work 10 correctly, what should your grade be, considering the prob- lems of equal value in grading? 5. 23 pupils in a class of 25 were promoted. What per cent of pupils failed? 6. A man has an annual income of $1500 and pays $420 a year for rent. What per cent of his income does he pay for rent? 7. A liveryman bought a team of horses for $350. After" using them for two years, he sold them at a loss of 40%. What did he receive for the team? 8. A contractor figured a house to cost $4375 and secured the contract for $5500. What was his per cent of profit if his estimate was correct? 9. An abandoned beach hotel which cost $80,000 is sold for $48,000 at what per cent of loss? The purchaser reopens it for a new class of patronage and sells it to a company for the original cost. What was his per cent of profit? 10. A boy gave his playmates 75% of his apples and had 4 left. How many had he at first? ir rhis list of problems is designed to give practice in stating equations for the three types of percentage problems. 72 SEVENTH YEAR 11. A teamster paid $100 each for 2 horses, $60 for a wagon, and $20 for a second-hand set of harness. At what price must he sell the outfit to gain 10%? 12. The sales of a certain store were $72,000 for the year and the profit, $8000. Find the per cent of profit on the sales. 13. A mill is sold for $856,000 at an advance of 14f % on its cost price. How much did it cost? 14. A man's expenses in a year are $1200. His salary is 133^% of that amount. How much money can he save in a year out of his salary? 16. A grocer buys eggs at wholesale for 36f and sells them for 40^ per dozen. What is his per cent of profit? 16. I paid my rent with a check for $37.50, which was 5% of my deposits in the bank. What was the balance remaining in the bank? 17. A collector charged $60 for collecting a debt of $1200. What per cent did he charge for collecting? 18. The engine in my automobile is 40 H. P. My neighbor's engine is 60 H. P. His engine is how many per cent as powerful as mine? 19. A factory employing 40 equally paid operators of machines, reduces its force by 25% and increases by 25% the wages of those that remain. Does it pay more or less in wages than before? 20. Helen spent 35% of her Christmas money on one shop- ping trip and 28% on the next trip. What per cent of her money was left? If she had $7.40 left, how much money 'had she at first? 21. A merchant sold goods for which he paid $30,000 at an average of 30% higher price, but lost 5% from the failure of certain debtors. What was the amount of his profit? PERCENTAGE PUPILS' OWN PROBLEMS 73 . 22. If one cow yields 15 quarts of milk each day, the milk containing 3.5% of butter fat, and another cow yields 12 quarts of milk per day, containing 4.5% of butter fat, which cow is the more profitable for butter making? 23. A house and lot were purchased for $4000. The house was moved and sold for $2000 and the cost of moving. At what price must the lot be sold to realize a total gain of 25% on the investment? 24. The sales in a store were $960 for one day, which would have meant a profit of 20% but for the unfortunate acceptance of a counterfeit 20-dollar bill which could not be traced to the payer. What was the net per cent of gain? 25. Standard milk is 87% water, 4% fat, .7% ash, 3.3% protein and the remainder is made up of carbohydrates. What per cent of standard milk is carbohydrates? 26. A merchant marks a suit of clothes costing $20 at an increase of 60%. Later he discounts the marked price 20%. What was the cost to the purchaser? What was the merchant's per cent of profit on his cost? 27. After grooving, a 4-inch floor board is only 3j inches on its face. If you figure the number of board feet for a floor, what per cent must you add to allow for the grooving? Exercise 14 PROBLEMS COLLECTED BY PUPILS The following problems were gathered by a seventh grade class from their experiences and consultations with their parents. See how many of these problems you can solve. 1. I have done 8 of the 50 arithmetic drill cards. What per cent have I yet to do? 2. My father received an order from the army for $85,900 worth of goods. He receives 4% commission. How much does he receive? 74 SEVENTH YEAR 3. I bought a share of stock last year for $114. I have sold it for $181. What was my per cent of gain? 4. Last year flour was $6.75 per bbl. and this year (1916) it is $10.00 per bbl. What is the per cent of increase? 6. A bill of lumber was sold, the price being $864, but an allowance of 10% was made for poor grade. There was also a discount of 2% for prompt payment. Find the net amount of the bill. 6. A manufacturer makes and sells an article for $24.00 per dozen. His overhead charges 1 are 20% of this and he allows a cash discount of 7%. What is the net amount of his profit per dozen, after deducting $15.00 for materials and cost of manufacturing? 7. A wholesale dealer buys a boiler from the manufacturer at the list price of $24.00 less 40% discount. He sells it to his retail customer at 30% discount from the list price. How much profit does he make on the sale? 8. A corporation is capitalized at $50,000. How much busi- ness will they have to do yearly to pay a dividend of 10% on their capital stock, provided their profit is 5% of their total sales? 9. During 1915 a manufacturer employed 206 men at $2.00 per day. In 1916 he employed 175 men and his total daily wage bill was $395.00. By what per cent had the daily per capita wage increased? 10. In 1900, $100 would buy a certain number of articles of goods. In 1910, it took $120 to buy the same articles and in 1916 it took $160 to buy the same goods. By what per cent should wages have increased between 1910 and 1916 to have enabled the laborer to purchase the same quantity of goods in 1916 as he had been able to purchase in 1910? Overhead charges cover all expenses of a factory except cost of material and cost of labor. PERCENTAGE DAIRY PRODUCTS Exercise 15 75 Prepare a list of percentage problems based on the business conditions in your community. Each pupil should bring in at least two problems from which the teacher can select a list for review work in percentage. Try to get actual transactions to use in your problems. Exercise 16 MILK AND CREAM Efficient dairymen are now testing the milk of each cow to see which are the most productive. Those which are not profitable are sold and others secured in their places which produce a higher per cent of butter fat. The amount of butter fat is ascertained by means of the Babcock test. 1. Some pupil in the class should make a careful study of the Babcock test and make a full report to the class. 2. Standard milk is 87% water, 4% fat, 3.3% protein, .7% ash, and the remainder is made up of carbohydrates. What per cent of standard milk is carbohydrates: 3. Cream is 74% water, 2.5% protein, 4.5% carbohydrates, .5% ash and the remainder fat. What per cent of the cream is fat? The test for butter fat is made in bottles similar to the one shown in the illustration. The butter fat accumulates in the neck of the bottle and can be measured on the scale with a pair of dividers. The bottle in the illustration shows a test yielding 4% of butter fat. 76 SEVENTH YEAR 4. A farmer took a can of milk weighing 275 Ib. to the creamery. The test for this milk showed 3.8% of butter fat. How much did he receive for this butter fat at 56 cents per pound? 6. A certain recorded Jersey cow yielded 17,557 pounds of milk in one year. From this amount of milk, 998 pounds of butter fat were obtained. What per cent of the milk was butter fat? 6. A certain recorded Guernsey cow yielded in one year 910 pounds of butter fat in 17,285 pounds of milk. What was the per cent of butter fat in her milk? 7. A Shorthorn cow yielded 18,075 pounds of milk in a year. The milk of this cow contained 735 pounds of butter fat. What was the per cent of butter fat in her milk? 8. A cow's milk was tested by a dairyman with a view to purchasing the cow. He found her milk to test 3.2% butter fat. If the price was satisfactory, would you buy the cow to add to a dairy herd? 9. A certain Holstein cow yielded an average of 14,134 pounds of milk per year for five years. If her milk tested 3.7% butter fat, how many pounds of butter fat did this cow produce in the five years? 10. How much was this butter fat worth at 56 cents per pound? 11. If one cow yields 30 Ib. of milk per day testing 3.4% of butter fat and another cow yields 25 Ib. of milk testing 4.4% of butter fat, which cow is the more profitable and how much per week? If whole milk is sold for city consumption, the quantity of milk is a more important consideration than the per cent of butter fat, providing that the percentage of butter fat does not fall below a minimum of about 3.4%. PERCENTAGE DAIRY PRODUCTS 77 12. A following dairyman tested results: Cow 1 ten cows for Pounds of mi per day 30 butter fat with the Ik Per cent of butter fat 3.9 3.4 4.0 4.1 3.3 3.9 3.8 4.2 3.5 4.0 2 28 3 24 4 35 5 26 6 32 7 22 8 29 9 21 10. . ..28 Which cows would you recommend that he keep and which ones would you recommend that he sell and buy others to take their places? Give reasons for your decisions. Duchess Skylark Ormsby, a Holstein-Friesian cow, has the record of being the world's champion butter producer. She produced 27,761 Ib. of milk in a year, yielding 1205 Ib. of butter fat. 13. Find the per cent of butter fat in the milk of the champion cow. 14. At 35 cents a pound, how much was that amount of butter fat worth? 15. How much would the whole milk from this cow have brought at $2.00 per hundred pounds? Courtesy of the International Harvester Co. 78 SEVENTH YEAR THE MEAT INDUSTRY (Applied percentage problems) The meat industry is one of the most important enter- prises in our country. In a recent year the production of beef, veal, mutton and pork amounted to 22,378,000,000 lb., an average of about 220 lb. for each person in the United States. Not all of this immense production of meat was consumed in this country, however, for a large portion of it was exported to foreign countries. Exercise 17 1. A farmer sold a carload of 20 steers averaging 1250 lb. in weight for $11.00 per hundred pounds. How much did he receive for them? 2. If one of these steers loses 40% in being dressed, what is the Wight of the dressed beef in a steer weighing 1250 lb.? 3. If a steer weighing 1093 pounds alive weighs 632 pounds when dressed, what per cent did this steer lose in being slaugh- tered? 4. The two loins of a hog weigh about 10% of the weight of a live hog. How much would each of the loins from a 220- Ib. hog weigh? 6. A farmer ships a carload of 95 hogs averaging 225 pounds in weight, receiving $12.35 per hundred. How much did he receive for the carload of hogs? 6. Find the broker's commission at $10.00 per carload of 19,000 lb. and 5 cents per hundred in excess of that weight. PERCENTAGE THE MEAT INDUSTRY 79 In slaughtering a beef, the waste materials are all used. From these waste materials or by-products are made leather, glue, oleo oil, soap and fertilizers. The carcass of a beef is divided into 8 different cuts as shown in the illustration at the left. The percentage of the dressed weight included in each cut of the beef is also shown. 1 Hound 4 -Rib 9.64 s.46 6riske( ff.OO 7-Chudt 22,05 ssu"t 3. 7. A dressed carcass of a steer weighs 670 Ib. Find the weight included in each of the different cuts for one-half of the carcass, using the percentages in the illus- tration. 8. If the by-products of a steer costing $132 were estimated as worth $36, what per cent of the original cost of the steer was obtained from the by-products? 9. A hog loses 25% to 35% of its weight in being dressed. How much will a 200-lb. hog lose in weight if the loss is 33%? 10. How much will the 200-lb. hog weigh when dressed? 11. How much will a 175-lb. hog weigh, dressed; shrinking 35%? 12. The two short cut hams of a hog are about 13 f% of the live weight of a hog. How much do the two short cut hams of a 230-lb. hog weigh? Oleomargarine is one of the most important products made by the packing industry. It is made from a mixture of oleo oil, neutral, vegetable oil, milk and cream, and butter. The oleo oil is made from the fat of cattle. Neutral is made from the finest leaf fat of hogs. The vegetable oils include such oils as cottonseed oil and peanut oil. 80 SEVENTH YEAR 13. The wholesale price on a certain brand of oleomargarine was 24^ per pound in December of a recent year. The cheapest brand made by the same firm was selling at only 75% of that price. What was the price of the cheaper grade? 14. The retail price of the best brand of oleomargarine mentioned in problem 13 was 28^ at a certain grocery store. The retail price was how many per cent greater than the whole- sale price? 15. A certain meat packing firm states that 80% of their sales go for the purchase of live stock, 8% for labor, 5% for freight and 4f % for other expenses. What per cent of their sales is left for dividends for the stockholders? 16. If their total sales amounted to $500,000,000 per year, compute the amount paid for live stock, the amount paid for labor and the amount left for dividends. The receipts at the nine principal live stock markets in the United States for the years ending October 1 are as follows: Cattle Sheep Hogs 1911 9,416,374 13,530,833 19,217,506 1912 8,861,404 14,148,096 21,035,035 1913 9,188,500 14,146,284 19,997,656 1914 8,193,856 14,702,889 19,366,263 1915 8,464,185 11,994,851 21,366,263 17. What has been the percent of decrease in the number of cattle from 1911 to 1915? 18. What has been the per cent of decrease in the number of sheep received from 1914 to 1915? 19. What was the per cent of increase in the supply of hogs from 1911 to 1915? 20. The average wholesale price of dressed beef in New York in 1911 was $8.77 and in 1915 it was $11.64. What has been the per cent of increase in the wholesale price of beef in that period? PERCENTAGE THE COTTON INDUSTRY 81 COTTON When picked, cotton is first ginned, 1 and then packed into bales weighing approximately 500 pounds. To economize space in ship- ping long distances these bales usually are com- pressed by powerful ma- chines into the smallest possible compass. The illustration Shows One of High Density Cotton Compress these machines compressing a bale of cotton. The following table gives the number of bales produced in the leading cotton-producing states. No. of bales 1913 Texas 3,945,000 Georgia 2,317,000 South Carolina 1,378,000 Alabama 1,495,000 Mississippi 1,311,000 Arkansas 1,073,000 North Carolina 793,000 Oklahoma 840,000 Louisiana 444,000 Tennessee Missouri Florida Virginia All other states . 379,000 67,000 59,000 23,000 32,000 United States 14,156,000 No. of bales 1914 4,592,000 2,718,000 1,534,000 1,751,000 1,246,000 1,016,000 931,000 1,262,000 449,000 384,000 82,000 81,000 25,000 64,000 16,135,000 No. of bales 1915 3,175,000 1,900,000 1,160,000 1,050,000 940,000 785,000 708,000 630,000 360,000 295,000 52,000 50,000 16,000 40,000 11,161,000 Total Value of Crop . $885,350,000 $591,030,000 $602,393,000 Winning is the process of removing the seeds from the cotton. 82 SEVENTH YEAR Exercise 18 1. What was the per cent of increase in the number of bales of cotton from 1913 to 1914? (See preceding page.) 2. Find the price per pound for cotton in 1913; for 1914 and for 1915. The large crop and the outbreak of the great European War in 1914 were responsible for the low price in 1914. Com- pute the prices per bale. 3. Note the decreased production in 1915. What was the per cent of decrease from the yield for 1914? 4. What per cent of the total production of the United States was the production of Texas in 1914; in 1915? 6. The production of Oklahoma in 1915 was what per cent of its production in 1914? 6. The total production of the United States for 1914 was what per cent greater than the total production for 1915? 7. The total exports of cotton for 1913 was 4,562,295,675 Ib. What was the value of our cotton exports in 1913 at 12.2 cents per pound? 8. Cotton constitutes about 53% of our total agricultural exports. From the data given in problem 7, compute the value of our total agricultural exports for 1913. 9. It is estimated that cotton forms 63% of the total crop production in Texas. From the data in the table and the cost per pound in problem 2, find the value of the total crop pro- duction of Texas in 1915. This offers a valuable type of work getting information from a table of statistics. Additional exercises of this type may be made from tables of statistics such as those found in the Statesman's Year Book or other similar publications. Make similar comparisons with recent data. PERCENTAGE FOOD PRICES 83 Exercise 19 The following table shows the increases in wholesale prices of some of the most important food products: Food Product 1915 Prices 1920 Prices increase Hams, fresh $ .16 $ .30 ? Bacon 24 46 ? Beef, No. 1 ribs 17 35 .... ? Chickens, broilers 20| 53 ? Eggs, No. 1 24 41*.... ? Potatoes, bushel 48 4.50 ? Corn, small cans, per doz 78 1.25 .... ? Navy beans, bushel 3.15 5.25 .... ? Apples, barrel , 3.25 10.50 .... ? Flour, barrel 6.25 15.50 .... ? Sugar, gran., per 100 Ibs 5.50 21.00 ? Rolled oats, pound 03 06 ? 1. Find the per cent of increase for each food product given in the table. 2. Find the average per cent of increase in all of these food products. 3. Ascertain if possible the present wholesale prices on the food products listed in the table and determine the per cents of increase or decrease from the prices in the record column. 4. From the market reports in today's paper get the prices of corn, oats, hogs, cattle, cotton, rice, wheat, eggs, butter, hay, potatoes, oranges, apples and other farm products in which you are interested. From a last year's paper of about the same time of the year, get the prices of the same products. Compute the per cents of increase or decrease for the last year. 6. Secure at a local grocery store the retail prices on a list of at least 10 food products for this year and also the prices for last year on the same quality of goods. Find the per cent of increase or decrease on each of the articles that you have listed. Ask the grocer to tell you the causes for the increases or de- creases on the various articles. 84 SEVENTH YEAR FOOD VALUES There are four principal food substances in the foods that we eat : (1) protein (pro'-te-in) (2) carbo- 73.7 % hydrate; (3) fat; (4) mineral matter. "WATER Water is also an important con- stituent of food products. Differ- 1 /I $^ Q/ ' PROTEIN en * ^ oo( ^ P rocm cts contain different % FAT proportions of these food substances. ASH Eggs, as shown in the illustration, are composed of 73.7% water, 14.8% protein, 10.5% fat and 1% ash or mineral matter. The protein compounds not only build up the tissues of the body but they also furnish energy to enable us to do our work. The carbohydrates and fats supply energy for the body. Exercise 20 1. Using the percentages given in the illustration above, find the number of ounces of each of the constituents in a pound of eggs. 2. The average composition of 1 pound of beef is as follows: water 10.72 oz.; protein 3.04 oz.; fat 2.08 oz.; and mineral matter .16 oz. Find the per cent of each substance in the average pound of beef. 3. A white potato is composed of 1.8% protein, .1% fat, 14.7% carbohydrates, .8% ash, 62.6% water and 20% refuse. Find the number of ounces of each constituent in 1 Ib. of pota- toes. (Refer to page 312 for additional data for problems.) 4. White bread is composed of 9.2% protein, 1.3% fat, 53.1% carbohydrates, 1.1% ash, 35.3% water. How many ounces are there of each food substance in a pound loaf of bread? 5. Compare amounts of various food substances in bread and potatoes. PERCENTAGE PROBLEMS FOOD VALUES 85 6. If cereals and their products supply 62% of the carbo- hydrates, and vegetables and fruits together 16% of the carbohydrates, what per cent of the total carbohydrates do both of these classes supply? 7. If meat and poultry supply 16% of the total food material in the average American home, and dairy products 18%, cereals and their products 31%, vegetables and fruits, together, 25%, how much of the total food materials do these items constitute? 8. If meat and poultry supply 30% of the protein, the dairy products 10% of it, cereals and their products 43% of it, and vegetables and fruits together 9% of it, how much of the protein is supplied by these four kinds of food? 9. If meat and poultry supply 59% of the fat, dairy prod- ucts 26% of the fat, cereals and their products 9% of the fat, and fruits and vegetables together 2% of the fat, what per cent of the total fat do these four kinds of food supply? Domestic science courses not only teach how to cook foods but also what kinds of foods to prepare in order to secure a proper proportion of the various food substances. When coal is burned, it supplies heat which may be converted into the energy of steam and run a -steam engine. In a similar manner the food which we eat is consumed by our bodies, supplying heat and energy to do our work. Experiments have been made to show the amount of energy which each food product yields. These amounts of energy are expressed in terms of calories (kal'-o-rles). A calorie is used in this connection to mean the amount of heat required to raise 1 pound of water 4 Fahrenheit. The number of calories per day needed by any person varies with his weight and the amount of work which he does. A man at hard work or an active growing boy may require' as 86 SEVENTH YEAR much as 5000 calories of food energy per day. An average man requires about 2500 calories when engaged in an occupation where he is sitting most of the day. The problem of the scientific cook is to serve foods which will contain the proper food substances and at the same time supply a sufficient number of calories each day. The following table 1 shows the amount of each food product which will yield 100 calories: Milk : f cup, whole; 1^ cups, skim Cream ^ cup, thin; 1^ tablespoons, very thick Butter 1 tablespoon Bread 2 slices 3 ff x3^"x* Fresh fruit 1 large orange or apple Eggs 1 large, 1 medium Meat (beef, mutton, chicken, etc.) About 2 oz. lean Bacon (cooked crisp) .About \ oz. (very variable) Potatoes 1 medium Sugar 1 tablespoon Cocoa, made with milk % of a cup Cooked or flaked breakfast foods f to lj cups Dried fruit 4 or 5 prunes or dates Exercise 21 1. A man requiring 2500 calories per day eats the following breakfast: 1 cup of breakfast food with \ cup of thin cream, 1 cup of cocoa made with milk, 2 slices of bread, 1 tablespoon of butter, 2 small slices of bacon and 1 egg (large). Find the number of calories supplied by this breakfast. 2. What per cent of the total requirement for a day is furnished by that breakfast? 3. It is desirable that a family of five consume 3 quarts of milk per day. If they consume 17 quarts per week, what per cent of the desirable quantity have they used? 'See Rose, Feeding the Family. PERCENTAGE PROBLEMS FOOD VALUES 87 4. From the preceding table, prepare a menu for breakfast that will furnish between 700 and 900 calories. 6. Prepare a menu for lunch to furnish approximately 1000 calories. 6. Which will furnish the largest number of calories, a large orange or a medium sized egg? (See table, page 74.) 7. How many calories will a dozen medium sized eggs supply? 8. How many calories are there in a quart of milk? (2 cups make a pint.) 9. How many calories are there in a pound of prunes (40 to the pound)? 10. A man requiring 3000 calories per day eats a breakfast furnishing 700 calories, a lunch furnishing about 900 calories and a dinner furnishing about 1400 calories. Find the per cent of the total furnished by each meal. 11. If the meals for a family for a week cost $5.60 and the meat costs $1.40, the vegetables 70 cents and the butter 48 cents, what per cent of the total was spent for each group? 12. What per cent of the weekly expense was left for other materials? 13. If it takes 1 hour to prepare an entire meal and 20 min- utes to make the dessert, what per cent of the whole time is given to the dessert? The following table shows the number of calories supplied by a pound of each food product : Beef, fresh lean 709 Beans 1564 Beef, fat 1357 Oatmeal 1810 Bacon (average) 2836 Lettuce 87 Butter 3488 Cabbage 143 Apples 285 Sugar 1814 Potatoes, white 378 Bread 1174 Milk, whole 314 Eggs 672 88 SEVENTH YEAR Exercise 22 1. The food value of a pound of fresh lean beef is what per cent of the food value of a pound of butter? 2. A pound of white potatoes furnishes what per cent as many calories as a pound of butter? 3. How does the food value of a pound of lettuce compare with the food value of a pound of white potatoes? (Express in per cent.) 4. In the same way compare the food values oi fat beef and bacon. 5. Which is cheaper, sugar at 11 cents per pound or beans at 12 cents per pound, considering the food values of each? 6. Which is cheaper, apples at 10 cents per pound or bacon at 35 cents per pound? 7. Which is cheaper, oatmeal at 8 cents per pound or eggs at 35 cents per dozen? (Figure eggs at 1? Ib. per doz.) 8. From the cost of milk and butter in your community, compute the cost of the amount of each necessary to supply 100 calories. 9. Find the cost of 100 calorie portions of cabbage, potatoes, lean beef, beans, sugar, bread, eggs and bacon in your commu- nity. 10. Prepare a menu for a lunch from the items listed on page 75, providing 900 calories for each of 4 persons. From local prices in your community, estimate the cost of this lunch for each person. 11; Prepare and present a problem on food values to the class for solution. 12. If you have a school lunch room, estimate the cost to the students of 100 calorie portions of as many of the dishes as you can find the data to compute. CHAPTER IV APPLICATIONS OF PERCENTAGE The subjects treated in this chapter do not involve any new principles of percentage but merely an application of the prin- ciples already mastered to new business situations. New terms and new business forms will have to be mastered in making the application of the principles already learned. The discussion, then, at the beginning of each list of problems should be thoroughly mastered in order to get a good knowledge of business terms and organization. BUSINESS TRANSACTIONS Exercise 1 The gross profit in any business transaction is the difference between the cost price and the selling price. The net profit is the gross profit less the expenses of the transaction. 1. A notion store sold 100 pairs of wooden knitting needles at 10 cents per pair, at a profit of 33^%. What was the cost of each pair of needles? 2. If the selling price of an article is 4 times the cost, what is the per cent of gain? 3. A fancy vest is sold for $7 at a profit of 40%. What was its cost price? 4. A village lot was purchased for "$1000, buL because of a decline in real estate values.was sold for $750. What was the per cent of loss? 5. A man sold a horse for $120 at a loss of 25%. What did the horse cost him? 89 90 SEVENTH YEAR 6. A merchant bought goods listed at $1200 at a reduction of 40%. He sold them at a profit of 25%. What was the total selling price of the goods? 7. A merchant having goods worth $10,000 increased his stock 25% and sold the entire stock at an average profit of 20%. For what sum did he sell it? 8. When an article that cost $24 is sold at a profit of 10% and the purchaser sells it again at a loss of 20%, what is its last selling price? 9. A liveryman sold a horse for $175 at a profit of 25%. What was the cost of the horse? 10. A man sold two farms for $7500 each. On one he gained 20% and on the other he lost 20%. Did he gain or lose on the entire transaction and how much? 11. A farmer bought a herd of 20 steers, averaging 1100 Ib. each, at $7.50 per hundred. He fed them 700 bu. of corn worth 65 i per bu., 15 tons of hay worth $12 per ton and roughage worth $60, If his pasture of 20 acres was worth $6 per acre, what was his profit on the herd of cattle if they weighed 1475 Ib. and brought $10.50 per hundred when he sold them? 12. A farmer sold his neighbor a cow at an advance of 10% of what she cost him. His neighbor sold her to a dairyman at an advance of 25%, receiving $110 for the cow. Find the amount of profit made by each. 13. A manufacturer sold a hardware dealer a stove at a profit of 10% on the cost of manufacturing. The hardware dealer sold the stove to a customer for $61.60 at a profit of 40%. Find the cost to the manufacturer. 14. A dairyman sold two cows for $90 each. On one he gained 20% and on the other he lost 10%. Find his per cent of gain or loss on the entire transaction. APPLICATIONS OF PERCENTAGE DISCOUNTS 91 DISCOUNTS Exercise 2 A discount is a sum deducted from the price of an article. Discounts are usually computed by per cents. To state that you will sell an article at a discount of 25% means that you will sell it for f off or 25% off the regular list price. Many firms give discounts for cash purchases. It is profitable for these firms to give small discounts for cash purchases because they can re-invest the money and be making additional profits. 1. A music dealer sold a piano which he had listed for $400 at a discount of 20%. How much did he receive for it? List price of the piano = $400 20% of $400 = J of $400= 80 = the discount. He received $320 The amount that is left after the discount is subtracted from the list price is called the net proceeds. In problem 1, $400 is the list price, $80 is the discount and $320 is the net proceeds. Find the discounts and net proceeds of the following list prices at the stated discounts: 2. $100, 25%. 6. $1.00, 30%. 10. $20, 15%. 3. $ 25, 10%. 7. $1.50, 33 \%. 11. $40, 25%. 4. $250, 20%. 8. $500, 2%. 12. $5.00, 10%. 6. $ 30, 40%. 9. $125, 20%. 13. $452.75, 2%. 14. After using a motorcycle, costing $150, for a month, a boy offered it for sale at a discount of 15% of the cost price. How much did he want for the motorcycle? 16. A merchant bought a bill of goods amounting to $1240 and received a cash discount of 2% for prompt payment. What was the net proceeds of his bill? 92 SEVENTH YEAR CLEARANCE SALES Exercise 3 Retail stores have clearance sales in order to dispose of old goods on hand and make room for new styles and up-to-date patterns. They often give reductions of 10%, 20%, 33f %, or even as high as 50%. In order to dispose of goods left on hand in which the styles are likely to change, the merchant may offer the goods at cost in order to prevent a loss at a later date when the goods are out of style. 1. A merchant advertised a 20% discount sale on shirts., How much was the price on a shirt listed regularly at $2.50? 2. A clothier offers a discount of 15% on all suits and over- coats in his store. What is his sale price on suits listed at $25? 3. A furniture store advertised a closing out sale, offering a discount of 33^% on the regular prices. Find the cost of the following articles listed regularly as follows: 1 library table $30.00; 2 rocking chairs at $15.00 each; 1 davenport $42.00; 1 brass bed $24.00; 1 mattress $12.00; 1 set of springs $9.00; and 1 dresser $24.00. 4. In a clearance sale, a merchant gave a discount of 40% on novelty dress goods and 20% on the staple weaves. Why could he afford to give a larger discount on the novelty goods? 6. One shoe store advertised a ceitain shoe that retails regularly at $4.00 for $3.45; another store advertised the same shoe at a discount of 15%. Which was the better offer and how much? 6. A merchant advertised $2.00 silks at a discount of 20%. What was his sale price on those silks? 7. Straw hats worth $3.00 early in the season were sold late in the season at $1.50. What was the per cent of discount? APPLICATIONS OF PERCENTAGE DISCOUNTS 93 COMMERCIAL DISCOUNTS Exercise 4 Wholesale dealers and manufacturers often offer two or more discounts off the list price. These discounts axe called trade or commercial discounts. There are several advantages in using this system of com- mercial discounts. In the first place, catalogues are expensive to issue. By making the list prices of the articles high, fluctua- tions in the cost of materials will not make it necessary to issue a new catalogue. Instead, the firm can merely send out a new discount sheet which gives the discounts allowed on the various classes of articles. This discount sheet costs very little compared with the original cost of the catalogue. Further- more a retail dealer can show his customer the catalogue and give him a discount on the list price without the customer knowing the extent of his profit. Can you think of any other advantages of commercial discounts? If a firm is selling goods at a certain discount, a decrease in the cost of production may enable them to add a second discount. A discount is also usually allowed for prompt payment. Consequently, we occasionally see goods listed subject to a series of three successive discounts. Commercial discounts are computed in sucession. The first discount is taken from the list price and the second dis- count is then computed on the remainder and so on. 1. A bed room suite was listed at $80 less discounts of 20% and 10%. What was the net price? 20% X $80 = $16, the first discount. $80 -$16 =$64, the remainder." 10% X $64 = $6.40, the second discount. $64 -$6.40 = $57.60, the net price. The net price is the list price less the commercial discounts. 94 SEVENTH YEAR 2. A piano listed at $500 has discounts of 30% and 5%. Find the net price. 3. A hardware firm quotes a certain grade of hammers at $12 a dozen, less discounts of 33^% and 25%. What is the cost of each hammer to a local dealer? What must he mark a hammer to make a profit of 50%? 4. A merchant buys sweaters from a factory at $24 per dozen at discounts of 20% and 5%. What must he sell them at in order to make a profit of 60%? 6. Stoves are quoted by a manufacturer at $40 each, subject to discounts of 25%, 10% and 5%. What is the net price to the retail dealer if he is allowed a further discount of 2% for cash? 6. Find the net price on a dining table and set of six chairs listed at $80 if discounts of 20% and 15% are allowed. 7. A music cabinet is listed at $65 with discounts of 25%, 10% and 5%. Find the net price. List price Discount Net price 8. $175 20%, 10% and 5% ? 9. $150 25% and 5% ? 10. $400 30%, 10% and 5% ? 11. $40 20% and 3% ? 12. $75 25% and 2% ? In order to save computation, firms have tables showing a single discount which is equivalent to the series of successive discounts. 13. What single discount is equivalent to successive discounts of 20% and 10%? 20% X 100% = 20% 10% X 80% = 8% 100% - 20% = 80% 80% - 8% = 72%, net price. APPLICATIONS OF PERCENTAGE DISCOUNTS 95 100% -72% = 28%. Therefore, 28% is equivalent to successive discounts of 20% and 10%. 14. What single discount is equivalent to successive discounts of 30% and 20%? 15. Find the single discount equivalent to commercial dis- counts of 25%, 10% and 5%. 16. Which is better, a single discount of 40% or successive discounts of 25% and 20%? How much better? 17. Find the net price of a bill of goods amounting to $280 with discounts of 25% and 10% with an additional discount of 2% for cash. 18. Find the net price on a set of harness listed at $60, subject to discounts of 20% and 10%. NOTE: Bank Discount will be treated under the topic Banks. INTEREST Exercise 5 Much of the business of the world is carried on with borrowed money. Men of ability and industry often do not have enough money of their own to supply the capital necessary for estab- lishing or conducting their business enterprises. On the other hand there are men who prefer to loan their money rather than attempt to run a business of their own. Thus money is loaned, in the business world, not as a matter of personal favor or accommodation, but as a matter of busi- ness based on benefits to both lender and borrower. The person who lends the money receives pay for the use of it from the borrower. Money paid for the use of money is called interest. 96 SEVENTH YEAR The borrower in receiving money loaned to him, gives a dated and signed promise to return the money loaned (or the principal} with a certain interest at a stated date. Such a paper is called a note. Here is a note of simple form: *L5QBM ., after date ..... ____Q^_ promise to pay to '/ubHu/ndAj^JDolla/ib with interest at .,. *?_.>/_-_ for value received. \00. In a new community, where capital is greatly needed, money would often command a much higher rate of interest than the law would allow. Most states provide penalties for charging a higher rate of interest than the legal rate fixed by law. The laws of the different states are not uniform as to the rate of interest that will be permitted. Interest that is unlawful in rate is called usury. Find what is the legal rate of interest in your state by inquiring at the bank. In ordinary transactions involving interest any month is considered one-twelfth of the year and thirty days constitute a month. In the case of large amounts of money, where exactness as to time is very important, the time of the loan is often stated in days and is reckoned according to agreement or custom. In exact interest 365 days are considered a year. Since banks consider 360 days a year in computing bank discount, it is customary to figure interest on that basis. The following form is very convenient for computing simple interest because it allows one to use cancellation: APPLICATIONS OF PERCENTAGE INTEREST 97 Find the interest on $300 for 1 year, 3 months and 15 days at & 93 x= = 20 4 In the above problem, the rate is used as a common fraction ; the time 1 year (360 days) +3 months (90 days) + 15 days =465 days which is ^-f^ of a year. The interest for 1 year ($300 X TITO) must therefore be multiplied by | to find the interest for the given time. When the time is expressed in years and months, the form can be shortened by expressing the years and months as twelfths of a year. Find the interest on $200 for 1 year, 6 months at 6%. Find the interest on: 1. $500 for 6 months at 6%. 2. $350 for 1 year at 7%. 3. $1000 for 2 years at 6%. 4. $2000 for 2 years at 5j%. 6. $250 for 2 years, 6 months at 7%. 6. $6500 for 5 years, 6 months at 5%. 7. $325 for 2 years, 9 months at 6%. 8. $480 for 1 year, 8 months, 15 days at 6%. 98 SEVENTH YEAR 9. $2000 for 2 years, 8 months, 20 days at 5%. 10. $500 for 1 year, 5 months, 18 days at 6%. 11. $425.50 for 1 year, 3 months, 21 days at 6%. 12. $218.50 for 2 years, 10 months, 12 days at 6%. 13. $350.75 for 2 years, 8 months, 19 days at 6%. 14. $875.25 for 1 year, 3 months, 27 days at 6%. 15. $5000 for 4 years, 7 months, 18 days at 5%. 16. $150 for 1 year, 3 months, 20 days at 7%. 17. $200 for 6 months at 3%. 18. $175 for 1 year, 2 months, 15 days at 6%. 19. $300 for 2 years, 4 months at 6%. 20. $2500 for 1 year, 9 months, 18 days at 5%. Some teachers prefer to use the Six Per Cent Method in finding interest instead of the Cancellation Method used in the preceding explanation. The Six Per Cent Method may be used by teachers who prefer it or whose course of study requires it. This method uses the following data: The interest on $1 for 1 year =$.06 The interest on $1 for 1 month = .005 The interest on $1 for 1 day = .000 Find the interest on $250 for 3 years, 3 months, 18 days at 6%. Interest on $1 for 3 years = 3X.06 =$.18 Interest on $1 for 3 months = 3X.005 = .015 Interest on $1 for 18 days = 18 X .000 = .003 Interest on $1 for the entire time =$.198 Interest on $250 for 3 years, 3 months, 18 days = 250 X$. 198 =$49.50. The interest at any other rate than 6% can be found by taking -^ of the interest at 6% and multiplying by the given rate. When the times are stated for the beginning and end of the interest-bearing period, the following form is used in determining the time for computing the interest: APPLICATIONS OF PERCENTAGE INTEREST 99 21. What is the interest on a note for $300 dated April 1, 1906, and paid May 15, 1908, at 6%? Year Month Day 1908 5 15 1906 4 - - 1 2 1 14 Therefore, the time is 2 years, 1 month and 14 days. Com- pute the interest. 22. Find the interest on $200 from Sept. 26, 1915, to Jan. 24, 1917, at 6%. Year Month Day yf e can not subtract 26 days from 24 916 12 54 days, so we reduce 1 month, taken from Z0Z7 Z 24 the months column to days, making 30 days; 1915 9 26 a dd the 30 days to the 24 days, making 1 3 28 54 days. 26 days from 54 days leaves 28 days. We have already used the 1 month in the months column, so we must take a year from the year column (leaving 1916) and reduce it to 12 months. 12 months 9 mo. leaves 3 months. 1916 1915 = 1 year. Therefore, the time is 1 year, 3 months, 28 days. Compute the interest. Find the interest on: 23. $750 from April 7, 1915, to July 14, 1917, at 6%. 24. $350.Y5 from Dec. 18, 1912, to March 16, 1915, at 6%. 26. $2000 from Nov. 1, 1916, to Jan. 1, 1918, at 5%. 26. $150 from July 25, 1910, to March 15, 1912, at 7%. 27. $275 from Oct. 9, 1913, to March 3, 1915, at 6%. 28. $5000 from Aug. 16, 1916, to August 16, 1921, at 5%. 29. $500 from May 22, 1914, to Sept. 22, 1917, at 6%. 100 SEVENTH YEAR 30. $850 from Mar. 1, 1915, to Oct. 5, 1916, at 6%. 31. $425 from Feb. 10, 1917, to Mar. 13, 1918, at 6%. 32. $1500 from Jan. 12, 1916, to July 3, 1917, at 5%. 33. $236.25 from Dec. 6, 1916, to Oct. 12, 1917, at 6%. 34. I borrowed $300 on July 18, 1916, at 6%, promising to pay the note on demand. The owner presented the note for payment on April 21, 1917. How much interest was there on the note at that time? What was the total sum due the lender? Bankers and other firms who have a great deal of interest to compute use tables in order to save time and insure greater accuracy. The following interest table was computed on the basis of 360 days to the year. Some tables are computed on the basis of 365 days to the year if the exact interest is wanted. INTEREST ON $1.00 Time 5% 6% 7% 1 $.000139 $.000167 $.000194 2 .000278 .000333 .000389 3 .000417 .000500 .000583 4 .000556 .000667 .000778 & 5 .000694 .000833 .000972 6 .000833 .001000 .001167 7 .000972 .001167 .001361 8 .001111 .001333 .001556 9 .001250 .001500 .001750 10 .001389 .001667 .001944 20 .002778 .003333 .003889 1 .004167 .005000 .005833 2 .008333 .010000 .018667 9 c 3 .012500 .015000 .017500 4 .016666 .020000 .023333 s 5 .020833 .025000 .029167 6 .025000 .030000 .035000 1 Year .050000 - .060000 .070000 APPLICATIONS OF PERCENTAGE INTEREST 101 Exercise 6 1. Find the interest on $200 for 2 years, 3 months, 13 days at 6%, using the above table: Interest on $1.00 for 2 years =$.12 Interest on $1.00 for 3 months = .015 Interest on $1.00 for 10 days = .001667 Interest on $1.00 for 3 days = .0005 Interest on $1.00 for total time =$.137167 Interest on $200 for the given time, 200 X$. 137167 =$27.43 + . Using the interest table, find the interest on: 2. $300 for 1 year, 6 months at 6%. 3. $250 for 1 year, 4 months, 20 days at 7%. 4. $500 for 2 years, 7 months, 9 days at 5%. 6. $75 for 1 year, 6 months, 5 days at 7%. 6. $2000 for 3 years, 6 months at 5%. 7. $700 for 8 months, 25 days at 6%. 8. $100 for 2 years, 9 months, 24 days at 7%. 9. $500 for 1 year, 2 months, 23 days at 6%. 10. $375 for 3 years, 6 months at 6%. PARTIAL PAYMENTS When a note is given for a long period, the interest is usually to be paid periodically, and not to be deferred until the principal becomes due. A part of the principal may likewise be paid from time to time. Such a payment is called a partial payment. The amount paid should be stated on the back of the note, together with the date on which it is received. The subject of Partial Payments in Arithmetics is one in which there has been much confusion, owing to the diverse 102 SEVENTH YEAR laws of different states. The tendency is towards unity of practice in partial payments, since nearly all of the states have adopted this rule sustained by the Supreme Court *f the United States in cases that have come before it. This is known as the United States Rule, and is in substance as follows: When a partial payment or the sum of two or more partial payments is equal to, or more than, the interest due, it is to be subtracted from the amount (principal -{-interest due) at the time; and the remainder is to be considered a new principal, from that time to the next payment. The following form shows the method of recording partial payments on a note i 1 .$WQ:QO. L,. Q//n/lJU/ *y>(&/lfy _ afterdate C/ .^promise to pay to ""ff the order of ._._JQ/W_jUj^__<3b^M^ with intereit at S?- J.9j... ...... for value received. I,W7*75. 1,IW*100. Payments on a note are usually made at interest- bearing dates. If the interest is payable on Jan. 1 and July 1 of each year, it is often specified that partial payments may be made on those dates. APPLICATIONS OF PERCENTAGE 103 Exercise 7 1. Find the amount of the note on p. 90, due on settlement at maturity. Solution : $400.00 1st principal. 24.00 interest from July 1, 1915, to July 1, 1916. 424.00 amount due July 1, 1916. 50.00 payment July 1, 1916. 374.00 new principal. 11.22 interest from July 1, 1916, to Jan. 1, 1917. 385.22 amount due Jan. 1, 1917. 75.00 payment Jan. 1, 1917. 310.22 new principal. 18.61 interest from Jan. 1, 1917, to Jan. 1, 1918. 328.83 amount due Jan. 1, 1918. 100.00 payment Jan. 1, 1918. 228.83 new principal. 6.86 interest from Jan. 1, 1918, to July 1, 1918. $235.69 amount due on note at date of maturity. 2. Find the amount due at maturity Jan. 15, 1918, on a note drawn at Indianapolis, Ind., Jan. 15, 1916, for $1000 with interest at 6%, having the following credits indorsed upon it: July 15, 1916, $80. Jan. 15, 1917, $107. July 15, 1917, $29. 3. What was due at maturity, Aug. 10, 1917, on a note drawn at San Francisco, Gal., Feb. 10, 1915, for $650 with interest at 6%, having the following partial payments indorsed upon it? Aug. 10, 1915, $109.50. Aug. 10, 1916, $219.50. Feb. 10, 1916, $116.50. Feb. 10, 1917, $50.00 4. What amount was due at maturity July 15, 1917, on a note drawn at St. Louis, Mo., July 15, 1915, for $800 with interest at 5%, having these credits indorsed upon it? Jan. 15, 1916, $210. July 15, 1916, $215. Jan. 15, 1917, 104 SEVENTH YEAR COMMISSION If a fruit grower or farmer wishes to sell his produce in a distant city, he can not usually afford to leave his work and go to the city to attempt to find a buyer. It is more profitable for him to have some firm in the city sell the produce for him. Refrigerator cars now make it possible to ship fruits and vegetables thousands of miles to distant cities where higher prices can be secured for them. There are two ways in which the grower can dispose of his products: (1) he can sell directly to some wholesale firm or (2) he can consign it to a commission firm to sell for him at a certain per cent of the sale. If the grower sells directly to a firm, he usually sends a sight draft attached to a bill of lading, making it necessary for the firm to pay the draft before they can secure the bill of lading and get possession of the goods from the railroad company, This sight draft can be deposited by the grower with the local bank for collection. The local bank then sends this draft to a bank in the city, where the debtor does business, for collection. It is customary for the local bank to allow the grower to check against the amount of the draft, but he must replace the money if the draft is refused by the firm to which he sent the goods. If a grower asks a commission firm to sell the goods for him, he consigns the shipment to them and they dispose of it to the best advantage, charging a certain commission for their work. After deducting commission, freight, cartage, storage or any other necessary expenses, the commission firm sends the proceeds to the shipper. APPLICATIONS OF PERCENTAGE COMMISSIONS105 Wheat, com and other grains are bought and sold in large cities in boards of trade where the members, called brokers, are required to pay for the privilege of buying and selling produce. Exercise 8 1. A fruit grower in Michigan consigned to a commission firm in Chicago 240 barrels of apples to be sold to the best advantage. The freight charges were 12 per 100 Ib. and the apple barrels were considered as weighing 160 Ib. each. Find the amount of the freight charges. 2. The cartage (or drayage) on these apples amounted to 6ff per barrel. Find the cartage charges. 3. 128 barrels were placed in cold storage at the rate of 15 for the first month and 12 for each month thereafter. 80 barrels were sold out of cold storage during the first month and the remainder during the second month. Find the storage charges. 1 4. The following .sales were made: 60 bbl. of Wolf Rivers at an average of $4.25 per bbl.; 35 bbl. of Baldwins at $3.75 per bbl.; 52 bbl. of Northern Spys at $5.00 per bbl.; 93 bbl. of Greenings at $3.50 per bbl. What was the commission on the total sales at 7%? 5. After deducting the commission, storage, cartage and freight, find the proceeds which the commission firm sent to the shipper. 6. A potato grower sold a carload of potatoes consisting of 240 even-weight sacks of 150 Ib. each at 80 cents a bushel. What did he receive for the carload? (1 bu. potatoes = 60 Ib.) 7. The buyer paid freight at the rate of 27 cents per hundred pounds. What was the freight bill? 1 Any fraction of a month counts as a whole month in computing storage. 106 SEVENTH YEAR 8. James Condon of New Jersey had 186 bbl. of sweet potatoes which he wished to sell. He wired his broker in Detroit, Mich., to sell them to the best advantage. The broker was offered $3.25 per bbl. F. O. B. loading point. This, Condon accepted. How much did Condon receive for the carload of potatoes? 9. How much must he send his broker at 15 i per bbl. brokerage? 10. What were Condon's net proceeds on the sale? 11. A woman canvasser sells an improved kitchen utensil on a commission of 15%. What must be the amount of the sales to pay her $30.00? 12. An administrator for an estate of $750,000 gave a bond for double that amount. The premium of the bond was $1185. The agent securing the bond received a commission of 15% of the premium. What was his commission? 13. A firm bought 42,070 Ib. of onions in 111. at 75j per bu. of 57 Ib. and sold them in Michigan at 95^ per bu. of 54 Ib. They paid freight at the rate of 7< per 100 Ib. How much was the firm's actual gain on the onions? 14. If a travelling salesman receives a commission of 10% on his sales, what will be the amount of his commission if his yearly sales amount to $25,000? 16. A real estate agent sells a building for $15,500, receiving a commission of 3%. What does he receive for his services? 16. A collector remits to his customer $114 after deducting a commission of 5%. How much did he collect? 17. A produce broker received $927 to invest in potatoes at 90jif per bushel, on a commission of 3%. How many bushels did he buy? 1 1 First find the cost of each bu. of potatoes, including the commission. APPLICATIONS OF PERCENTAGE TAXES 107 18. A farmer placed 2000 bu. of new corn in crib in Novem- ber, 1915, to be sold by a commission firm when the price reached 85^ per bu. This corn was sold at that price in June, 1916. The shrinkage on the corn was 12%. The commission was 5%. Find the amount of the commission. 19. A real estate agent sold a farm for $20,000, receiving for his services, from the owner, a commission of 2%. What was the amount of his commission? 20. A real estate agent purchased a farm for a customer, and added to the price 5% commission. His bill was what per cent of the price he paid? The bill was for $10,500. What was the price paid? 21. Having deducted $5.00 for expenses, and $45.50 for commission at 5%, a commission merchant forwarded to his principal the remainder of the cash received for a consignment of farm products. What amount was remitted to the con- signor? 22. A broker receives $4010 to be invested in wheat at $1.00 per bushel, his commission being j% for making the purchase. What will his customer pay for each bushel so purchased? How many bushels can be purchased for the amount stated? TAXES The state, the county, the city and the school district must have funds to pay the expenses of the officers and laborers who render services to those divisions of government. 1. What are some of the services that the officers of the city perform for the people in that city? 2. What benefits do the inhabitants of a school district get from the funds spent for school purposes? 3. How do the state and county governments serve the people? 108 SEVENTH YEAR The funds necessary for carrying on the government of the state and various local divisions are usually raised by taxing the people on the amount of property which they own. Property is divided into two classes: (1) real estate, includ- ing lands and buildings; and (2) personal property, consisting of movable possessions such as clothing and jewelry, household furnishings, domestic animals, and farm products, the merchan- dise and productions of stores and shops, machines and engines, vehicles, mortgages and notes, stocks and bonds, money, etc. Officers, generally called assessors, determine the value of the property. Then the proper officers of each local division of government estimate the amount of money that they will need to carry on the government of their division for the next year. This levy is turned in to some county or state officer who divides the levy by the assessed valuation of the property to find the rate of taxation for each local division. Collectors then collect the proper amount from each person according to the amount of his property. The following table gives an illustration of the manner in which the various rates of taxation are computed: HOW THE TAX RATES ARE COMPUTED Division of Government Levy Assessed Valua- tion of Property 1 Rate of Taxa- tion = Levy -s- Assessed Val. State $19,994,495.11 198,703.42 1,500.00 4,000.00 14,259.27 $2,499,311,888 42,277,324 1,228,410 295,443 534,055 .0080 .0047 .0012+ .0135+ .0267 + County Town Citv . . School District Total Rate of T a.xation .0541 + 'Assessed valuation of the property in this state is taken as actual value. Systems of taxation vary in different states. of the APPLICATIONS OF PERCENTAGE TAXES 109 Exercise 9 1. What would be a man's taxes who lived in all these divisions if his property was assessed for $15,350? Compute the amount of tax in each local division and then find the total. Why must a collector compute these various amounts separately? 2. What is the rate of taxation in your county for county purposes? In your state for state purposes? In your school district for school purposes? Appoint some one in the class to get this information from the collector, the county clerk, or consult a tax receipt. 3. If property is taxed at the rate of $5.50 per $1000, what is the per cent of taxation? How many mills is that on the dollar? 4. In a certain village the assessed valuation of the property is, in round numbers, $300,000. The amount of tax needed for carrying on the government is $5000. What will be the rate of taxation for village purposes? 6. A school board estimates that the expenses of running their school will be $4500 and make a levy for that amount. If the assessed valuation of the property in the district is $350,000, what will be the rate of the school tax? 6. The assessed valuation of a tract of land adjoining a city is valued at $15,000 and the present rate of taxation is 1.5%. If the land is annexed to the city in which the rate of taxation is 2.5%, what will be the increase in the taxes of the owner of the land? What benefits will he receive for the extra taxes that he pays? 7. If the assessed value of the property in a certain county is $18,596,482 and the total taxes levied upon it for state and local purposes is $650,876.87, what is the total rate of taxation? 8. In a certain township (town) a tax of $20,000 is to be 110 SEVENTH YEAR raised. If there are 500 citizens to pay a poll tax of $1 each, how much of the tax must be laid on property? A poll tax is a small tax levied on males without regard to their property. "Poll" means head; that is, the tax is so much a head. Poll taxes are being abolished in many places. Find whether your community still has a poll tax. 9. A man has $1200 loaned out at 6% interest. He is assessed on ^ the amount of his loan and the rate of taxation is 4^%. How much will be his net returns each year on the loan after he pays his taxes? 10. In a village containing propeity assessed at $200,000, the rate of taxation is 3%. If a poll tax of $2 can be collected from 800 citizens, how much can the assessed rate of taxation be reduced? 11. A village levied $4800 in taxes on property valued at $600,000. Find the rate of taxation. SPECIAL ASSESSMENTS If a city wishes to pave a street, it assesses the cost upon the owners of the adjoining property because the pavement will add to the value of the property. The city usually pays for the pavement of the intersections of the street. Such assess- ments are called special assessments. Drainage ditches are also paid for in special assessments, the amount of the tax depending upon the distance from the ditch. The owners of land adjoining the ditch are benefited most and hence must pay the highest tax. If the object of the special assessment is equally beneficial to all the inhabitants of the city, such as parks and libraries, the special taxes are levied upon all the property in the city. ' Find an example of a special assessment that has been levied in your community. How was the tax assessed? Make five problems out of the information .you secure on this special assessment. APPLICATIONS OF PERCENTAGE ASSESSMENTS 111 PROBLEMS 1. If the assessment valuation for a certain city is $1,800,000 and there is to be raised for a special purpose $48,000, what will be the rate of taxation required for this purpose? 2. What will this add to the tax of a resident who owns property assessed at $6000? 3. A drainage district was formed for reclaiming some of the low land along the Illinois River. The area drained was 1280 acres. The cost of the work was $25,600. What was the assessment on each acre if the amount was equally distributed? 4. The streets of a city are being paved at a cost of $1.20 per sq. yd. The width of the paving is 30 feet. The cost of the curbing is 60 cents per running foot. How much will be the tax on a man owning a frontage of 50 feet if he is required to pay for the pavement to the middle of the street? 6. What will be the assessment on the owner of a corner lot in the same city if his lot is 150 feet long and 45 feet wide? The city pays for the intersections of the streets. EXPENSES OF THE NATIONAL GOVERNMENT The principal items in the yearly expenses of the national government in a recent year were as follows : EXPENSES Treasury Department $ 227,277,657.81 War Department 8,995,880,266.18 Navy Department 2,002,310,785.02 U. S. Shipping Board 1,820,606,870.90 Miscellaneous 1,889,773,159.71 Total $14,935,848,739.62 Money must be raised by our national government to meet these expenses. The main sources from which the national government derives its income are: 112 SEVENTH YEAR RECEIPTS Customs Duties ' $ 183,428,624.71 Internal Revenue 1,239,468,260.01 Income and Excess Profits Taxes 2,600,762,734.84 Interest on Obligations of ForeignGovernments 322, 162,228.04 Miscellaneous Receipts 301,782,004.86 Total Ordinary Receipts $4,647,603,852.46 Where does the money come from to meet the difference between the expenditures and the ordinary receipts of the government? (See page 221.) CUSTOMS DUTIES Congress has the authority to fix the duties on imports. They pass a law enumerating various schedules or classes of articles and give the duty on each item in a schedule. Such a law is called a tariff. Since tariffs are frequently discussed in political campaigns, you, as future voters, should understand how a duty is levied and its effect upon prices in this country. Suppose that it costs $1.00 per yard to make a certain grade of cloth in Europe. If the duty on this kind of goods is 35% of the value of the cloth, the duty will amount to 35 cents per yard. Since the importer can not afford to lose this duty of 35 cents, he must sell his cloth in the United States for at least $1.35 per yard. 1. Suppose on the other hand that it costs $1.35 to manu- facture the same grade of cloth in the United States. Can our factories compete with the European goods after the importers pay the tax of 35%? 2. Could our factories compete with the European manu- facturer of that grade of cloth if he only had to pay a duty of 20%? 3. Could the importer compete with our factories if he had to pay a duty of 60% on the cloth? APPLICATIONS OF PERCENTAGE REVENUE 113 Since a duty of 35% in the above illustration protects our factories against the lower prices of imported goods from Europe, it is said to be a protective duty. The principal discussions in political campaigns have been over raising, lowering or main- taining the tariff duties then in force. In 1916, Congress passed a law creating a tariff commission to consist of representatives from the leading political parties of our country. This commission is to determine accurately the costs of production of various articles in the United States and in foreign countries and to report this information to Con- gress. This should enable Congress to form a much better list of tariff schedules than it has done in the past. Not all imports are taxed. There are some necessities that we want to encourage people to ship to this country and we allow them to come in free. Among the articles on the free list are agricultural implements, bibles, coffee, corn, cotton, hides, meats, potatoes, salt, wool, milk and cream. Tariff duties are of two kinds, ad valorem and specific. Ad valorem duties are those levied against the value of the goods imported. Specific duties are duties based upon the number, weight, etc. For example, if a duty on dress goods is 30% of the value of the goods, such a duty is said to be an ad valorem duty. If the duty is 5 cents per pound, the duty is said to be specific. Ad valorem duties are more difficult to levy than specific duties because the goverment must keep experts who can accurately judge the quality of the various kinds of goods. Specific duties on the other hand are easily levied because the quantity expressed in yards, pounds, gallons, etc., has merely to be measured. Specific duties, however, have the disadvantage of putting the heaviest burden on the cheaper grades of goods. If the duties are too high, foreign goods will not be imported and there will be a decrease in the amount of revenue obtained from customs duties. 114 SEVENTH YEAR Among the many duties of the Tariff Act of 1913 are the following: Article Schedule Duty Ink Powders A 15% fl-d valorem. Window Glass B Ic per Ib. between 154 and 384 sq . in. Automobiles . . c Over $2000 45% ad valorem. Less Mahogany Lumber Horses D G than $200030% ad valorem. 10% ad valorem in rough boards. 10% ad valorem. Beans G 25c per bu. of 60 Ib. Cotton Stockings . . Wool Clothing I K Value up to 70c per doz., 30% valorem. More than $1.20 per 50% ad valorem. 35% ad valorem. ad ioz., Silk Clothing L 50% ad valorem. Writing Paper .... M 25% ad valorem. Firecrackers N 6c per Ib. Roman Candles Cut Diamonds" . . . Typewriters N N Free List lOc per Ib. 20% ad valorem. No duty Potatoes Free List No duty. Tell which of the above duties are ad valorem and which are specific. Goods are classed under different schedules. For instance, Schedule A includes chemicals, oils, and paints; Schedule G includes agricultural products and provisions, etc. Similar articles are grouped together in the same schedule. The letters of the alphabet A to N are used to designate the different schedules. Exercise 10 Use the preceding table to find the corresponding duties. 1. Find the duty on a French automobile costing $2500. APPLICATIONS OF PERCENTAGE REVENUE 115 2. Find the duty on an imported automobile costing $1500. 3. I buy a team of work horses in Canada for $300. How much duty must I pay to bring them into this country? 4. A firm in New York buys from a firm in London the following goods: 20 reams of writing paper @ 50^ per ream; 100 Ib. of firecrackers; 100 Ib. of Roman Candles; 3 typewriters @ $60 each. Find the total amount of the duties on these goods. 6. If I buy 2000 ft. of mahogany lumber in Central America at $50 per M and import it into this country, how much duty shall I have to pay? 6. A firm imports the following bill of goods: 3 dozen silk handkerchiefs @ $3.95 per dozen; 50 ready-made wollen dresses at $12 each; 6 dozen cotton stockings at $1.80 per dozen. Find the total duties on this bill of goods. 7. A jeweler imported cut diamonds to the value of $50,000. How much import duties did he pay? 8. A firm imported 10 bags of beans weighing 120 Ib. each and 20 sacks of potatoes weighing 150 Ib. each. Find the amount of his duty. 9. A school supply firm imported ink powder invoiced at $2500 in Liverpool, England. How much duty did they pay on this bill of goods? 10. A glass firm imports window glass in sizes from 154 sq. in. to 384 sq. in. If the glass weighed 1000 Ib., how much duty did they pay on the shipment? INTERNAL REVENUE Another important source of revenue for the government is the income from internal duties or excises which are levied on certain kinds of manufactured products as substitutes for butter, tobacco goods and non-beverage distilled spirits. 116 SEVENTH YEAR During the World War the expenses of the national govern- ment were extremely heavy. In order to meet these increased expenses Congress levied special revenue taxes which will be removed when the expenses are reduced. Among these special taxes are: railroad tickets, express and freight bills; telegraph, telephone, and radio messages; automobiles; admissions to theatres, concerts and cabarets; non-intoxicating beverages, including soft drinks, mineral waters, etc.; and stamps on bonds, notes, etc. 1. The total receipts from internal revenue for 1919 were $3,839,950,612. This was an increase of $145,330,973 over the receipts for 1918. What was the per cent of increase? Income Taxes The sixteenth amendment to the Constitution of the United States, adopted in 1913, gave Congress the authority to levy an income tax. The income tax in force Jan. 1, 1920, allows an exemption (or deduction) from a person's net income of $1000 for a single person and $2000 for a married person. An addi- tional exemption of $200 is allowed for each child under 18 years of age, and also for any other dependent who is mentally or physically defective. In computing his net income a person is allowed to deduct from the gross income the expenses of conducting his business. Living expenses cannot be deducted in computing the net in- come. All net income up to $4000 is taxed 4%. All income above $4000 is subject to a tax of 8%. All income above $5000 must pay an additional tax, called a surtax. The table showing the rates for the surtax is given on the following page. Why should a married man have a larger sum for exemption than a single man? SURTAX RATES FOR 1919 117 Surtax Rates for 1919 Amount of Net Income Rate Amount of Net Income Rate Amount of Net Income Rate $ 6,000 1% $42,000 19% $78,000 37% 8,000 2% 44,000 20% 80,000 38% 10,000 3% 46,000 21% 82,000 39% 12,000 4% 48,000 22% 84,000 40% 14,000 5% 50,000 23% 86,000 41% 16,000 6% 52,000 24% 88,000 42% 18,000 7% 54,000 25% 90,000 43% 20,000 8% 56,000 26% 92,000 44% 22,000 9% 58,000 27% 94,000 45% 24,000 10% 60,000 28% 96,000 46% 26,000 11% 62,000 29% 98,000 47% 28,000 12% 64,000 30% 100,000 48% 30,000 13% 66,000 31% 150,000 52% 32,000 14% 68,000 32% 200,000 56% 34,000 15% 70,000 33% 300,000 60% 36,000 16% 72,000 34% 500,000 63% 38,000 17% 74,000 35% 1,000,000 64% 40,000 18% 76,000 36% 1,000,000 + 65% Explanation of Table: Of the first amount $6000, the) exemption for the surtax is $5000, hence a person with an income of $6000 would pay a surtax of 1% of $1000. A person with an income of $8000 would pay a surtax of 2% on the income between $6000 and $8000 (or $2000) and 1 % on $1000. The 3% rate is for the portion between $8000 and $10,000. Exercise 11 1. A married man has an income of $15,000 a year. Find the amount of his income tax, allowing exemptions for 2 children. $2000 + $400 = $2400, total exemptions. $15,000 - $2400 = $12,600, net income. 4% of $4000 $160.00 8% of $8600 ($12,600 - $4000) 688.00 1% of $1000 ($6000 - $5000) 10.00 2% of $2000 ($8000 - $6000) 40.00 3% of $2000 ($10,000 - $8000) 60.00 4% of $2000 ($12,000 - $10,000) 80.00 5% of $600 (Excess over $12,000) 30.00 Total income tax . . . $1068.00 118 SEVENTH YEAR 2. The net income of a married man is $9750 per year. He has no children. Find his income tax. 3. The yearly income of a single woman is reported in her tax schedule as $5320. She has one dependent to support. Find her tax. 4. What is the income tax of an unmarried man with an income of $7500, if he has no dependents? 6. A merchant has a gross income of $8750 per year. The expenses of running his business amount to $2500. He is married, and has a child under 18 years of age. Find the amount of his income tax. 6. A milliner (unmarried) has a gross income of $6350 per year, and the expenses of her shop amount to $2790 a year. Compute her income tax. 7. Find a married man's income tax on a net yearly income of $42,350. Allow additional exemptions for 3 children and 1 other dependent. 8. Find the tax of a single person on a salary of $4500. 9. Why should a person with a large income pay a higher rate on amounts above a certain sum? INSURANCE Insurance is a contract whereby, for a certain payment called a premium, a company guarantees an individual or firm against loss from certain perils. The contract is stated in a document called a policy. Instead of one person carrying all the risk on his life or property, insurance distributes the risk over a large number of persons so that no one person has to bear an extremely heavy loss. The most common forms of insurance are: APPLICATIONS OF PERCENTAGE INSURANCE 119 Fire Insurance insures against loss from injury to property, or destruction of it, by fire. Life Insurance insures a person against loss through the death of another. Accident Insurance insures a person against disability caused by an accidental injury to him; and in case of his death from the injury received, it insures an indemnity to a specified beneficiary. Casualty Insurance, of various kinds, insures against loss resulting from accidental injury to property, such as live stock, plate glass, etc. Fidelity Insurance insures against loss arising from the default or dishonesty of public officers, or of clerks or agents in the employ of the insured. Marine Insurance insures against loss by injury to, or dis- appearance of, ships, cargoes, or freight, by perils of the sea. FIRE INSURANCE In order to prevent insurance from having the nature of a betting or gambling contract, an agent is not supposed to insure property for its full value against loss by fire. The person whose property is insured must bear a portion of the risk himself. The rate of the premium is generally stated at so much per hundred dollars and varies according to conditions such as the kind of fire department, nearness to other buildings, con- struction of the building, etc. Most firms insure property for three years at two and a half times the yearly rate. Insurance on furniture is strictly construed in accordance with the exact terms of the policy. If the furniture is removed at all without express permission from the building in which it is insured, the insurance fails. 120 SEVENTH YEAR Exercise 12 1. If I- deem my house worth $5000, and desire to insure it for one year for three-fifths of its value, what must I pay for the policy when it costs $7.50 for each $1000 of insurance taken? 2. A farmhouse and barn and other buildings pertaining to them, valued at $15,000, are insured for one year for two- thirds of their value, at 75 cents for each hundred dollars of insurance. What is the cost of the policy? 3. If the furniture in my cottage is worth $1000, and I wish to insure it for 60% of its value, having to pay $1.66f for each hundred dollars of insurance, what will the policy cost me? 4. A church pays, in all, $180 yearly, for insurance to the amount of $10,000, in each of three separate companies, the rate of insurance being the same in each company. What is the rate of insurance? If my house, insured for $4000, is destroyed and I am unable to prove that it was really worth over $2000, I can recover from the insurance company no more than the latter amount. 6. If when insured against fire for $5000 it was destroyed, and I can prove its value only to the amount of 60% of this sum, what amount of compensation do I receive? To insure a house for three years at a time, one has to pay two and one half times the rate for a single year. 6. My insurance for a three-year period is $31.25. What would have been my insurance for a single year? By insuring a house for five years at a time, one has to pay four times the rate for a single year. 7. If a man pays $200 for the five-year period, what would the insurance cost him for a single year? For a period of three years? For five separate periods of one year each? APPLICATIONS OF PERCENTAGE INSURANCE 121 8. If I have furniture insured for $1200, temporarily stored in an outbuilding which is not mentioned in my policy, and the outbuilding and furniture are destroyed by fire, what amount can I recover on my loss of furniture? 9. A rug worth $150 is hung out in the yard to air, and is ruined by sparks from a passing fire engine. If it formed a part of the household furniture that is insured for $1000, can the owner recover its value from the insurance company? 10. What could be recovered if it had been thus destroyed while hung on a line on a porch of the residence? 11. A dozen books supposed to be rare and valuable are insured for $1200. They are destroyed by fire, and it is then proved that they were recently manufactured, and of no greater possible value than $3 apiece. What is the limit of indemnity that the company should pay for them? Insurance Applied Mr. Manning owned a suburban lot on which he contracted with a house construction company to build a home at a total cost of $4500. On the completion of the new home, Mr. Manning, rec- ognizing the importance of proper protection to his family, took out an insurance policy on the house. Exercise 13 1. An insurance company insured the house for 80% of its cost. Find the amount of his policy. 122 SEVENTH YEAR 2. Why will an insurance company not insure a house at its full value? 3. The rate of insurance on this house was 72 cents per $100 for a "three-year period." What was the cost of the insurance per year? 4. Mr. Manning made out an inventory of his household goods and estimated them to be worth $950. He decided to take out $800 on his household goods. Why was it a good plan to make out an inventory of the goods before insuring? What should be done with this inventory? 6. The rate of insurance on his household goods was 79 cents per $100 for three years. Find the amount of the premium on the household goods. LIFE INSURANCE There are two principal kinds of life insurance companies: the "old line 1 ' companies and the mutual companies. The old line companies have worked out definite rates for different ages and the premium for each year is definitely stated in the policy. The mutual companies usually levy an assessment at certain intervals, generally each month, to pay the death claims. The "old line" companies usually have several kinds of policies such as 15-payment life; 20-payment life; endowment policies; ordinary life policies. In the 15-payment life policy, the person insured makes fifteen yearly payments at the end of which his insurance is paid for the rest of his life. The 20-payment life, as the title indicates, is paid for at the end of 20 yearly payments. An endowment policy usually requires a larger premium and if the insured person lives to the end of the period named in the policy he can draw out the amount of the policy. In an ordinary life policy a definite yearly payment is required each year until the person dies. All of these forms usually APPLICATIONS OF PERCENTAGE INSURANCE 123 have a cash surrender value which will be paid the insured person upon the surrender of the policy. Most policies also have a table showing the amount of money which the company will loan on a policy. Since the risk of the death of a person increases with age, the premium increases each year. It is therefore an advantage to take out insurance as early as possible. The age nearest the birthday of the person insured is the age considered. A medical examination is also required to protect the company from undesirable risks. Premiums per $1000 Age Ordinary Life 20-Payment Life 20- Year Endowment 20 $19.21 $29.39 $48.48 21 19.62 29.84 48.63 23 20.51 30.80 48.96 25 21.49 31.83 49.33 27 22.56 32.94 49.73 30 24.38 34.76 50.43 35 . 28.11 38.34 51.91 40 33.01 42.79 54.06 45 39.55 48.52 57.34 50 48.48 56.17 62.55 Exercise 14 1. At the age of 21, a man insured his life for $2000 on what is called the ordinary life plan, for an annual payment of $39.24. What does he pay in fifteen years? 2. Had he deferred the insurance for five years, it would have cost him $44.10 for each year. How much more would this have been than the amount the insurance actually did cost him for the same period of ten years? 3. A man took out a 15-payment life policy for $1000 at the age of 30 at $40.25 for each annual payment. What was 124 SEVENTH YEAR the total amount of his fifteen payments? How can the com- pany afford to insure him at an amount which will yield less than the face of the policy? 4. A man insured his life on the endowment plan for $1000 at the age of 21, paying $48.63 annually for a 20-year period, and lived beyond the time and received the amount of the policy. What was the total amount of his payments? 6. What did the insurance company receive to pay them for taking the risk of his death during that period? 6. A man took out a 20-payment life participating policy for $2000 at the age of 24, with a premium stated at $62.16 per year. If his dividends on the policy amounted on an average to $10 per year for 19 years, how much did the insurance cost him? A participating policy pays dividends to the holder after the first year according to the profits of the company. These dividends are usually deducted from the premium, the insured person paying the balance due the company. 7. At the end of the period, the policy had a cash surrender value of $994. If he surrendered his policy at the end of the period, how much will his insurance cost him besides the interest on his payments? ACCIDENT INSURANCE 1. A man has paid $18 for 4 years for an accident insurance policy. Owing to an accident, he is disabled for a period of 6 weeks, during which time he receives $25 a week. What has been the net financial value of the insurance to him? What has been the net loss to the insurance company? 2. A horse insured for $300 is choked to death, being ignor- antly tied with a running noose of rope for a halter about its neck. Is the owner entitled to the insurance? If by a com- promise 40% of the policy is paid, what sum does the owner receive? REVIEW. PERCENTAGE 125 Exercise 15. Informational Review References refer to page numbers. 1. What is a discount? Define net proceeds. (91) 2. Give two advantages of using commercial discounts. (93) 3. What is usury? (96) 4. State the United States Rule for partial payments. (102) 6. If you had a carload of potatoes to ship to a large city for sale, describe the steps that would be taken before you received pay for them. (104) 6. Why do we pay taxes? What are some of the services which we secure from the money paid out in taxes? (107) 7. Distinguish between real estate and personal property. (108) 8. Give the chief items in the expenses of our national gov- ernment. State the chief sources of income for our national government. (112) 9. What is a tariff? (112) 10. What is a protective duty? (112-113) 11. Explain the difference between a specific and an ad valorem duty. (113) Which kind of duty is easiest to pay? Why? 12. What are some of the special taxes that were levied during the World War? (116) 13. Describe the system of levying our national income tax. (1 16) 14. Name and describe five forms of insurance. (119) 15. Describe the different kinds of life insurance poli- cies. (122) 16. What is a participating policy? (124) 17. What is accident insurance? (124) 18. What income tax will a married person pay with a net income of $4500, there being no dependents in the family? 19. What income tax will a married person pay with a net income of $5750, there being two children under 18? 20. Find the rate of insurance that your parents pay on their household goods. 126 SEVENTH YEAR Exercise 16 1. A farmer bought a horse for $120 and later sold it for $200. What was his per cent of gain? 2. Two buildings valued at $2000 were destroyed by fire. The insurance received was $1500. What was the per cent of loss to the owner? 3. Lulu Alphea, a yearling cow of Ashburn, New York, pro- duced 13,669 pounds of milk from which 1000 pounds of butter were made. The per cent of butter fat in butter is about 85%. Find the per cent of butter fat in the milk of this cow. 4. Silk hose costing $1.50 were sold at $2.00. What was the per cent of profit? New hose were bought for 20% more than the cost of the old stock. What must be the selling price of the new hose in order to yield the same per cent of profit as the old stock? 6. Mr. Gleason built a house for $2400. He sold it two years later for 80% more than it cost. What was the selling price of the house? 6. In 1920 a certain grade of hard coal sold for $14.50 in a city of the middle west. In the winter of 1919 it sold for $13.30. What was the per cent of increase during that year? 7. Grace bought 2 cakes of Palmolive soap for 18 cents at a sale. What per cent had the price been reduced for the sale if the regular price was 10 cents a cake? 8. A girls' organization, consisting of 38 members, was as- sessed 5 cents per member. What per cent of this assessment was left in the treasury after a bill of 88 cents for sending a telegram was paid? 9. In selling a house for $4900, a man lost 30%. What did the house cost him? 10. A newsboy received 30 Saturday Evening Posts. He sold 18 of them the first evening. What per. cent of the papers did he sell the first evening? What per cent of the 30 papers did he have left to sell? REVIEW. PERCENTAGE 127 11. A real estate dealer bought a farm for $225 an acre and sold it for $240 an acre. What was h\s per cent of gain per acre? 12. A new house costing $4500 was damaged by a fire to the extent of $3000. If the building was insured for only 60% of its value, what was the owner's loss? 13. Alice purchased a $125 typewriter on the installment plan. She paid $25 cash, 10% of the remainder in the next payment, and 20% of the remainder the next payment. What did she have left to pay? 14. Alice purchased a ream (480 sheets) of typewriting paper for $1.00. If she had bought the paper in small quantities, it would have cost $.01 for 4 sheets. What is the per cent of gain by buying this paper by the ream? 16. Irene was given $40 with which to buy a dress. She paid $25.00 for the satin, $4.00 for the trimmings, and $7. 00 for mak- ing. What per cent of her allowance did she spend on her dress? 16. A farmer bought a team of horses for $500. One of the horses died and he sold the other horse for $325. What per cent did he lose on this investment? 17. Karl bought a calf for $12. When it was 2 years old he sold it for $90. The expenses amounted to $42. Find his per cent of profit. 18. What is the interest for 6 months on $3650 at 6%? 19. Mr. Pelton owns two cottages at a summer resort. The cottages are worth $900 each. He pays the state $25 per year rental for each of the two lots on which they are built. He rented one for $150 for the season of 10 weeks. He rented the other to various parties at $18 a week for the 10 weeks. Find the per cent of profit which he made on the two cottages that season. 20. Mr. Rose listed his house with a real estate firm. They sold it for $5500 and charged 3% for their services. How much did he receive as the net proceeds of the sale? 21. Martha bought a suit at a January clearance sale for $22.50 which had originally been marked $45. What was the per cent of reduction? 128 SEVENTH YEAR 22. Find the interest on $150 for 60 days at 6%. 23. Mrs. Rose has a. $1000 Victory Bond bearing 4f% interest, payable semi-annually. What is the amount of each interest payment? 24. The price of the best grade of "No Protest" silk hosiery is $2.70. A reduction of 25% is given on "seconds." How much will two pairs of the "seconds" grade cost? 26. Kathryn paid $9 for a pair of shoes. This was 25% of what she paid for a suit. What was the cost of the suit? 26. A lawyer secured a loan of $3500 for a client and charged him 3% commission for his services. What was the lawyer's commission? 27. Three-fourths of a pound of flour is required to make a pound loaf of bread. What per cent of bread is flour? 28. It takes 4^ bushels of wheat to make a barrel of flour. What per cent of the wheat is used in making flour? (A bushel of wheat = 60 Ibs. ; a barrel of flour = 196 Ibs.) 29. A certain grade of canned peas sells at $1.50 per dozen or 15 cents per can when bought in less than dozen lots. What per cent is saved by buying in dozen lots? 30. What premium will a man 35 years old pay on a 20-pay- ment life insurance policy for $3000 at the rate quoted in the table on page 123? 31. The assessed valuation of a city residence is $7400. How much taxes must the owner pay if the rate is $24.18 per thousand? I 32. A davenport is listed in a furniture catalogue at $250. What will be the cost if discounts of 30%, 10%, and 2% are allowed? 33. Find the import duty on a shipment of silk dress goods invoiced at $8540. (See page 114 for rates.) 34. A house worth $6000 was .insured for 75% of its value at $30 per hundred. What was the premium? CHAPTER V BUSINESS FORMS AND ACCOUNTS The Memorandum or Salesman's Slip Brown &Du$tf J.C.T. Quipcy. Jll. Jan. 11 4 Pea. Hana 12/14#* 4 " Bacon 4/6$ (unwrpd) 4 " Cooked Kama 3 " Italian Style Haoa 54 15 48 35 .17 .23 .23 .24 *The abbreviation 12/14# means from 12 to 14 pounds. In the above invoice, the number in the first column at the right of the descriptions of the articles shows the number of pounds. The corresponding numbers in the next column give the cost per pound. Multiply the cost per pound by the number of pounds and enter the result in the next column which contains the totals for each article. Exercise 2 1. Extend the invoice shown above, filling in the sums as shown by the dots. 2. Find the net amount of the bill if it is paid within 10 days. (Terms 2% 10 days, means that 2% discount will be allowed if the bill is paid within 10 days.) 132 SEVENTH YEAR Extend the following invoices. You may omit the headings but make a drawing for the rest of the invoice form : 3. 2 10# Carton Regular Frankforts 20 13 J 2 Pieces Cooked Pork Loin 8 31 10 Pieces Fresh Ox Tails 10 8 2 Pieces Bacon 5 to 8# 11 25 4. 1 Piece Fresh Beef Round 93 14 J 3 Pieces Fresh Pork Loins 19 16 10 Pieces Fresh Spare Ribs 10 12 J 15 Pieces Fresh Pigs Feet 15 5 1 Piece Cooked .Ham 13 29 6. 1 Piece Fresh Beef Ribs 86 13 f 20 Pieces Fresh Spare Rib 10 12| 1 Piece Fresh Pork Loin 14 15 \ 2 Pieces Cooked Hams 27 28 l-25# Plain Fresh Pork Sausage 25 15 6. 1 Fresh Side Beef 179 8 8 Fresh Beef Shanks 11 7 2 Jelly L. Tongue 11 27 J 2 Boxes Frankforts 20 12 J 20# Polish Sausage 20 11 Make out bills for the following goods, using fictitious names for the firm and the purchaser : 7. 1 parlor lamp @ $2.95; 3 glass candlesticks @ 29?f; 1 chafing dish, $7.50; 2 brass jardinieres at $1.75; 2 vases at $3.00; 2 cut glass salt cellars at 95jf. 8. 2 granite stew pans @ 39 ff; 2 muffin pans @ 27^; 1 can opener @ 10^; 2 aluminum measuring cups @ 10^; 2 pair scissors @ 75 j; 2 butcher knives @ 50j; 1 electric iron @ $3.79. 9. 1 pair slippers @ $2.00; 1 pair rubbers @ $1.25; 2 bottles gilt-edge polish @ 25^; 3 pairs shoe strings @ 10^; 1 pair ladies' shoes $5.50. BUSINESS FORMS AND ACCOUNTS 133 The Monthly Statement When salesman's slips 01 bills are rendered with orders, the customer is supposed to keep these forms with the various items shown on them in order to check the monthly statement which is sent at the end of each month. The following is one form of a monthly statement that is used : IN At. yr. STATEMENT couifT'Wfm of S CLARKE . Harvty Buchanan r. V. 1 . 1 117. Aug. 1 4 5 14 19 26 30 Oroerii i 2 3 2 1 3 37 69 46 78 55 30 25 15 62 When the customer so desires, an itemized statement will be ren- dered, but this makes a great deal of extra work for the firm and is un- necessary if the customer keeps his slips or bills to check the totals listed under the various dates of the monthly statement. Exercise 3 1. Make out a monthly statement to Mrs. F. R. Fitzgerald from Adams Bros., Grocers, for the following grocery orders, showing only the totals for each day: Aug. 1: 2 loaves of bread @ 15f; 2 pounds prunes @ 30jf; \ pound cheese @ 40fi; 10 pounds sugar @ llff. Aug. 3: % pound dried beef @ 60< a lb.; \ dozen lemons @ 40ff a dozen; 1 peck potatoes 45 Aug. 4: 2 cans corn @ 18ff; 1 basket tomatoes 35?f. . Aug. 9: Celery 15^; 1 head lettuce 15f; 1 package of rolled oats 28ff. Aug. 12: 10 bars soap 79^; 1 basket tomatoes 30ff; 1 sack flour $1.50; 1 head of cabbage 18^. Aug. 17: 10 pounds sugar @ 11^; 2 dozen eggs @ 38ff; 2 pounds butter @ 56fL 134 SEVENTH YEAR Aug. 20: 1 peck potatoes 42^f; 2 packages crackers @ 15?f; 1 box salt lOff. Aug. 23: 2 quarts of peas for 25^f; 1 package puffed rice 15ff; 10 pounds apples @ 8fi. Aug. 26: 1 jar olives 35^; 2 pounds navy beans @ 12?f; 5 pounds rice @ 15?f. Aug. 30: 1 dozen eggs 38i; 1 pound butter 57jf; 1 half-pound can cocoa 23^; 1 pound coffee 45^. 2. Make out an itemized statement of the same account, showing each of the items and the total for each day. 3. Make out a series of purchases from a dry-goods store during some month and render a monthly statement for them. Receipts When a sum of money is paid on an account, the customer should receive a receipt, showing the date and amount paid as in the following form: GALVESTON, TEXAS, figj? J5 S 1Q1 / N. m/iJhsj/ru _ % Dollars ~ oru If the full amount of the account is paid instead of a portion of it, the words "in full of account to date" would be used in place of the expression "on account." If an account is paid by a check, the check stands as a suffi- cient receipt for the payment. For this reason, many persons pay all their accounts by checks. This saves the firm the trouble 'of making out extra receipts or returning the receipted bill to the customer, because the cancelled checks are returned by the bank with their monthly statement. BUSINESS FORMS AND ACCOUNTS 135 Exercise 4 1. R. A. Milton owes Schneider & Co. $30.25 for hardware supplies. He pays them $25.00 to apply on his account. Write a proper receipt for this payment. 2. J. R. Kennedy pays Dr. L. J. Hammers, $15.75 as payment in full for his professional services. Write a receipt for the settlement of this account. 3. Write a receipt for Hogan Bros, to Mrs. J. C. Veeder for a settlement in full of her account of $11.75. 4. Write a receipt for Adams Bros, to Mrs. F. R. Fitzgerald for a settlement in full of the account shown on page 117. 5. Write a receipt for some actual payment in which you have been the receiver of the money or have paid a sum of money to some other person. 6. I ordered a suit from a tailor. He required a deposit of $10.00 and gave me a receipt for this amount, in part payment for the suit. Write such a receipt for a tailor. 7. Write a receipt to a plumber from his employer for $15.00 in payment for 20 hours' work at 75 cents per hour. The Cash Account Most methodical people, whether engaged in active business or not, keep a cash account of their receipts and expenditures. The cashbook represents the owner's pocketbook or cash drawer. "Cash" is treated as a real person. It is debited, or charged with all money received; and is credited with all moneys paid out. Two pages are usually used for a cash account, the left hand page being used for the debits and the right hand page being used for the credits. The "Balance" or difference between the amounts of the two pages will be the cash on hand. The first entry on each debtor page is the amount of cash on hand. 136 SEVENTH YEAR Debit Side of a Boy's Cash Account HOY. 1 Balance on hand 5 90 M 3 Errand 25 4 Ass lot ing in Grocery store 1 50 N 11 M l M 1 50 M 18 N N N N 1 50 10 65 Credit Side of the Same Boy's Cash Account Nov. 6 School Supplies 45 N 10 Sweater Vest 2 50 N 17 School Entertainment 25 N 21 Book 50 II 30 Toalance 6 95 MM_ 10 65 At the end of each month a cash account is "balanced" as shown in the above account. This account shows the boy to have a balance on hand of $6.95 on Nov. 30, because it takes that amount to make the credit side of the account "balance" the debit side. Exercise 5 Prepare a cash account for this boy during December, starting with the cash on hand as shown in the preceding account and entering the following items on the proper side of the account. 1. Dec. 2, Bought a necktie 50j; Dec. 2, Received $1.50 for working in the grocery store; Dec. 5, Received from sale of old books $1.15; Dec. 9, Received from the grocery store $1.50 for services; Dec. 14, Bought Christmas present for mother $2.50; Dec. 15, Received for assistance at opera house $1.25; Dec. 16, Wages from store $1.50; Dec. 19, For Christmas presents bought $3.85; Dec. 23, Wages from store $1.50; Dec. 25, Received as present from mother and father $10.00 in cash; Dec. 30, Wages from store $1.50. BUSINESS FORMS AND ACCOUNTS 137 2. Balance the account on Dec. 31 and enter the proper amount under "To balance" on the credit side of the account. 3. What would be the first item of this boy's account for January, 1917? The Daybook or Journal When goods are sold on credit, the merchant enters the sales, as they occur, in an account book called the Daybook, or Journal, stating the separate items and the price of each. A single page of such an account book may contain business transactions with various persons. Where memorandum slips are kept, many firms do not keep a day book but keep these slips as a record of the daily transac- tions. These memorandum slips are filed in some systematic way, each customer's slips being kept together. The following illustration shows a typical page of the journal of a men's clothing store: 135. 1916. Nov. 7 William Smith, Dr. To 3 pairs socks @ .25 75 To 1 shirt 1 50 To 1 necktie 50 To 4 collars @ .15 60 To 1 pair suspenders 1 00 4 35 Nov. 7 R. P. Jones, Dr. To 3 handkerchiefs .20 60 To 2 union suits @ 1.50 3 00 To 2 collar buttons @ .10 20 3 80 Nov. 7 John F. Brown, Cr. By cash 7 50 Nov. 7 L. B. Strayer To 1 hat 4 50 138 SEVENTH YEAR It will be seen that the preposition to is used with debits and by with credits. The abbreviation Dr. is used for debtor and means that Wm. Smith and R. P. Jones are debtors to the firm for the goods which they have purchased. The abbre- viation Cr. is used for creditor and means that John F. Brown is to be given credit on his account for the cash which he has paid. Exercise 6 Prepare a page of a day book containing the following transactions for Nov. 2: 1. Sold J. R. Stock 1 pair of shoes at $5.00; 1 box of Hole- proof hose at $1.50; 2 collars at 15 cents each; and a shirt for $2.00. 2. Received a cash payment from Wm. Smith for $7.50 to apply on his account. 3. Sold Mrs. J. F. Doan 1 pair shoes at $6.00; 1 box of Shinola at 10 cents; and 2 handkerchiefs at 35 cents each. 4. Add other accounts that a general dry-goods and shoe store would have. Fill out the page in this way. Personal Accounts In a book called a ledger a page or portion of a page is devoted to transactions with a single person. These accounts then are called personal accounts and it is from these accounts that the monthly statements are prepared. These accounts are "posted" by a bookkeeper from the memorandum slips or daybook. The account may be itemized or the totals only may be entered for each day's purchase. A page of a ledger containing a personal account is divided into two parts. A person's indebtedness to the firm is shown on the left or debtor side of the page; and his payments are BUSINESS FORMS AND ACCOUNTS 139 shown on the right or creditor side. This account is usually balanced once a month. Here is an account on the page of a ledger: Dr. Williem Smith Cr. 1916 1916 Nov. 1 Balance froo> Oct. 7 50 Nov. 2 Cash 7 50 " 7 ydoe. 4 35 " 30 Balance 16 10 " 15 3 50 " 29 6 25 23 60 23 60 Dec. 1 Balance 16 10 The above personal account of William Smith shows a balance of $7.50 from his Oct. account still due the firm. He was sent a monthly statement and promptly responds on Nov. 2 with a cash payment. The account shown in the illustration of the daybook on page 121 is shown here entered on the Dr. side of Wm. Smith's account as indicated in the daybook. On Dec. 1, Wm. Smith will be sent a statement of his account, showing a balance due of $16.10. Exercise 7 1. Prepare a similar personal account for December for Wm. Smith using imaginary amounts and balancing his account on Dec. 31. 2. Prepare a personal account for R. P. Jones, including as one of the items, the account shown in the daybook on page 121. Use imaginary accounts for the rest of his account. 3. Prepare a personal account for F. W. Trowbridge from the following items found in the daybook: Balance due Nov. 1, as shown in ledger, $8.75; Nov. 3 paid cash, $8.75; Nov. 5 bought a hat at $4.00 and a tie for 75 cents; Nov. 9 bought 1 box of hose at $1.50; Nov. 15 bought a suit for $27.50; Nov. 26 bought a pair of shoes for $6.00; Nov. 29 paid cash, $30.00. HO SEVENTH YEAR 4. Prepare a personal account of a farmer with a hardware and implement company, inserting items that a farmer buys at such a store. 6. Prepare a personal account of a woman at a druggist's, showing purchases of various medicines, spices, and other supplies which a drug store in your community keeps. The Inventory An inventory consists of a list of articles on hand at the time the inventory is taken together with a statement of the value of the various articles. An inventory is a necessity for a firm in estimating the amount of gain or loss in their business. Inventory of a School Recitation Room Furniture: 1 teacher's desk $15.00 25 single desks at 3.50 87. 50 2 chairs at 2.00 4.00 1 filing cabinet 20.00 * 1 desk book rack . . 1 . 25 Supplies: 2 sets practice exercises in arithmetic $19. 20 1 ream white practice paper 48 1 hektograph (2 faces) 2. 50 3 arithmetic texts (Chadsey-Smith) 1.92 2 boxes crayon at 20 cents 40 Pictures and Flowers: 2 window boxes of ferns at 5.00 $10. 00 1 picture 10. 00 Total value . BUSINESS FORMS AND ACCOUNTS 141 When there has been a loss of household goods by fire, insurance companies usually demand that an inventory be made of the goods destroyed by fire. It is therefore a good policy to make out an inventory of your household goods at the cost price and keep it in a safe place for reference in case of the destruction of your goods by fire. Exercise 8 1. With the help of the teacher and a supply catalogue, make out an inventory of the supplies and furniture in your school room. This may be presented to the school board for reference in case of fire. 2. Make an inventory of the furniture and furnishings in your home, estimating the goods at cost and give this to your parents to deposit in the safety deposit box in the bank for reference if it were needed in making out an inventory in case of fire. 3. If your father is on a farm or in a business in the city, assist him in making out an inventory for his supplies that he has on hand. 4. Make an inventory of your own school supplies. The Pay Roll In factories, stores, and offices where the employees are paid by the hour, there must be some system for keeping a record of their time. Some firms employ a card system on which each employee has his time checked when he begins and leaves. Others use a system of checks, the worker taking out his check when he begins and returning it when he leaves. Some employers have an electric clock with various numbers, each laborer punching his number on entering and also on leav- ing. The record is made on a revolving sheet of paper on the proper time space. 142 SEVENTH YEAR The following form is a simple arrangement for making out the pay roll: No. Name Ton. Tues. Wed. Thure. Fri. Snt. Tott.1 Tine Rate per hr. Atrount Due 1. A. Brave 8 8 9 8 10 6 49 25* ;12 .25 2. S. Jont* 8 8 9 8 9 9 51 25* 12.75 3. J . Scheldt 9 8 8 9 9 8 35* 4. F. Jensen 9 9 7 8 9 9 35* 5. P. Gregory 8 8 8 8 10 6 40* ft. R. Doreey 7 8 9 9 8 ft 40* 7. S. Stodd*rd 9 9 9 9 10 6 32 8. V. Strlppi 9 9 8 8 9 8 35 9. N. Coetello 8 8 8 8 8 8 30* The amount of time is multiplied by the proper rate per hour for each employee and the various sums placed in the last column showing the amount due. From this pay roll the cashier makes out a memorandum showing the number of each kind of bills and each kind of coin in order to put the exact amount in each employee's envelope, to be handed to him at the close of the week. The following form gives one plan for the cashier's memorandum : Cashier's Memorandum No. 4 6 8 TOIAL 12.7$ 50N) ( OR COLLECTK DRAFTS ... CHECKS .... CURRENCY ' 68 20 13. 65 Q> W TOTAL ... 118 .25 In filling out this deposit slip you must indicate the various items which make up the whole deposit. This is done for the convenience of the re- ceiving teller of the bank who checks the amounts which you have placed on your deposit slip to see if they are correct. If he finds the total correct he places this amount to your credit in a small bank book upon which he writes your name. This bank book should always be taken to the bank when additional deposits are made. Exercise 1 1. Make a deposit slip similar to the form given and fill out the deposit slip for John Smith for the following items: a draft for $50.00; three checks for $7.50, $3.75, and $14.25; and the following amount of money: 2 ten-dollar bills; 7 five- dollar bills; 13 one-dollar bills; 11 half-dollars; 17 quarters; 22 dimes; 31 nickels; 48 pennies. 2. Write a deposit slip for Richard Roe on a deposit slip secured from one of the local banks. Turn in a list of the kinds of money, etc., as shown in Problem 1. (It will be more con- venient for the teacher to secure the blank forms from a bank for class use.) BANKS AND BANKING. CHECKS 201 Checking against Your Account Check books with blanks which can be easily and rapidly filled out are supplied by the banks. They contain stubs from which the checks may be torn. These stubs contain blank spaces for the amount of the check, the number of the check, the date issued, to whom the check was issued, and for what it was written VO.S1S- Stub Check The above illustration shows a check and its corresponding stub properly filled out. Note that the amount of the check in figures is written close to the dollar sign and the amount in words is written at the extreme left end of the line and the space at the right filled in with a line. These precautions should al- ways be taken to prevent any dishonest person from putting in extra figures and prefixing extra words and thus "raising" the amount of the check. The stubs, if properly filled out, form a record of all money paid out and can be used to check the monthly statement of your account which is sent by the bank. The returned checks may serve as receipts for bills paid. Exercise 2 1. To whom was the above check issued? By whom was it written? For what purpose was it issued? 2. Write a check for $25.40 to John Doe and sign your own name. (Secure blank checks from a bank for this work.) 202 EIGHTH YEAR The person who presents the check to the paying teller, to be "cashed," must indorse it. This is done by writing his name on the back of the check, as shown below: 1 If the depositor makes a check payable to himself and indorses it, any one may present it for payment. If he makes it payable to some particular person, that person (called the payee) must indorse it, whether he transfers it to any one else or pre- sents it for payment at the bank. Checks should be presented promptly for payment. When checks are received by a bank for deposit, they are credited as cash, for they are immediately collected from the banks on which they are drawn. 3. If you receive a check made payable to yourself and you lose it before you have indorsed it, can the finder cash it at the bank without forging your name? 4. If you receive a check made payable to yourself and you indorse it and then lose it, can the finder cash it at the bank? 6. If you receive a check made payable to "bearer," can any one cash it at the bank without your indorsement of it? Is it best to make checks in this way? 6. If in sending a check you indorse it with an order to pay a certain person (giving his name), can any other person who finds it cash it? x An indorsement should be on the back of the left end of the check at least one inch from the end. BANKS AND BANKING CHECKS 203 A check so indorsed is said to be "indorsed in full." An Indorsement in Full 7. If you receive a check made payable to yourself, and if, instead of presenting it personally at the bank, you send it to another person with the mere indorsement of your name (which is called an indorsement in blank), and it is lost in transit, can any finder of it cash it? 8. Write a check for a fictitious amount to be paid to John Doe, 1 and sign the name Richard Roe. 9. Write a check for a fictitious amount to be paid to Richard Roe, and sign the name John Doe. 10. Indorse in blank the check written in Problem 8 above. 11. Indorse in full the check in Problem 9, using any other fictitious name. 12. On a check made by John Doe to himself, write an indorsement in full, authorizing payment to Richard Roe. The use of checks renders it easy to pay bills by mail, and in various ways it lessens the risk of loss in the transmission of money. At stated periods, usually at the close of each month, the paid checks are returned by banks to the persons who issued them; and they thus serve as receipts, since they show that the moneys have been paid. ^'John Doe" and "Richard Roe" have been for centuries legal desig- nations for supposititious or unknown personages. 204 EIGHTH YEAR Savings Accounts State banks usually have savings departments in which they pay a small rate of interest (usually 3% or 4%) on savings deposits. One dollar is usually required for opening a savings account. When the interest is due, it is added to the depositor's account and draws interest the same as the original deposits. The following quotation from a savings account book shows their method of computing interest : "Interest will be allowed from the first day of the month following the deposit, except that deposits made up to the 5th of any month shall be considered as being made upon the first day of the month, and will draw interest accordingly. Interest will be computed on the first days of Janu- ary and July of each year on all sums then on deposit, at the rate of three per cent per annum on all savings deposits which have remained on deposit for one month or more, but interest will not be allowed upon fractional parts of a dollar, nor for fractional parts of a month, nor on any sum with- drawn between interest days, for any of the periods which may have elapsed since the preceding interest day. All withdrawals between interest days will be deducted from the first deposit." Woodlawn Trust and Savings Bank. Form of a Savings Account Date Teller Withdrawals Deposits Balance 7/ 2/16 W $100 $100 8/15/16 W 50 150 10/ 1/16 W 30 180 10/30/16 W $20 160 11/26/16 W 10 170 Exercise 3 1. Compute the interest on the above savings account for the interest-paying date Jan. 1, 1917, according to the rules given in the quotation from the Woodlawn Trust and Savings Bank. BANKS AND BANKING INTEREST 20o 2. If there were no deposits or withdrawals between Jan. 1, 1917, and July 1, 1917, what would be the balance on the latter date? Compound Interest If, when due, the simple interest is added to the principal to form a new principal for the next interest period and this process is repeated during all the interest periods of the loan, the difference between the final amount and the original prin- cipal is called compound interest. From the preceding exercise it is seen that savings banks make use of compound interest. The calculation of compound interest for any considerable length of time involves so many steps that it is generally avoided by the use of a Compound Interest Table. The following table shows the amount of one dollar for twenty annual interest periods: TABLE SHOWING AMOUNT OF $1.00 AT COMPOUND INTEREST, EXTENDED TO FIVE DECIMALS FOR EACH OF TWENTY PERIODS FROM 1 TO 7 PER CENT. YEAR 1 PERCENT 2 PERCENT 3 PEBCENT 4 PER CENT 5 PERCENT 6 PER CENT 7 PER CENT 1 1.01000 1.02000 1.03000 1.04000 1.05000 1.06000 1.07000 2 1.02010 1.04040 1.06090 1.08160 1.10250 1 . 12360 1.14490 3 1.03030 1.06121 1.09273 1.12486 1.15763 1.19102 1.22504 4 1.04060 1.08243 1.12551 1.16986 1.21551 1.26248 1.310SO 5 1.05101 1.10408 1.15927 1.21665 1.27628 1.33823 1.40255 6 1.06152 1.12616 1.19405 1.26532 1.34010 1.41852 1.50073 7 1.07213 1 . 14869 1.22987 1.31593 1.40710 1.50363 1.60578 8 1.082S6 1.17166 1.26677 1.36857 1.47746 1 . 59385 1.71819 9 1.09368 1.19509 1.30477 1.42331 1.55133 1.68948 1.83846 10 1.10462 1.21899 1.34392 1.48024 1.62889 1.79085 1.96715 11 1.11567 1.24337 1.38423 1.53945 1.71034 1.89830 2.10485 12 1.12682 1.26824 1.42576 1.60103 1.79586 2.01220 2.25219 13 1.13809 1.29361 1.46853 1.66507 l.ssr.r.f) 2.13293 2.40985 14 1 . 14947 1.31948 1.51259 1.73168 1.97993 2.26090 2.57853 15 1.16097 1.34587 1.55797 1.80094 2.07893 2.39656 2.75903 16 1.17258 1.37279 1.60471 1.87298 2.18287 2.54035 2.95216 17 1.18430 1.40024 1.66285 1.94790 2.29202 2.69277 3.15882 18 1.19615 1.42825 1.70243 2.02582 2.40662 2.85434 3.37993 19 1.20811 1.45681 1 . 75351 2.10685 2.52695 3.02560 3.61653 20 1.22019 1.48595 1.80611 2.19112 2.65330 3.20714 3.86968 206 EIGHTH YEAR The preceding table is made out for annual payments. For semi- annual periods take half the rate for double the number of years. For example: to find the compound amount on $1 at 6% for 10 years compounded semi-annually find the amount in the table for 3% for 20 years. The compound interest is the difference between the com- pound amount and the original principal. Exercise 4 1. Find by the table the compound amount of $1000 at 6% for ten years, payable annually. 2. Find the compound interest of the same. 3. How much greater is this than the simple interest would be? 4. Find by the table the compound amount of $1000 at 6% for ten years, payable semi-annually? 5. How much greater is this than the compound amount of the same principal at the same rate per cent, the interest being paid annually? 6. What is the nearest full year at which the original principal will double itself at compound interest at 6%, payable annually? 7. What is the nearest full year at which the original principal will treble itself at compound interest at 6%, payable annually? Some banks pay 4% interest on savings deposits but usually require that the money be left on deposit at least one year. 8. What will a savings deposit of $100 amount to in 8 years, compounded semi-annually at 4%? See explanation of table at top of the page. 9. Find the amount of a savings deposit of $300 in 10 years, compounded semi-annually at 4%. BANKS AND BANKING. NOTES 207 Borrowing Money at a Bank Since the depositors do not often check out their entire ac- counts or all of them present checks at the same time, banks are only compelled to keep a portion of their deposits on hand and may loan out the remainder. $500.00 3ht)taJ^,JJ& ( h^ for value received. A Bank Promissory Note The above illustration shows one form of a bank promissory note. A bank usually requires the person who borrows the money to get some other responsible person to sign the note with him. If the signer of the note is unable to pay the note, the second person who signed the note as security is held re- sponsible for its payment. Instead of getting another person to go on the note as security, a person may give a mortgage on his property which gives the bank the authority to sell the property in the event that the signer does not pay the note. In this type of note the bank collects the principal with the accrued interest on the date when the note is due. 1. Find the amount due on the above note when it is due. 2. Find the amount due on a note of $1200 for 1 year at 6% interest. 208 EIGHTH YEAR Bank Discount Instead of loaning money on a promissory note bearing inter- est, banks sometimes make out a promissory note without inter- est. They then deduct interest for the given time from the face of the note and the borrower receives the remainder. The money which a borrower actually receives on such a note is called the proceeds of the note. The interest deducted in advance is called bank discount. Bank discount differs from regular interest by being deducted at the beginning of the discount period instead of being added at the date of maturity. Exercise 5 1. What is the bank discount on the above note? 2. What are the proceeds of the above note? 3. Find the bank discount on a note for $450 for 60 days at 6%. Find the proceeds. 4. What is the bank discount on $180 for 30 days if the rate of discount is 6%? 6. If you give a bank your note for $250 for 90 days at, 6% discount, what proceeds will you receive? BANKS AND BANKING. EXCHANGE 209 A promissory note which may be transferred from one per- son to another by being indorsed in called a negotiable note. Banks frequently buy promissory notes from persons who need the money before the notes are due. In such cases banks dis- count the amount of the note at the date of maturity for the time between the date of discount and the date of maturity. 6. A bank bought a note for $300 for 1 year bearing 6% interest. How much money did the owner of the note receive if the period of the discount was 90 days and the rate of the bank discount was 6%? 7. A music dealer sold a phonograph for $275. He received a note for that amount for 1 year at 6% interest. He dis- counted the note at 6% the same day. Find the proceeds. Exchange One of the most important functions of a bank is the payment of debts without the actual transfer of money, through the interchange of checks and drafts. To collect a debt from a debtor in another town or city, the creditor may "draw" on him for the amount due. This is done by sending to a bank in the debtor's home town or city an order to pay the amount. This order is called a draft. Generally the draft is sent to a bank with which the debtor does business. The draft may be made payable to the creditor himself, and sent to the bank for collection, or it may be made payable to the bank itself. The order is addressed directly to the debtor drawn upon, the address being written generally in the lower left corner of the paper. If the debtor is ordered to pay the draft "at sight," the paper is called a sight draft. If the order calls for payment at a stated later time, it is called a time draft. 210 EIGHTH YEAR Sight Draft At sight pay to the order of Vmv for value received^ind charge the same to the account of Time Draft V- jnm sight, pay to the. order of JtoMidu** feu. dM. q tm. V- ............ /- ..... - ............ of ^M^nff.T.SlS^S^ -value If a draft is a time draft, the bank receiving it immediately presents it to the party addressed and if it is satisfactory that party writes his acceptance and the date across the face as shown in the above illustration. A check drawn by one bank upon another is called a "bank draft." It is used largely to avoid the needless transmission of actual money from one city to another. The cashier signs for the bank making the draft and the name of his institution appears at the top of the paper, as on a letterhead, while the name of the bank drawn upon appears below. BANKS AND BANKING DRAFTS 211 A Bank Draft Pay to the order of C.$*l$uA^ in current funds. The banks in large cities have a clearing house where each bank presents checks and drafts which they have cashed for the other banks hi the city and only the balances due are paid in actual currency. Clearing houses in central banking cities provide for the exchange of checks and drafts of banks in different cities. Balances are paid hi clearing house certificates or in actual currency. Where the obligations of the business houses (including banks) of one city to those of another city are pretty evenly balanced by obligations of the latter to the former, there will be no occasion for the transmission of cash from one city to the other for the settlement of the obligations; the obligations of the business houses of the one city will largely cancel those of the other, and this is effected by the use of drafts. If the business houses of St. Louis owe to those of New York a large surplus over the indebtedness of New York to St. Louis, there must be a shipment of money to settle the balance. Be- cause of the desire to avoid the actual shipment of money, bank drafts on New York will be sold in St. Louis at a slight premium; 1 while drafts on St. Louis will be sold in New York at a slight discount. *A premium is an extra amount over the face value. The premium or discount is calculated on the face of the draft. 212 EIGHTH YEAR According to the condition of the money market, drafts may be "at par" or they may "appreciate" or "decline." Exercise 6 1. Write a sight draft, using fictitious names. 2. Write a time draft, using fictitious firms' names. 3. Find the cost of a sight draft for $500 where there is in the money market a premium of f %. 4. Where exchange is at a discount of f %, what will be the cost of a sight draft for $500? 6. What is the cost of a sight draft for $1200 where exchange is at a premium of %? 6. What will be the cost of a sight draft for $625 where exchange is at a discount of ^%? Time Drafts In the case of time drafts, the element of time has to be taken into account. The bank discount for the time specified is deducted from the face of the draft, and the premium, or discount, is then calculated on the face of the draft and added to or subtracted from the remainder. Exercise 7 1. A sixty-day time draft for $300 must be bought where exchange is at premium of -|%. What is the bank discount? 2. What can be obtained for a draft for $400 payable in 90 days from sight, and discounted at the time of its acceptance? What was its cost at a discount of f %? 3. What must I pay for a 60-day sight draft for $600, the premium being j%, discount 6%? 4". What will be the cost of a draft for $1000 payable 60 days after sight, at a premium of ^%, discount 6%? BANKS AND BANKING ' 213 How a Bank Is Organized When a group of men wish to organize a bank, they first decide upon the amount of capital stock which they wish to raise. They then sell shares for $100 each until that amount of capital stock is raised. Then they have a meeting of the owners of the stock and elect a board of directors. In this meeting each person votes in proportion to the number of shares that he owns. The board of directors then elect the officers to conduct the actual business of the bank. Before the bank can open for business a charter must be obtained either from the national government or from the state government. National banks are authorized by the Secretary of the Treas- ury and are inspected by national officers who see that the business is conducted in compliance with the regulations of the National Banking Act. National banks must have a capital of at least $100,000, "except that banks with a capital of not less than $50,000 may, with the approval of the Secretary of the Treasury, be organ- ized in any place the population of which does not exceed 6,000 inhabitants." For the protection of their depositors, National banks are required to keep on reserve at least 12% of their deposits. Experience has shown that this is sufficient to meet the daily withdrawals by depositors. Part of this reserve may be de- posited in certain city reserve banks. Only National and Federal Reserve banks can now issue bank notes which circulate as paper money. Hundreds of years ago men who made a business of borrowing and lending money had benches in the market places of the principal cities and drove bargains with borrowers and lenders. The Italian word banca meant bench and from it we derive our word bank. When one of the old- time bankers failed, his bench was broken. "Bankrupt," meaning broken bench, came to mean a debtor who could not pay. 214 EIGHTH YEAR Issuing Bank Notes National banks are required to keep on deposit with the Secretary of the Treasury at Washington, government bonds equal to one-fourth of their capital stock, as security for their circulating bank notes which they may issue to that amount. If a national bank fails, the government pays the bank notes that the bank has in circulation from the sale of the govern- ment bonds which had been deposited to secure them. The bank notes, then, are accepted by people as readily as the gov- ernment paper money called "greenbacks." Federal Reserve Banks National banks are limited in issuing bank notes to one-fourth of their capital stock. There are times when the business inter- ests of the country demand more money. In order to meet this need Congress established the Federal Reserve banks 1 . These banks can issue bank notes to meet an urgent and temporary need for more money and then withdraw them from circulation after the emergency is past. Federal Reserve banks are to be found in only twelve large cities, viz.: New York, Chicago, Philadelphia, Boston, St. Louis, Cleveland, San Francisco, Minneapolis, Kansas City, Atlanta, Richmond, and Dallas. The national banks are all required to be members of a Fed- eral Reserve bank. A Federal Reserve bank must have a cap- ital of $4,000,000 or more. Anyone may own shares in a Federal Reserve bank, but only a member bank of its district is permitted to own at any one time more than $25,000 of the capital stock of one of these banks. iA Federal Reserve bank is essentially "a banker's bank." It sus- tains with its members much the same relation that ordinary banks sustain with their depositors. BANKS AND BANKING 215 Exercise 8 1. If a capitalist owns the maximum amount permitted in a Federal Reserve bank in each of the cities named, what is the par value of his investment? 2. What was the minimum capital required for the be- ginning of business by the 12 Federal Reserve banks? 3. The shares of stock of a Federal Reserve bank are of the par value of $100 each. How many shares are required to be taken, to amount to the minimum sum required for beginning the business of the bank? 4. Three state banks and two business houses each purchase the maximum permitted amount of stock in a Federal Reserve bank. What is the amount of their stock in it? 6. If a certain Federal Reserve bank has a capital of $20,000,000 and yields profits of 6% annually on the capital stock, what will be the amount of the profits that may be dis- tributed in one year? State banks are organized under state laws and are inspected by state officers. A smaller amount of capital stock is usually required for their organization than for a national bank. Trust companies, organized under state laws, not only con- duct a banking business but also settle estates, take care of property of minors (persons under legal age), and perform various other services not permitted in state or national banks. In some states certain individuals or partnerships call their offices "private banks," although they possess no bank charters and are not subject to any official inspection. There is a grow- ing demand that these banks be placed under regular state in- spection to protect their depositors. Make a study of the various kinds of banks in your com- munity, noting the amounts of their capital stock, total depos- its, etc. 216 EIGHTH YEAR STOCKS AND BONDS Stocks To a very great extent the business of the country is now conducted by corporate companies, called corporations. A corporation is regarded in law as an artificial person created by law for specified purposes and having specified powers. The capital stock of a corporation is divided into shares generally having a face or par value of $100 each and are usually spoken of as stocks. A corporation with a capital stock of $50,000 has 500 shares of $100 each which have been sold to different individuals. All who own any of the stock of a corporation are members of it and have votes in it in proportion to the number of shares of stock which they possess. If the corporation is large and its members widely scattered, the members elect a Board of Directors to manage the affairs of the corporation. The advantages of corporations are: (1) They enable a large amount of money to be collected from small investors who would not be able to invest this money profitably in small amounts. (2) The stockholders of a corporation are subject to a limited liability (usually the money invested in the stock) in the case of failure in the business of the corporation. In a partnership or an unincorporated company each person must stand responsible for the debts of the firm and even his private property can be taken to pay the debts of the firm. The certificates of stock issued to the members of a corporation state the numbers of shares held, the face value of each and how the stock may be transferred. The following reproduction illustrates the form of a stock certificate: STOCKS AND BONDS STOCKS 217 Kegal Hat Corapanj Stock certificates vary somewhat in statement, but the Common Stock Certificates are usually in the general form here illustrated. Exercise 9 1. What is the par value of each share of stock? 2. How many shares of stock are there in this company? 3. In what state was this company incorporated? 4. How may the stocks in this company be transferred? A dividend is a sum received for each share when all or a portion of the profits of a corporation are distributed to the shareholders. 5. If the dividends of the Regal Hat Company were $5000, how much of a dividend would be paid on each of the 500 shares? 218 EIGHTH YEAR 6. The dividend of $10 on each share would be what per cent of the par value of each share? 7. Will investors be anxious to buy stock that is paying 10% dividends when money usually only yields 6% interest? In order to secure stock which pays a high dividend, investors will pay more than the par value of the stock. They may pay $150 for a share of stock whose par value is only $100. Such stock would be quoted as worth 150 in the newspaper report of the stock exchange. The following were among the items in the report of a daily paper on the New York Stock Exchange for Nov. 11, 1916: Sales High Low Close Net Change 1. Am. B. Sugar 2900 102^ 10l lOlf -| 2. Am. Exp 200 139^ 136 139^ 3j 3. Am. Wool 1000 53 52| 53 4. do. 1 pf 100 98 98 98 5. Beth. Steel 200 670 665 665 - 10 6. do. pf 600 152 149 152 We see from the above sales that stocks in items 1, 2, 5 and 6 are selling above par. Hence those companies must be paying good dividends to the investors. Items 3 and 4 show those stocks were sold below par. What are the net changes in each kind of stock since the preceding day? 8. Bring to the class for study extracts of the stock quo- tations in the daily paper showing a table similar to the above table. Large corporations sometimes issue stock of two kinds or classes, common and preferred stock. The preferred stock guarantees that all dividends up to a certain per cent of the par value must first be divided among the holders of the pre- ferred stock. If there are any profits left, they are distributed among the holders of the common stock. x The expression do. in the above table means the same as the preceding item and thus is a short way of expressing Am. Wool again. STOCKS AND BONDS STOCKS 219 The stock quotations given in the preceding table show that the preferred stock in Item 4 is more valuable than the common stock in Item 3. That corporation then is not doing a profitable enough business to enable sufficient dividends to be paid regularly to the common stock holders. In Item 6 of the table, the common stock is selling at $670 per share. This extremely high price was caused by unusually large profits coming from the manufacture of munitions for use in the European War. The excess profits were divided as shown above among the common stock holders, thus making their stock much more valuable than the preferred stock in that company. The amount a broker receives for buying and selling stock is called brokerage. In buying and selling stocks the brokerage is generally 5% of the par value of the stocks. When stocks are bought, the brokerage is added to the market price to find the total cost. When stocks are sold, the brokerage is taken from the selling price to find the proceeds due the owner of the stock. If the class can secure data from some local corporation, a study of the organization of this local company will prove a valuable exercise. Exercise 10 1. If a gas and electric company, incorporated, pays quarterly dividends, two of them being 3% and two of them 2%, what income is derived annually from 10 shares, of $100 each? 2. What will be the cost of 100 shares of stock of a certain railway (par value $100) if you buy them at 125% and pay 5% brokerage? Solution: 125%+i% = 125j%. 125j%X$100 = $125.125, cost of 1 share. 100 X $125. 125 = $12.512.50, cost of 100 shares. 220 EIGHTH YEAR 3. A broker sells 200 shares ot American Express stock at 139 |-%, brokerage \%. Find the amount of the proceeds which he sends the previous owner of the stocks. Solution : 139 J% - J% = 139 J%, proceeds from 1 share. 139 J%X $100 = $139.125, proceeds from 1 share. 200X139. 125 = $27,825.00, proceeds from 200 shares. 4. A broker sells 500 shares of American Wool preferred at 98, brokerage \%. What is the amount of the proceeds which he sends his principal? 5. If money is worth 5%, what must be the dividends from one share of the Bethlehem Common Steel in order for it to sell for 670? What per cent of the par value is this? Solution: 5% X $670 = $33.50, amount of dividends on one share. $33.50 = X%X $100. = .335 or 33.5%, per cent of par value. 6. If money is worth 5%, what will be the market quotation for stocks of good security paying an annual dividend of $9.00 per share? $9.00 is 5% of what value? 7. If the common stock of a great steel manufacturing corporation is sold at 72% (par value $100 per share), what will be the cost of 300 shares, including brokerage at ^%? 8. If the preferred stock (par value $100 per share) of a certain coal mining corporation sells at 115%, what will be the cost of 10 shares of it, including the brokerage of \ %? 9. What profit is made by purchasing 100 shares ($100 each) of stock of a certain railway at 97% and selling them at 107%, paying \ % brokerage for each transaction? 10. How much stock of a certain street car company, incor- porated, must be purchased to insure an income of $600 from it if the stock pays semi-annual dividends of 4%? STOCKS AND BONDS BONDS 221 Bonds While corporate companies usually provide the necessary capital for the conduct of their business, through the sale of stock certificates, they may also provide for additional capital by the sale of bonds, which are generally secured by the tangible property of the corporation, and the bonds become the first lien on the business. In case of default in the payment when due, either of the accrued interest or of the principal, the holders of the bonds are in most instances legally empowered to sell the property of the corporation issuing the bonds, and to re-imburse them- selves from the proceeds. Bonds bear a fixed rate of interest, while the stock proceeds are governed by the earning power of the business. Bonds issued by the Federal government, by a state or by a county must be previously authorized by legislation, or by a direct vote of the people, who become the guarantors. On page 222 is given an illustration of a typical city bond. In addition to the signature of the proper executive officers, all stocks and bonds must have affixed to them the seal of the government, the state, the county or the business corporation issuing them. Facsimile of the Seal of the State of New York, reduced to about % of the usable sise. Facsimile of the great Seal of the United States, re- duced to about }> of the usable size. Facsimile of the Seal used by a business corporation, reduced to about % of the usable sice. 222 EIGHTH YEAR ' STOCKS AND BONDS BONDS 223 Detachable interest coupons, or small dated certificates, are generally issued with and as a part of each bond. These are to be separated from the bonds and presented for payment on the dates named upon them. 1 Bonds, like stock certificates, necessarily vary more or less in statement. The illustration on the preceding page shows the general form of a corporation bond, and the illustrations on this page the general form of the detachable coupons. These coupons are usually transferable, being deemed equivalent to cash, and are collectible by any person holding them. Bonds without coupons are called registered bonds, and their transfer from one holder to another must be recorded upon the books of the corporation issuing them. What are the advantages of registered bonds in case of theft? Exercise 11 1. A village issues corporation bonds to the amount of $40,000 to build a school house. The bonds bear 5^% interest. What is the amount of interest paid to the bondholders in one year? 2. If a man receives $480 for the coupons of his bonds, bearing 6%, what amount of the bonds does he hold? 1 The coupons attached to a bond are numbered from right to left, or from the bottom up. In this way they may be detached in the order of number and date. For the bond here illustrated thirty-nine coupons are required one for each semi-annual interest payment from January, 1915, to January, 1934 covering a period of 20 years. 224 EIGHTH YEAR 3. In order to secure an income of $1200 annually, how many bonds of the denomination of $100, bearing 6% interest, must I buy? 4. A bank buys 50 U. S. bonds of the denomination of $1000, paying for them a premium of 3 j% and a brokerage fee of f %. What do the bonds cost the bank? 6. How much must be paid for the Gas and Electric Com- pany bonds of a certain city, at a premium of 3%, the brokerage being J$%? 6. If I paid $3200 for bonds of the face value of $4000 and receive 5% interest on the face of the bonds, what do I receive in a year, and what per cent do I receive on my invest- ment? 7. Which is the better investment, a 5% bond bought at $92 for $100 face value, or a 6% bond bought at par? Suggestion: $5 is what per cent of $92? 8. What must be paid for 5% bonds in order to receive an income of 6% on my investment? Suggestion: $5 is 6% of what amount? 9. An American business corporation operating a rubber plantation in Mexico issues bonds for $60,000, payable in 15 years. If they are sold at $93 for $100 of par value, what is realized from them when 80% of the issue is "taken," or sold? 10. Find out what bonds have been issued in your commu- nity. For what amounts were they issued? What rates of interest do they bear? 11. If a commercial corporation issues bonds to the amount of $60,000 to run eight years at 7%, and after paying interest for five years fails, and after a year of delay pays only 78% of the face of the bonds, what does the holder of each $100 bond receive in all? INVESTMENTS 225 12. What would he have received on a 6% bond for the full period? 13. To secure an income of 8%, how much below par must I buy bonds bearing 6%? The organization of an imaginary corporation or a study of seme local corporation by the class would prove an excellent means of understanding stocks and bonds. If the time permits, fche class should undertake such a problem. INVESTMENTS The supply or amount of money on hand, together with the demand for loans, determines, to a large extent, the rate of interest which must be paid to secure a loan. If the supply of ready money is large and the demand for loans is weak, the rate of interest will be low. On the other hand, if the supply of ready money is small and there is a large demand for loans, the rate of interest will be high. The risk involved in a loan is also an important factor in determining differences in the rates of loans. If the risk of loss is great, a high rate must be paid to secure a loan. If there is very slight chance of any loss, the rate of interest is low. Many new enterprises are started in the United States every year. Some of these enterprises are successful and yield large dividends. On the other hand, a large per cent of these enter- prises fail and the investors suffer either a partial or a total loss. One should never take only the agent's word as to the safety of an investment, but should consult some reliable disinterested party who is well posted in the field of investments, such as a reliable banker or broker. The policy of "Safety First" is a very good one to follow in the field of investments. 226 EIGHTH YEAR Exercise 12 1. Before the World War, government bonds sold at par value when the rate of interest was as low as 2%. The rates of interest on Liberty Bonds varied from 3f % to 4f %. Find out whether these bonds are now selling above or below par. 2. Municipal bonds usually bear from 4% to 5% interest. Why is the rate higher on these bonds than on U. S. Govern- ment bonds? 3. What is the usual rate that is paid on certificates of deposit or safety deposits in a bank? 4. Why are careful investments in real estate considered good investments? What are some disadvantages of such investments? 5. A certain company advertised that they would give 2 shares of common stock free with each share of preferred stock purchased before a certain date and claimed that both kinds of stock should soon be worth more than par. Would you invest in this stock? Why? 6.. Another company advertises a certain sugar stock that will pay 10% on the investment. How would the risk on this investment compare with a good municipal bond yielding 5% interest? 7. The following advertisement appeared in a daily paper: "Absolutely safe, exceptionally profitable, long-time invest- ment; 1 as good security as municipal bonds, with five times the returns." As an investor, how would that advertisement appeal to you? 8. An agent for a certain mining company was selling stock at about ^ of the par value. He stated to a prospective buyer that he would guarantee that the value of the stock -would 'Teachers should show that the investment could not yield five times the returns if the security was as good as municipal bonds. INVESTMENTS 227 double in less than 6 months. Would you have bought this stock on the strength of the agent's statement? 9. An insurance company loaned a farmer $3000, taking a first mortgage 1 on his farm valued at $5800. Was this a safe investment for the insurance company? 10. If you had $20,000 to invest, would you invest it in one place or divide it among several forms of investment? Discuss the advantages and disadvantages of both of these methods. Exercise 13 1. A girl deposited $75 in a State bank, receiving a certifi- cate of deposit, bearing 3% interest. How much interest should she receive at the end of 6 months? 2. How much interest would she have received in a Postal Savings bank for 6 months at 2%? Was her risk of losing her money any greater in the State bank than it would have been in the postal savings bank? 3. If I buy a municipal bond bearing 4^% interest for $106.50, including brokerage, what is the rate of income on my investment? Suggestion: $4.50 is what % of $106.50? 4. What is the rate of income on stock costing $138.50, including brokerage, if the yearly dividend amounts to $6.50 per share? 5. In deciding which is the better investment, a municipal bond bearing 4^% interest, quoted at 106f , or a stock quoted at 138 1 and known at that time to be yielding yearly dividends of $6.50 per share, what other factors must be considered besides the present rate of income? 'A mortgage is a contract by which the owner of the property agrees to let the party loaning the money sell his property to secure payment for a loan if he fails to meet the terms stated in the contract. 228 EIGHTH YEAR 6. A man wishes to buy a city residence. It rents for per month, and he estimates that his expenses for this property would amount to $240 a year. How much can he offer for the property if he wishes to secure an income of 6% on his invest- ment? 7. A carpenter in a certain village bought a house for $1875. After spending $400 on improvements, he sold the property for $2850. Find his per cent of gain on the money invested. 8. An 80-acre farm sold for $4000 in 1900. In 1903 the same farm was sold for $4800. In 1915 it was sold for $9000. Find the per cent of increase in its value between 1900 and 1903; between 1903 and 1915. What other returns were secured by the owners beside the increase in the value of the land? 9. Mr. Bentley inherited $5000 from his father. He has an opportunity to loan it to a farmer at 5% on a first mortgage on a farm valued at $12,000 or invest it in a pecan grove which an agent assures him will yield 10%. His banker tells him the latter investment is very risky. Which should he take? 10. An agent of a mining company canvassed the citizens of a small village to sell mining stock. He told them that the company wanted to keep the stock from getting into the hands of rich capitalists. Would this statement have induced you to buy or deterred you from investing in the stock? 11. A company invests $12,000 in "stump lands," from which the pine timber has been removed, and $3000 in machinery to uproot and pulverize the stumps, for the extraction of turpentine. The annual profit is 15% on the investment, for four years, at the end of which time the land has doubled in value, and the machinery is sold for half the cost price. What is the real per cent of annual profit? 12. Does it pay to invest money in an education? See if you can get figures to prove your answer to that question? BANKS AND BANKING. REVIEW 229 Exercise 14 1. State 5 services that banks perform for us. 2. Tell how to open an account at a bank. 3. How can you withdraw money which you have on deposit at a bank? 4. What special precautions should be taken in filling out a check? 6. Show two ways in which a check may be indorsed. What are these kinds of indorsement called? 6. What should you do in the event that you lose a check made out to you? 7. What are the advantages of paying bills by checks? 8. What are the interest rules in your local savings banks? How do they differ from those given on page 204? 9. What is bank discount? 10. Find the bank discount for 90 days on a note for $350 for 1 year, bearing 7% interest. The discount rate is 6%. 11. What is a draft? Name and describe two kinds of drafts. 12. What is a clearing house for the banking system? 13. Find the cost of a draft for $2000 when money is at a premium of ^%. 14. Tell how a bank is organized. 16. Give an account of the origin of the term, bankrupt. 16. What is the minimum amount of capital stock that is necessary for the organization of a national bank? 17. What was the purpose of the organization of our Federal Reserve banks? 18. What is the minimum amount of capital stock that is required for a Federal Reserve bank? 19. Why are national bank notes as good as government "greenbacks"? 230 EIGHTH YEAR Exercise 15 1. What is a corporation? 2. What is the usual par value of the shares of a corporation? 3. Why do most men prefer to organize as a corporation than as a partnership? 4. What is a dividend? What is brokerage? 5. What is the difference between common and preferred stock? 6. Find the cost of 50 shares of stock bought at 104j, brokerage f %. 7. Find the amount of the proceeds which the owner of the 50 shares of stock (mentioned in the preceding problem) would receive, brokerage \%. 8. What is the difference between the stock certificates and the bonds of a corporation? 9. What is a coupon bond? A registered bond? Which is the easiest to transfer to another party? Which is safest from danger of theft? 10. What are the chief factors which determine the rate of interest which must be paid to secure a loan? 11. What are the safest forms of investment? 12. An owner of a cottage offered it for 29 one-hundred dollar bonds which were then selling at 91. What was the value which he placed on his cottage, making no allowance for bro- kerage? 13. What is a mortgage? 14. A firm with a capital stock of $20,000,000 declared an annual dividend of 8% on its stock. What was the total amount of the dividends? How much would a man receive who owned 75 shares of this stock? 16. Find the cost of five Liberty 3^% Bonds at their quota- tion in today's paper, brokerage 5%. CHAPTER III REMITTING MONEY On account of the heavy expense of shipping actual money, much of the business of the country is carried on by means of commercial forms of various kinds. Postal Money Order One of the most common forms for sending small amounts of money is the postal money order. The government charges a small fee for these orders, varying with the amount of the order. United States Postal Honey Order |8iioo" A/lflele * >CaL "" Coupon for Paying Office ran MOK TNjgi LA | mOICATKO ON UP The following table shows the fees for the various amounts: Not exceeding $2.50 %t Exceeding $ 2.50 and not exceeding $ 5.00 5f Exceeding 5.00 and not exceeding 10.00 8f Exceeding 10.00 and not exceeding 20.00 10 Exceeding 20.00 and not exceeding 30.00 12^ Exceeding 30.00 and not exceeding 40.00 15ff Exceeding 40.00 and not exceeding 50.00 18j Exceeding 50.00 and not exceeding 60.00 Exceeding 60.00 and not exceeding 75.00 Exceeding 75.00 and not exceeding 100.00 231 232 EIGHTH YEAR Actual money may be sent by registered mail for a charge of 10 cents in addition to the regular postage. An indemnity not to exceed $25.00 will be paid by the government if a first- class package or letter is lost. Exercise 1 1. How much will money orders for the following sums cost: $2.50; $15.00; $30.00; $52.14; $7.25; $75.00? 2. Which will be cheaper, to send $25 in a letter by regis- tered mail or to buy a postal money order for $25? (The postage on the letter is extra in both cases.) 3. Which is cheaper, sending $10 by registered mail or sending a postal money order for $10? 4. What is the fee on a postal money order for $5.00; for $50.00; for $100.00? Express Money Orders Express companies issue express money orders which are similar in form to the postal money order and for which the same fees are charged. The table on page 231 may also be used in computing charges on express money orders. WHEN COUNTERSIGNED 15. 0000000 15-0000000 An Express Money Order REMITTING MONEY DRAFTS 233 Exercise 2 1. Who purchased the express money order here shown? 2. To whom is this order made payable? 3. How could Mr. Brooks transfer this order to some other person for collection? 4. How much will an express money order for $18.75 cost? 6. How much will an express money order for $50 cost? Bank Drafts A bank draft is really a check by one bank on another bank. For regular patrons of the bank who have checking accounts, most banks write drafts for small amounts without extra charge as a matter of accommodation. For large amounts drafts are sold at a premium or a discount, depending on the state of the balance between the banks of the two cities involved. A Bank Draft Exercise 3 1. Where was the above draft purchased? 2. To whom was it made payable? 3. How can it be transferred to some other person? 234 EIGHTH YEAR 4. On what bank is the draft drawn? 5. A farmer wishes to pay off the mortgage on his farm that is held by a certain insurance company. He finds that the rate for a draft on the city where the insurance company is located is 20 cents per $100. Find the cost of the draft for $3000. 6. How much would an express money order for the same amount have cost him? Checks Business firms and most individuals have checking accounts in some bank. Instead of buying drafts, most firms send checks to settle their accounts. A check is returned by the local bank to the firm who issues it when the account is bal- anced. The check thus serves as a receipt for the transaction. 5-39 ^~Si-^W/^ri A Business Firm's Check Exercise 4 1. What firm issued the above check? In what bank do they carry their banking account? 2. To whom is this check made payable? 3. When the check is returned to the First National Bank of Boston for collection, how will they-enter it on their accounts? REMITTING MONEY CHECKS 235 A Personal Check 4. Who issued the above personal check? To whom is it made payable? Show how this check would have to be indorsed when it is cashed. (See page 190.) 6. If a certain man has a balance of $125.82 in the bank on Jan. 1, 1917, and issues three checks as follows: for rent, $35.00; for light bill, $1.58; for gas bill, $2.56; how much will he have to his credit in the bank? 6. Mr. Hill issues Mr. Johnson a check for $25.00 to pay for services rendered. Mr. Johnson loses the check and promptly notifies Mr. Hill of his loss. How can Mr. Hill arrange to pay Mr. Johnson without danger of having to pay twice should the check be found at a later date? 7. Why do banks refuse to cash checks for strangers? 8. Discuss the advantages and disadvantages of remitting money by means of checks. Foreign Remittances Remittances to foreign countries may be made by inter- national money orders, by foreign express orders or by foreign drafts called bilk o/ exchange. 236 EIGHTH YEAR Emergency Remittances When an agent wishes money immediately in order to close an important transaction, he often finds it an advantage to have his firm telegraph him the money. In the telegram in the illus- TKE WESTERN UNION TELEGRAPH COMPANY" tration Richard Doe of Wash- ington is sending his brother , Doe m New Orleans a . Trgent ^. ^ certain sum of money by tele- jjr (LJ+tta^Lt; _ a sj> ^ sj *, *,, graph. In order to prevent S&trt. #t.e. l^fe^At. five. TL^el^a^il . , others from learning about the amount of money involved in the transaction, the message is expressed in terms of a code. _. , . The word ring in the telegram refers to the amount of money and can be understood only by a person familiar with that particular code. Note the writing in the last line. It was made by the sending agent with his left hand while he was transmitting the message with his right hand, showing a high degree of efficiency in operation. Upon the receipt of this message, the agent in New Orleans sends to John Doe the following notice: "We have received a telegraphic order to pay you a sum of money upon satisfactory evidence of identity. The amount will be paid at our office if called for within 72 hours; other- wise under our arrangement with the remitter the order will be canceled and the amount thereof refunded." When money is remitted by telegraph, there is a transfer charge on the money in addition to the regular charge for the telegram which is computed on the basis of a 15- word message. Exercise 5 1. In remitting $25 (or less) by telegraph between certain cities, the charge for that amount is 60 cents. The telegraph charges between these cities is 35 cents for a 15- word message. Find the transfer charge for that amount. REMITTING MONEY BY CABLE 237 2. What would be the cost of remitting $25 by an express money order? How much cheaper is the express money order than the remittance by telegraph given in Problem 1? When is money usually remitted by telegraph? 3. The cost of a 15- word message between two cities is 35 cents. What will be the total charges for remitting $100 by telegraph if the transfer charges for the money are 85 cents per $100? 4. The charges for remitting $200 by telegraph between those cities are $1.45. How much is charged for the extra $100? At the same rate per $100 beyond the first $100, what will be the charges on remitting $1000 between those cities? Remitting by Cable If an emergency arises for a quick transmission of money to a firm or person in a foreign country, money can be remitted by cable in the same manner that it is telegraphed in this country. The amount of the money is then expressed in the money values of the foreign country to which it is sent. The following illustration shows a form for such a cablegram: In the cablegram shown in the illustration "Bruzzolo, Lon- don" stands for the registered address of the London telegraph office that pays the money. "Rabbit" is a guard word neces- sary in sending such messages. "Jewel" is the code word for "pay to." "John Doe, 76 Downing Street, London" is the payee. "Bracket" is a code word which stands for the , ^n.-^- j^, JL >. j^.j^ ^^^1,^-- amount to be paid John Doe. "Darby" means "from." "Richard Roe" is the name of the sender of the money and "Jentant" is the code word standing for the signature of the transfer agent at New York. 238 EIGHTH YEAR Exercise 6 The charges on sending money by cablegram are $4.65 for the cable charges (15 words) and 1% premium on the amount of money sent. 1. Find the total amount that must be paid the agent in New York to remit $100 to a party in London. 2. What will be the transfer charges on remitting $500 by cable? Find the total amount which must be paid the transfer agent in this country. 3. If the word "Bracket" stands for $250, how much did Richard Roe have to pay the transfer agent in New York? 4. Find the total transfer charges by cable on $300, on $1000, on $5000. Remitting Money by Wireless To facilitate business, leading banks and express companies, in normal times, keep large amounts of money on deposit at the principal commercial centers in the European countries. During the period of the European War communication with . _. . certain countries in Europe was maintained Fort DeaAorn mostly by radio means, and the transmission of money by "wireless" reached large pro- MONEY REMITTED BY WIRELESS TO Germany and Austria-Hungary K.,... **.* < , M* 43M portions at rates indicated in the following problem: Exercise 7 1. A firm in Chicago remitted $1000 by a wireless radiogram to a firm in Berlin on Jan. 28, 1917. The charges were quoted by the bank at $4.00 per order of 6 words, plus the usual postal charges of 15 cents per order, excess words to be paid at the rate of 57 cents per word. If the radiogram contained 9 words, what were the charges on the radiogram? CHAPTER IV PRACTICAL MEASUREMENTS Exercise 1. Review of Quadrilaterals 1. State the principle for finding the area of a rectangle. 2. What is the area of a rectangle 16 inches long and 8f inches wide? (See page 137.) 3. Find the number of square yards in the area of a baseball diamond which is 90 feet square. 4. How many square inches are there in a sheet of paper 8^ inches by 11 inches? How many square feet of space would a ream of 500 sheets of this paper cover if the sheets were placed edge to edge? 6. How many square feet are there in a rectangular garden 15 yards long and 30 feet wide? How many square yards? 6. A certain farm is 1^ miles long and f of a mile wide. How many square rods does it contain? How many acres? 7. A field 60 rods long and 40 rods wide yielded 360 bushels of wheat. What was the yield per acre? 8. There are usually 40 apple trees planted on an acre of ground. How many square feet of space does that allow for each tree? 9. A ball club bought a field for a ball park. It was 400 feet long and 395 feet wide. How much did it cost at $310 an acre? 10. School architects usually allow 16 square feet of space as the proper amount for each pupil. How many pupils can be properly seated in a school room 24' x 28'? 239 240 EIGHTH YEAR 11. How many pupils are there in your school room? Find the number of square feet of floor space for each pupil, using the total area of the room for the computation. 12. The area of a rectangle is 96 square inches and the base is 16 inches. Find the altitude. 13. The area of a rectangle is -fa of a square foot. The width is f of a foot. What is the length? 14. Find the area of a parallelogram with a base of 18 inches and an altitude of 12 inches. (See page 142.) 15. The length of a parallelogram is f of a foot and the alti- tude is f of a foot. What is its area? 16. Find the area of a trapezoid with its parallel sides equal to 8 inches and 15 inches and its altitude equal to 12 inches. (See page 144.) 17. Two converging roads form a field in the shape of a trapezoid. The two parallel sides are 60 rods and 100 rods and the altitude is 64 rods. How many acres are there in this field? 18. How much is this tract of land worth at $175 an acre? Exercise 2. Review of Triangles 1. State the principle for finding the area of any triangle. 2. What is the area of a triangle whose base is 8 inches and whose altitude is 7 inches? (See page 146.) 3. The area of a triangle is 54 square inches and the altitude is 9 inches. Find the base. 4. The area of a triangle is \ of a square foot and the base is f of a foot. Find the altitude. 6. A triangular flower bed has a base of 3 yards and an altitude of 4 yards. Find its area in square yards. PRACTICAL MEASUREMENTS SQUARES 241 Squares and Square Roots A square is a rectangle with all of its sides equal. What kind of angles has a square? If a side of a square is 4, the base and altitude are each 4, and the area of the square is 4X4, or 16. A Sed 1 brick thick? (A brick is 8 inches long.) 6. A farmer builds a circular barn having a diameter of 40 feet. What is the length of the circumference of the barn? 7. The Equator of the earth is approximately 25,000 miles. What is the equatorial diameter of the earth? 8. How much fringe is needed to trim the edge of a circular lamp shade 14 inches in diameter? PRACTICAL MEASUREMENTS SHOP PROBLEMS 255 9. How long a piece of tatting would it take to edge the cuffs of a girl's sleeves if the cuffs are 2f inches in diameter? 10. A farmer's roller is 32 inches in diameter. How many revolutions will the roller make in rolling a corn row a quarter of a mile long? 11. A bicycle has wheels 28 inches in diameter, outside measurement. How many revolutions will each wheel make in going a mile? 12. A circular wading pool 40 feet in diameter has a concrete side walk 3 feet wide extending around the border. How much longer is the outside circumference of this walk than the inside circumference? Exercise 10 1. The trough of a pen tray is 2 inches wide. How wide apart must I set the points of my compass in order to draw the semi-circle at each end? 2. If the board is 2f inches wide and the end of the trough is to be ^ inch from the end, locate the point for the center of the semi-circle at each end. 3. A boy in the forge shop wishes to make a ring 8 inches in diameter out of f -inch stock. Allowing 3 times the diameter of the rod for extra in welding, how long must he cut the piece of stock to make this ring? 4. How long must a rod be cut out of f -inch stock to make a ring 18 inches, inside diameter? Make allowance for welding. 5. A grindstone 36 inches in diameter makes 40 revolutions per minute. What is the cutting speed in feet per minute of this stone? (Find the number of feet of the circumference that will pass under the edge of a tool in 1 minute.) 256 EIGHTH YEAR 6. Another grindstone in the shop is only 24 inches in diameter. How many revolutions per minute must it make to have the same cutting speed as the grindstone described in Problem 5? 7. A pulley on a countershaft in a shop is 14 inches in diameter. How many inches of belt will pass over this pulley in one revolution? 8. The pulley on a wood lathe is 6 inches in diameter. How many inches of belt will pass over this pulley in one revolution? 9. How many revolutions will the lathe pulley make for one revolution of the pulley on the countershaft? 10. If the speed of the countershaft is 720 revolutions per minute, what is the speed of the lathe? 11. If you have a shop in your school, visit it and make other problems similar to the ones given above Area of Circles When a circle is cut into pieces as shown in this i llust ration, the pieces are al- most triangular in shape, the bases being slightly The circle divided into triangles curved. If we arrange these triangles in a row with half of the triangles pointing up and half of them filling in the spaces between as shown in the diagram on the next page, we should have approximately a parallelogram: PRACTICAL MEASUREMENTS CIRCLES 257 The base of this parallelogram is what part of the circumference of the circle? The altitude of the parallelogram is the same as the radius of the circle. Since the base of the parallelogram = \ of the circumference of the circle (which = 27rr), the base of the parallelogram = XT. The area of the parallelogram = base X altitude or 7rrXr = 7rr 2 . But the area of the circle is the same as the area of the parallelogram. Therefore the area of a circle = Trr 2 . PRINCIPLE: The area of a circle is equal to the square of the radius multiplied by 7T. Exercise 11 1. Find the area of a circle 8 inches in diameter. Solution: Radius of circle 8 inches in diameter =4 inches. Area of circle =-7^ = 3.1416X16 = 50.2656. Therefore the area of the circle = 50.2656 square inches. 2. What is the area of a circle with a radius of 8 inches? 3. Find the area of a circle 3 feet in diameter? 4. Find the area of the 8-inch circle in the diagram at the left. Find the area of the 12-inch circle. Find the area of the ring. 6. A cow is tethered to a stake in a grass field by a rope 100 feet long attached to one of its fore feet. What is the area in- cluded within the sweep of the rope around the stake? 6. If the rope be attached to one of the hind feet of the cow, giving the animal a reach of five feet more from the stake, how much additional area will she have to graze over? 258 EIGHTH YEAR 7. A circular lake three miles in diameter is drained until it is only two miles in diameter. What area has been reclaimed by the receding of the water? Draw diagram. 8. By irrigation from a central artesian well, with radiating ditches extending half a mile in each direction, a circular area of arid land has been reclaimed. How many acres does it contain? Draw diagram. 9. If the radiating ditches be extended to twice their length, what will be the gain in irrigated area? Draw diagram. 10. Bottles two inches in diameter are packed in a box one foot square, inside measure. How much of the area of the bottom of the box is covered by the bottles? Would this be the same if there were but one bottle, and if it were one foot In diameter? Draw diagram. 11. A certain revolving searchlight illuminates the land to a distance of five miles. What area is included in the circle of its illumination? 12. A farmer builds a circular barn having a diameter of 40 feet. Its circular wall will have 3.1416 times the length of the diameter. What will be the length of it? Suppose this length of wall were used to enclose a square. What would be the length of one of the sides? What would then be the area of the barn? 13. What is the area of the circular barn? What is the gain in area from having the barn circular in form? 14. A concrete side walk 3 feet wide surrounds a circular fountain 15 feet in diameter. How many square feet are there in the surface of the walk? 15. How many 3-inch circles for jelly glass lids can be cut from a rectangular piece of tin 24 inches wide and 36 inches long? How many square inches are left in the waste pieces? Have pupils bring to class other practical problems on circles. PRACTICAL MEASUREMENTS CIRCLES 259 16. The square in the figure at the right is said to be circum- scribed about the circle. The circle is said to be inscribed in the square. If the side of the square is 12 inches, what is the area of the square? What is the area of the inscribed circle? 17. Divide the area of the inscribed circle by the area of the square. If your work is accurate, the result should be .7854. That is, the area of a circle is .7854 of a square with a side equal to the diameter. 18. From this fact we get the rule: To find the area of a circle multiply the square of the diameter by .7854. 19. Find the areas of circles 6 inches, 8 inches and 12 inches in diameter by this rule. Exercise 12. Review of Circles 1. How many square feet are there in the area of a circular flower bed 7 feet in diameter? 2. Two girls made a set of doilies consisting of a center- piece 18 inches in diameter and 6 small doilies 5 inches in diameter. How many inches of crochet edging did they have to make to trim all the doilies in that manner? 3. How many square inches of muslin were wasted in the squares from which the doilies were cut? 4. Find the area of a circle 3 inches in diameter. Find the area of a circle 6 niches in diameter. The area of the second circle is how many times the area of the first circle? 5. In a 4-inch steam pipe the iron is j of an inch thick. Find the area of the opening in the pipe. 6. Find the area of a circular flower bed 8 feet in diameter. Find its circumference. 260 EIGHTH YEAR 7. The cold air inlet for a furnace should have the same area as the sum of the areas of the hot air pipes. If there are six 6-inch hot air pipes leading from the furnace, what should be the area of the cold air inlet? 8. If the cold air inlet is rectangular in shape and has a length of 15 inches, what should be its width to furnish sufficient air for the six furnace pipes? 9. A circular asbestos pad is 7\ inches in diameter. How many of these pads can be made from a piece of asbestos padding 30 inches square? Draw a diagram to show the arrangement of the circles. 10. How many square inches of waste material would be left in cutting out these circular pads from the 30-inch square? Hexagons A regular hexagon is a six-sided figure with equal sides and equal angles. A regular hexagon may be inscribed in a circle by taking the compass spread to the length of the radius used in drawing the circle and marking off six arcs intersecting the circumference as shown in the figure at \N. ^^ the left. Then join the six points of division as indicated to form the regular hexagon. Exercise 13 1. Construct a regular hexagon with a ruler and compass as directed above. 2. Divide the regular hexagon into six triangles as shown in the figure at the left. How do these six triangles compare in size? Why? PRACTICAL MEASUREMENTS SOLIDS 261 3. Find the area of an equilateral triangle with a side equal to 6 inches. (See page 238.) 4. Since the six equilateral triangles of the hexagon are all equal, show how to find the area of a regular hexagon. 5. Find the area of a regular hexagon with each side equal to 6 inches. 6. What is the perimeter of the regular hexagon described in the preceding exercise? 7. Find the area of a hexagon with a perimeter of 48 inches. Find the area of a square with the same perimeter. Also find the area of a circle with a circumference of 48 inches. Which figure contains the greatest area for the given perimeter? 8. Why do bees have hexagonal-shaped cells? Consider both area and convenience of arrangement. Measurements of Solids We have been studying triangles, rectangles, trapezoids, hexagons, circles, etc. All of these figures have two dimensions, length and breadth. The term polygon is a general term, meaning many-sided, which applies to all of these figures. A figure which has three dimensions, length, breadth and thickness, is called a solid. The term solid does not mean that the figure be composed of some compact material, for it may apply equally well to an empty bin, box or jar. There are certain solid figures with which we ought to be familiar because we see them about us in daily life. A prism is a solid having two bases which are equal and parallel and whose lateral (or side) faces are parallelograms. The most common prisms are triangular and quadrangular. 262 EIGHTH YEAR Triangular Prism Quadrangular Prism Triangular glass prisms are used for bending rays of light. They are used in some forms of opera glasses. The luxfer prisms are used in upper parts of the windows of large rooms to bend and throw the light farther across the room. You will find how a prism bends a ray of light hi your science work. The most common forms of quadrangular prisms are rec- tangular solids such as bins, rooms (rectangular in shape), boxes, freight cars, bricks, etc. . Exercise 14. Area of Surface of a Prism In finding the area of the surface of a prism, we are using no new principles. We simply find the areas of the two bases and the areas of the lateral surfaces and add these to get the total surface of the prism. 1. Find the total surface of a room 15 feet long, 12 feet wide and 10 feet high. 2. What is the area of the surface of a triangular glass prism 3 inches long and whose bases are equilateral triangles with each side equal to 1 inch? 3. What is the area of the surface of a brick 8 in. x 4 in. x 2 in.? 4. What is the area of the surface of a rectangular block of wood whose length is 4 feet and whose bases are 6 inches square? 6. Find the number of square inches of cardboard in a box 6 in. x 3^ in. x if in. without a top. PRACTICAL MEASUREMENTS PRISMS 263 Volumes of Prisms If you made a quadrangular or rectangular prism out of inch cubes as shown in the figure which is 3 inches long, 3 inches wide and 3 inches high, how many cubes would it take to make one row along the bottom? How many such rows are there in one layer? How many layers are there in the prism? How many cubes are there in the volume of the prism? How many inch cubes are there in the volume of the prism? The volume of a prism is generally expressed in cubic units, though it may be expressed in gallons, barrels, bushels, and various other measures which are made up of a certain number of cubic units. A short way of thinking the above process is: - PRINCIPLE : The volume of a prism is the product of the area of the base and the altitude. The above prism is a cube, which has 6 equal square faces. The volume of the cube is equal to (3 X 3) X 3, or3 3 . The expres- sion 3 3 is read 3 cubed and means that the volume of a cube is equal to the cube of its edge. Exercise 15 1. What is the volume of a rectangular prism 12 inches long, 8 inches wide and 6 inches high? 2. How many cubic feet are there in a box 4 feet long, 3 feet wide and 2 feet high? 3. How many cubic inches are there in a brick? (A brick is 8 \ inches long, 4 inches wide and 2 j inches thick;) 4. How many cubic inches are there in a cubic foot? How many bricks would make a cubic foot if there was no mortar between them? 22 bricks are figured as making a cubic foot of wall. How many bricks are saved by the space occupied by the mortar? 264 EIGHTH YEAR 6. An excavation for a house is 40 feet long, 32 feet wide and 4 feet deep. How many loads of earth were removed? (1 cubic yard = 1 load.) 6. A bin is 20 feet long, 8 feet wide and 6 feet deep. How many bushels of wheat will it hold? (1 bushel = how many cubic inches?) 7. What is the volume in cubic feet of a rectangular horse trough 6 feet long, 3 feet wide and 1\ feet deep? 8. How many gallons will the tank in Problem 7 hold? (1 cubic foot = how many gallons?) 9. The swimming tank in a certain club house is 40 feet long, 20 feet wide and has a uniform depth of 5 feet. How many gallons of water are there in this tank? 10. A freight car is 30 feet long, 83- feet wide and 4 feet deep. How many tons of anthracite coal will it hold if 1 ton of anthra- cite coal occupies 34 cubic feet of space? 11. A rectangular block of ice is 30 inches long, 24 inches wide and 9 inches thick. How much will it weigh if a cubic foot of ice weighs 57.5 pounds? 12. An excavation for a house contains 6000 cubic feet. If it is 40 feet long and 30 feet wide, how deep is it? 13. A bin 22^ feet long and 6 feet wide must be how deep to contain 576 bushels, estimating the bushel at 1 \ cubic feet? 14. A wagon box is found to have the following inside measurements: 36 inches wide, 26 inches high and 10 feet 4 inches long. How many bushels of corn on the cob will it hold if 4000 cubic inches of corn on the cob = 1 bushel? 16. A rectangular corn crib 20 feet long and 12 feet wide is filled with ear corn to a depth of 10 feet. How many bushels of corn does the crib hold? COMPUTING RADIATION 265 Exercise 16. How to Compute Radiation In computing the number of square feet of radiating surface needed for any room, three things are taken into consideration: (1) the contents in cubic feet; (2) the num- ber of square feet in the outside or exposed walls and (3) the area of the windows. 1. Find the steam radiation needed for a room 15 feet long, 12 feet wide and 8^ feet high, one exposed wall 15 feet by 8 feet and two windows 5 feet by 1\ feet. Cu. ft. in contents = 15 X 12 X 8j = 1530. Sq. ft. in exposed wall = 15 X 8j = 127 J. Sq. ft. in area of windows = 2 X 5 X 2^ = 25. From the table on the next page we find the number in the cubic con- tents nearest 1530. 1500 is the nearest. The radiation for that number of cubic feet for steam is 15 square feet. Next find the radiation for the exposed wall. 127J is about half way between 112 and 144 so 8 square feet of radiation are required for the exposed wall. 26 is the nearest num- ber in window area so 9 square feet are required for this factor. The total number of square feet required for steam = 15 + 8 + 9 = 32. The number of square feet per section of a standard 3 column radi- ator is shown in the table at the left. If a 38 inch radiator was used in the room just figured, we would need as many sections as 5 is con- tained in 32 or 6 f sections. 7 sec- tions would meet the requirements and leave a little margin. If we wish to compute the radiation for 20 degrees below zero, we must add 20% (or 1% for each degree below zero). 20% X 32 = 6.4. 32 + 6.4 = 38.4, the number of square feet for 20 degrees below zero. At 5 sq. ft. per section, it would take approximately 8 sections for that temperature. Height of Radiator in Inches Sq. Ft. per Section 22 3 26 3.75 32 4.5 38 5 45 6 266 EIGHTH YEAR Radiation Table 1 Cubic Contents Sq. Ft. of Radiation Sq. Ft. of Exposed Wall Sq. Ft. of Radiation s i | i Sq. Ft. of Radiation * 1 1 co | I 3 i B 1 1 G 1 500 8 5 6 16 2 1 1 6 3 2 2 700 12 7 9 48 5 3 4 10 5 3 4 900 15 9 11 80 8 5 7 14 7 5 5 1100 18 11 14 112 11 7 9 18 9 6 6 1300 21 13 16 144 15 9 12 22 11 7 8 1500 25 15 19 176 18 11 15 26 13 9 9 1700 28 17 21 208 21 13 17 30 15 10 10 1900 31 19 24 240 24 15 20 34 17 11 12 2100 35 21 26 272 27 17 23 38 19 13 13 2300 38 23 29 304 30 19 25 42 21 14 14 2500 41 25 31 336 34 21 28 46 23 15 15 2700 44 27 34 368 37 23 31 50 25 17 17 2900 48 29 36 400 40 25 33 54 27 18 18 3100 52 31 39 432 43 27 36 58 29 19 20 3300 55 33 41 464 47 29 39 62 31 21 21 3500 58 35 44 496 50 31 41 66 33 22 22 3700 61 37 46 528 53 33 44 70 35 23 23 3900 65 39 49 560 56 35 47 74 37 24 25 4100 68 41 51 592 59 37 49 78 39 26 26 4300 71 43 54 624 63 39 52 82 41 27 28 4500 75 45 56 656 66 41 55 86 43 29 29 4700 78 47 59 688 69 43 57 90 45 30 31 4900 82 49 61 720 72 45 60 94 47 31 32 iThese figures are based on a temperature of 70 F. inside and out- side. Add 1 % to radiation for each degree of difference. 2. Find the amount of radiation needed for the room de- scribed on the preceding page if hot water is used. How many sections of 22-inch radiators would be needed? 3. Compute the amount of radiation needed for the same room if a vapor system of heating is used. How many 38-inch sections would be needed? 4. Find the number of 38-inch radiator sections needed for steam heat in a living room 20 feet long, 12 feet wide, and 9^ feet high. A side and an end of this room are exposed to the weather. There are 3 windows 5 feet by 1\ feet. COMPUTING RADIATION 267 5. Find the number of 22-inch hot-water sections needed in zero weather for the same room. (See problem 4.) 6. Find the number of 32-inch sections needed for zero weather for a vapor system for the same room. (See problem 4.) 7. Find the number of 38-inch sections needed for steam at 20 degrees below zero for a schoolroom 28 feet long, 24 feet wide, and 14 feet high. A side and end are exposed and the area of the windows is approximately one-fifth of the area of the floor. Suggestion : For cubic contents greater than the numbers given in the table, use a proportional amount. The cubic contents of this room = 9408 cu. ft. Double the radiation for 4700 cu. ft. 8. Find the number of 26-inch sections needed for hot-water heating at zero weather for each of the rooms in the house shown on page 283. Study the floor plan for dimensions of rooms, windows, and exposed walls. Figure the height of all rooms as 9 J feet. 9. Compute the number of 38-inch sections needed for steam at 20 degrees below zero for each room of this house. 10. How many 32-inch sections are needed for a vapor system for 10 degrees below zero for each room of this house? 11. Compute the steam radiation for your schoolroom at 20 degrees below zero. How many radiators would you have for this room? What height would you order? How many sec- tions would be needed in each radiator? 12. Compare your results with the actual amount of radiation in your schoolroom. The protection of hills, trees, shrubs, etc., would affect the warmth of a house. Rooms on the north side of a house would also be colder than those with a southern exposure. Well built houses are also warmer than those not designed for protection against cold weather. Allowance should be made for all of these factors in determining the radiation for a room. The figures given in the table are for average conditions. 268 EIGHTH YEAR Cylinder A cylinder is a solid bounded by a uniformly curved surface and two parallel circular bases. The cylinder, on account of the small amount of material in its walls, is one of the most common of the solid forms in practical use. Cisterns, stove pipes, water pipes, hot water tanks, boilers and silos are usually cylindrical in shape. PRINCIPLE: The volume of a cylinder is equal to the area of the circular base multiplied by the altitude (or height). Exercise 17 1. Find the volume of a cylinder whose base is 6 inches in diameter and whose altitude is 20 inches. 2. A cistern is 6 feet in diameter and 8 feet deep. How many gallons of water will it hold? (1 cubic foot = 7.5 gallons.) 3. A barber once gave me this problem. "I have a hot-water tank 14 inches in diameter and 60 inches high. How many gallons of water does it hold?" What answer should I have given him? 4. A farmer has a silo 12 feet in diameter and 35 feet high. How many tons of silage will it hold, counting 34 pounds to the cubic foot? 6. A cylindrical boiler is 3 feet in diameter and 12 feet long. If it is half full of water, how much water does it contain? 6. A bushel measure contains 2150.42 cubic inches. If it is 12 inches in diameter, how high is it? 7. A cylindrical bucket 8 inches in diameter and 15 inches high will hold how many gallons? 8. Bring to class for solution any problems you can find on the volumes of cylinders, such as gasoline tanks, cisterns, standpipes, stock watering tanks, etc. PRACTICAL MEASUREMENTS THE SILO 269 The Silo The silo is one of the chief factors in successful dairy- ing and cattle rais- ing. It is usually filled with corn, the stalks and ears be- ing chopped up while still green. To secure the pressure necessary for the best preser- vation of silage, the silo should be of a height equal to at least twice its diameter. The greater the height of the silo, the greater will be the weight of the silage and the more it will be compressed. The cylindrical form allows the greatest area in proportion to the wall space and also offers less friction in the settling of the silage. Exercise 18 1. If the silo in the above illustration is 14 feet in diameter and filled to a depth of 28 feet, what is the total weight of the silage, the average weight being 38 pounds per cubic foot? 2. How many days will this silage last a herd of 20 cows, allowing each cow 35 pounds each day? 3. How long will a silo 15 feet in diameter and filled to a depth of 32 feet feed a herd of 30 cattle, allowing 1 cubic foot of silage for each head? 4. In order to prevent silage from spoiling, a layer 1 ^ inches deep must be fed each day. If my silo is 12 feet in diameter and filled to such a depth that it weighs 36 pounds per cubic 270 EIGHTH YEAR foot, how many cows should I keep to feed a layer of that depth, allowing each cow 38 pounds each day? The weight of silage varies from about 32 pounds per cubic foot for 18 feet in depth to about 43 pounds per cubic foot for a depth of 36 feet. 6. A certain silo is 14 feet in diameter and is filled with silage to a depth of 25 feet. If the silage weighs 36 \ pounds per cubic foot, what is the amount of it in tons? 6. How long will this silage last a herd of 24 cows, allowing each cow 40 pounds each day? 7. I wish to build a silo large enough to supply a herd of 20 cows for 190 days. Plan the dimensions for a cylindrical silo, allowing about 1 cubic foot per day for each cow. (See Problem 4 for minimum depth that must be fed each day to keep the silage from spoiling.) IRRIGATION Elephant Butte Dam, New Mexico The Elephant Butte Dam, built across the Rio Grande River in New Mexico by the United States Reclamation Service, IRRIGATION 271 is 1250 feet long and 200 feet high. It is 18 feet wide at the top and 215 feet wide at the bottom. 610,000 cubic yards of masonry were used in the construction of this immense dam. Water for irrigation is measured by the acre-foot, which is the amount of water necessary to cover an acre to a depth of one foot. Exercise 19 1. An acre-foot is equal to how many cubic feet of water? 2. The storage capacity of the Elephant Butte Reservoir is 2,642,292 acre-feet. This is equal to how many cubic feet of water? 3. What is the storage capacity in gallons of this reservoir? 4. The state of Connecticut has an area of 4965 square miles. How deep would the water stored in the Elephant Butte Reservoir cover an area equal to the state of Connecticut? 6. The water surface of this reservoir is 42,000 acres. Find the average depth of water in the reservoir. 6. The Roosevelt Dam in the Salt River Valley of Arizona stores up 1,284,200 acre-feet. The surface of this reservoir is 16,329 acres. What is the average depth of the reservoir? 7. It is estimated that 27,000 horse power of electric energy can be developed from the water in the Roosevelt Reservoir. If this energy is worth $50 per horse power per year, how much revenue would this yield per year if it were all used? 8. A weir (a device for measuring the amount of water) shows that a certain box in an irrigation canal is delivering water at the rate of 2 cubic feet per second. How long will it take to irrigate 40 acres of land, supplying ^ of an acre-foot per acre? 272 EIGHTH YEAR 9. Land was offered in the Salt River Valley, Arizona, at $30 per acre before the Roosevelt Dam was built. Unimproved land sold at about $100 per acre after the irrigation system was completed. The area of the completed system is 250,000 acres. Find the increase in the value of the land as a result of the building of this dam. 10. A farmer raised 8 tons of alfalfa hay per acre on irrigated land worth $200 per acre. He sold this hay at $10 per ton. If his expenses were $25 per acre, what were his profits on a field of 20 acres of alfalfa? What per cent was this on the value of the land? 11. A truck farmer planted a 10-acre irrigated tract in pota- toes on Feb. 10. He harvested this crop on May 10, making a profit of $100 per acre. On July 25 he planted corn and in the autumn of that year sold the roasting ears so as to yield a profit of $60 an acre. What was the total profit on the 10- acre tract for that year? 12. Find other examples of irrigation projects and make problems similar to the ones in this exercise. GOOD ROADS The Lincoln Highway When the Lincoln Highway is finished from New York to San Francisco, it will be a magnificent and useful memorial to the great president for whom it was named. This road is planned to be concrete throughout its entire length of over 3000 miles. 273 Exercise 20 1. In 1916 the distance on the Lincoln Highway from New York to San Francisco was 3331 miles. How many days will it take a touring party to make the journey if they drive 8 hours per day at an average speed of 15 miles per hour? 2. The distance from Boston to New York by road is 234 miles. How far is it from Boston to San Francisco by way of the Lincoln Highway? 3. Of the distance from New York to western Indiana, 659 of the 802 miles of the Lincoln Highway are hard roads. How much will it cost to complete the rest of this section of the road at $12,000 a mile? 4. If the average cost for concrete roads is $13,000 per mile, what will be the total cost of the Lincoln Highway from New York to San Francisco when completed? 5. Mention other important state and national highways with which you are familiar. Exercise 21. The Construction of Good Roads 1. The maximum grade of ascent or descent for im- portant roads has been fixed, generally, at 5%, or 5 feet of rise or fall in 100 feet of length. For a rise of 528 feet, what would be the length of road, at this maximum grade? 2. Gutter grades, at the . , . 1.1 Courtesy Lincoln Highway Association sides of roadways, should have a minimum fall of 6 inches in 100 feet to the culverts. If the culverts are 600 feet apart, how much will the gutters slope to meet them at this minimum fall? 274 EIGHTH YEAR 3. For a road 15 feet or less in width, the middle line, or crown, should be 5 \ inches higher than the sides. For a greater width of road, the crown should be raised f inch for each foot of distance from the boundary. What should be the height of the crown of a road 18 feet wide? 24 feet wide? 4. A road commission found that 26,509 square yards of concrete roads cost $23,154. If the roads averaged 15 feet wide, find the average cost per mile of the concrete roads in that locality. 6. The same commission found that 13,699 square yards of brick-paved roads cost $20,294. Find the cost of brick pave- ment per mile for an 18-foot surface. 6. 651,123 square yards of macadam roads were found to cost $401,470. Find the cost per mile of a 15-foot macadam road. 7. A tar binder is often placed on macadam roads to hold the fine particles of crushed stone together. About 2 gallons are required for each square yard. If the binder costs 8 cents per gallon, what will be the cost of the binder for a mile of macadam road 15 feet wide? 8. The earth work on a certain road averaged about 5560 cubic yards per mile. Find the cost of this earthwork at 28.5 cents per cubic yard. 9. In building a burnt-clay road in the South for 300 feet as a test, the following expenses were incurred : 30^ cords of wood at $1.30 per cord; 20 loads of bark, chips, etc. at 30 cents per load ; Expenses for labor and teams $38.30. What was the cost of the 300-foot road? What would a mile of this road cost at the same rate? 10. If a ton of broken rock for a macadam road will cover 3.13 square yards of surface, how many tons of this material GOOD ROADS 275 will be required for a macadam road a mile long and 15 feet wide covering it to the same depth? 11. A county road commission decides to build 4 miles of macadam roads each year at an estimated average cost of $7600 per mile. The state pays ^ of this expense. If the assessed valuation of the county is $3,800,000, what will be the tax rate for hard roads in this county? Cross Section of a Concrete Road Concrete for road purposes should consist of a mixture of \ part of cement to 2 parts of sand to 3^ parts of gravel or crushed stone. 12. The cross section of the concrete road shown in the diagram shows the concrete to be 6 inches thick. How many cubic yards of concrete are there in a mile of this road? 13. The crown of this road shows a fall of 3 inches in half the width of the road. Find the fall per foot. 14. Under each edge of the concrete a longitudinal drain ditch is dug and filled with loose stone. How many cubic yards of stone will it take to fill a mile of these ditches if they are 8*xlO*? 16. How much stone will it take to fill 120 lateral drains for each side of the road per mile, the drains being 8"xlO"xlO'? 16. How much would the stone cost for both longitudinal and lateral drains at $1.00 per cubic yard? 17. How much would it cost to haul this stone at 50 cents per cubic yard? 18. How much would the concrete cost for a mile of this road at $6.00 per cubic yard? 276 EIGHTH YEAR Mr. Davis lives 2 miles from a hard road on which there is no grade exceeding 5%. A certain city, where he markets his produce, is located on the hard road 6 miles from the point where his branch road meets the hard road. Mr. Davis sold his crop of 1260 bushels of wheat to a firm in the city. 19. The road leading from his farm to the good road was so rough and hilly that he could only haul 18 two-bushel sacks of wheat to a load. How many such loads would he have had to haul to market the wheat in this manner? 20. If he had hauled two loads per day, what would have been the cost of hauling in this way, counting Mr. Davis and his team as worth $4.00 per day? Find the cost per bushel. 21. On the good road a team could haul 35 sacks of 2 bushels each at a load. Had the good road extended to his farm, what would have been the cost of marketing the wheat at $4.00 per day for 2 loads? Find the cost per bushel. . 22. Compare the cost per bushel for hauling on a good road with the cost per bushel on the unimproved road. 23. Mr. Davis decided to hire an extra team to haul sacks from his farm to be transfered to his wagon at the hard road. He then hauled the large loads from that point to the city-. By this system they marketed the wheat in 6 days. At $4.00 per day, for each team, find the cost of marketing the wheat in this way. 24. How much was saved over the method described in Problem 19? PRACTICAL MEASUREMENTS FARM PROBLEMS 277 Exercise 22 Problems Prepared by a Farmer 1. I sold my neighbor a crib of corn 20 feet long, 9 feet 4 inches wide and 10 feet 2 inches high. How many bushels of corn were in this crib, counting 4000 cubic inches to the bushel? 2. A neighbor asked me to help him measure three cribs of corn which he had sold. We found the cribs to measure as follows: Crib 19 ft. 3 in. long, 9 ft. 1 in. wide, 8 ft. 5 in. high. Crib 29 ft. 3 in. long, 8 ft. 11 in. wide, 8 ft. 4 in/high. .Crib 39 ft. 4 in. long, 8 ft. 11 in. wide, 8 ft. 4 in. high. How many bushels were there in the three cribs? (4000 cubic inches = 1 bushel.) 3. How many bushels of corn are there in a frame crib 20 feet long, 10 feet wide and 9 feet high if there are 20 studding 2"x4"x9 feet long to be deducted from the contents on account of being on the inside of the crib? 4. I sold 20 wagon loads of corn to be measured in wagons, counting 4000 cubic inches per bushel. How many bushels were there in the 20 loads if the wagon box was 10 feet 6 inches long, 3 feet 1 inch wide and 2 feet 1 inch high? 6. How many tons of hay are there in a mow 36 feet long, 14 feet wide and 17 feet high, allowing 512 cubic feet per ton? 6. I sold a stack of hay which was 24 feet long, 14 feet wide and had an average height of 15 feet. How much did I receive for the hay at $10 per ton? (Allow 512 cubic feet per ton.) 7. How many tons of hay are there in a mow 32 feet 6 inches long, 12 feet 8 inches wide and 14 feet high? 278 EIGHTH YEAR Measuring Lumber In buying lumber for building a house, a barn, a garage, or a shed one should know how to check the amount of the lumber and know where the different kinds of lumber are used. In measuring full-sized boards or timbers the following method for finding the number of board feet will be found to be the most practical: Multiply the number of boards by the length in feet by the width reduced to feet by the thickness in inches*. Lumber less than an inch in thickness is counted as an inch thick. Exercise 23 In building the house shown in the above plan, the following lists of boards and timbers comprise a portion of the lumber used. Find the number of board feet for each line: No. of Pieces Thickness 1. 1 6" 2. 2 6" 3. 1 6" 4. 2 6" 5. 10 6" Width 8" 6" Length 8' 9' 12' 14' 6' Purpose Girder Girder Girder Girder Girder posts A girder is a heavy timber used to support the first-floor joists. They are supported by posts in the basement, called girder posts. 6. 3 pieces 2" X 6" X 12' Sill plate 7. 3 pieces 2" X 6" X 14' Sill plate 8. 4 pieces 2" X 6" X 16' Sill plate The sill plates are the timbers which rest on the top of the foundation walls. PRACTICAL. LUMBER MEASUREMENTS 279 9. 280 pieces 2" X 4" X 9' Studding. 10. 52 pieces 2" X 4" X 6' Studding. 11. 74 pieces 2" X 4" X 8' Studding. The studding are the upright timbers comprising the main portion of the framework of a house. 12. 32 pieces 2" X 4" X 14' Outside plate. IS. 51 pieces 2" X 4" X 14' Inside plate. A plate is a timber resting on the top of the studding. 14. 29 pieces 2" X 10" X 10' First-floor joist and box sills. 16. 28 pieces 2" X 10" X 12' First-floor joist and box sills. 16. 32 pieces 2" X 10" X 14' First-floor joist and box sills. 17. 3 pieces 2" X 10" X 16' First-floor joist and box sills. 18. 11 pieces 2" X 8" X 9' Second-floor joists. 19. 12 pieces 2" X 8" X 10' Second-floor joists. 20. 14 pieces 2" X 8" X 12' Second-floor joists. 21. 40 pieces 2" X 8" X 14' Second-floor joists. Joists are timbers which support the floors. 22. 32 pieces 2" X 6" X 12' Rafters. 23. 26 pieces 2" X 6" X 22' Rafters. 24. 20 pieces 2" X 6" X 24' Rafters. Rafters are the slanting timbers which support the roof. In billing lumber the lengths of some of the different boards are not specified, but the total length in linear feet is given. 26. Find the number of board feet in 234 linear feet of 1" by 8" boards used for the base and frieze of this house. 26. How many board feet are there in 360 linear feet of 1" by 6" boards used for bracing? 27. Find the number of board feet in 5,240 linear feet of \" by 6" cypress siding. Additional work on lumber measure may be provided by getting local prices on these different boards and timbers and estimating costs as well as the number of board feet. EIGHTH YEAR Practice Exercises in Measurements These exercises involve a knowledge of the facts and principles of measurements as well as an ability to compute rapidly. If the pupils are not able to give the facts or solve the problems in the required time limits, they should be drilled until they can do so. Use the following time limits for these exercises: Excellent 1| minutes; Good 2 minutes; Fair 2^ mniutes. Exercise A Fill in the 11 ff\fi following blanks : fnn+ 17 1 f <-vn things. pounds. 3. 1 yard feet. pecks. cu ft . 6. 1 quart : 6. 1 pound pints. cu. in. 8. 1 minute 9. 1 acre = 10. 1 bushel 11. 1 foot = 12. 1 gross = 13. 1 sq. yd. 14. 1 cu. yd. 1K 1 milp rods. - cu. in. - inches. - things. er ff 25. 1 CU. ft. = 26. 1 ream = - 27. 1 rod = - - cu. in. sheets. yards. . ., , )'( vn.rHs 30. 1 sn ft. sn. in Exercise B Find the areas of the following figures: 1. Rectangle: 16 feet long and 12^ feet wide. 2. Parallelogram: base 12 inches; altitude 7f inches. 3. Triangle: base 40 rods, altitude 30 rods. 4. Square with a side of 80 rods. 6. Trapezoid: bases 18 in. and 12 in.; altitude 9 in. 6. Circle with a diameter of 10 inches. PRACTICE EXERCISES IN MEASUREMENTS 281 Exercise C Find the area of these figures : 1. Square with a side of 15 inches. 2. Circle with a radius of 40 feet. 3. Triangle: base 11 inches; altitude 8 inches. 4. Trapezoid: bases 80 rd. and 60 rd.; altitude 40 rd. 6. Parallelogram: base 15 feet; altitude 10 feet. 6. Rectangle : 80 rods long and 60 rods wide. Exercise D Find the volume of : 1. A room 12 feet long, 9 feet wide, and 8^ feet high. 2. A tank 8 feet long, 3 feet wide, and 1\ feet high. 3. A bin 18 feet long, 7 feet wide, and 6 feet high. 4. A cube with an edge of 8 inches. Exercise E Find the volume of : 1. A silo 12 feet in diameter and 28 feet high. 2. A cube with an edge of 7 inches. Exercise F Find the number of board feet in : 1. Two boards 1 inch thick, 8 inches wide, and 12 feet long, 2. Four timbers 2 inches thick, 6 inches wide, and 16 feet long. 3. Five boards 1 inch thick, 4 inches wide, and 12 feet long 4. Two timbers 2 inches thick, 4 inches wide, and 18 feet long Exercise G 1. How many cords of wood are there in a pile 16 feet long. 6 feet high, and 4 feet wide? 2. How many cubic yards of material are there in a wall 40 feet long, 5 feet high, and 1 foot thick? 3. How many tons of coal are there in a bin 12 feet long, 6 feet wide, and 5 feet deep, allowing 36 cubic feet to a ton? CHAPTER V EFFICIENCY IN THE HOME A Southern Colonial Bungalow 1 When one decides to build a house, he is interested in seeing two things : an exterior view of the finished house and a floor plan, showing the arrangement and sizes of the various rooms. The floor plan of the Southern Colonial Bungalow is shown in the illustration on the next page. Exercise 1. A Study of the Floor Plan 1. What are the outside measurements of the house, excluding the front porch? 2. Read the sizes of the various rooms from the floor plan. 3. How large is the front porch? 4. How many chimneys are shown in the plan? 6. Would you make any changes in the plan if you were going to build this house? 'Acknowledgment is made to the "Gordon -Van Tine Homes," Daven- port, Iowa, for the illustrations here given (also on p. 109), and for the reliable data on which these problems are based. 282 EFFICIENCY IN THE HOME 283 Exercise 2. Cost of the House 1. The basement excavation was 1.8 yards deep. Find the number of cubic yards of earth that was excavated. See the floor plan for the dimensions of the house. The basement is the same size as the house, exclusive of the front porch. 2. In excavating for the basement of the house, there were 200 cubic yards of earth removed. Find the cost of excavating at 25 cents per cubic yard. 3. In the foundation the following materials were used: 42 perch 1 of stone at $5.00 per perch; 40 cubic yards of poured con- crete at $5.50 per cubic yard; and block and foot- ings costing $195. Find the total cost of the foundation. 4. The contractor charged for 120 square yards of cement floor at 80 cents per square yard. Find the cost of cementing the base- ment. 6. The plastering was estimated at 600 square yards at 35 cents per square yard. How much did the plastering cost? 6. The carpenter labor amounted to 833 1 hours at 60 cents per hour. Find the total amount paid the carpenters. *A perch =24f cubic feet. 284 EIGHTH YEAR 7. The rear chimney was 35 feet high and cost $1.30 per linear foot. Compute the cost of this chimney. 8. The other items in the cost of the construction of the house were: Lumber $669.00; millwork $239.00; hardware $132.00; paint (material and labor) $190.00; brick for porch work $80.00; fireplace (chimney, hearth, stone, etc.) $105.00; wiring $14.00; and hot-air heating plant $129.00. Find the total cost of these items. 9. Find the total cost of the house as shown by the various items described in Problems 1 to 8 inclusive. 10. Find the total cost of the excavating, the foundation and the cement floor of the basement. These items amounted to what per cent of the total cost of the house? 11. The cost of the carpenter labor was what per cent of the total cost of the house? 12. The total cost of the lumber, millwork and hardware was what per cent of the cost of the house? Exercise 3. Furnishing a Home 1. What size rugs would you buy for the living room and the dining room? What are the advantages of rugs over carpets? 2. Would you buy rugs for the two bed rooms? If so, what size would you buy? 3. How many shades would be needed for the bungalow? 4. Would you put linoleum on the kitchen floor? Linoleum is made in 6-ft., 9-ft. and 12-ft. widths. Which one of these widths would be used on the kitchen with the least waste? 6. Make out a list of the various articles of furniture which you would buy to furnish this home and the approximate cost of each article. Find the total cost of these furnishings. EFFICIENCY IN THE HOME 285 6. An expert in interior decorations and home furnishings suggested the following as a model list of furniture for this five-room bungalow. Find the total cost of furnishing the bungalow in this manner: Living Room (Antique Mahogany) Davenport, with damask, velour or tapestry covering $100.00 Chair to match 55 . 00 Sofa table to go with davenport if used in front of fireplace 37 . 50 Overstuffed arm chair with velour, tapestry or damask covering . . 50 . 00 Occasional chair or rocker in cane or upholstered 18. 50 Sofa, and table at each end of sofa, each 12 . 00 Living room table, 30"X54" 45.00 Book case, 4' wide 40.00 Best Grade Wilton Rug, 10' 6"X 13' 6" 122.00 Dining Room (Tudor Walnut) 7 ghow how you would Buffet $78.00 f urn i s h this house with an Serving Table 38.00 , ,,. onA , Extension Table.. .58.00 allowance of $800 to cover Cabinet 60.00 Arm Chair 22.00 Side Chairs, 5 at $13.50 67 . 50 Wilton Rug, 11' 3" X 13' 0". . 110. 00 Chamber No. 1 (American Walnut) Bed Full size $42.00 Spring and Mattress 38 . 50 Chest of Drawers 56.00 Dresser 65.00 Night Stand 8.00 Side Chair and Side Rocker,ea. 9 . 00 Wilton Carpet, 9' XI 1' 46.00 Chamber No. 2 (Ivory Enamel) Bed Full size $48.00 Spring and Mattress 38 . 50 Chest of Drawers 36.00 Toilet Table 47.00 Night Stand 10.00 Toilet Table Bench 10 . 00 Side Chair and Side Rocker, ea. 1 1 . 75 Wilton Carpet, 9' XI 1' 46.00 all expenses for furnishings. Get prices on furniture from the local dealer in making your estimates. 8. Furnish the house on an allowance of $1000. 9. Which would be the better plan if your allow- ance were too small : to buy a full equipment of cheap furniture or to buy fewer pieces of higher-priced furni- ture? 10. What articles would you provide for the front porch? Estimate the cost of these articles. 286 EIGHTH YEAR Exercise 4 The house plan shown in this illustration is the one for the house shown on page 109. 1. Compare this plan with the plan of the bungalow. Which one would you prefer for a home? Why? 2. Estimate the cost of furnishing this house, listing the various articles and their prices as in the preceding exercise. 3. Discuss size of rugs, number of windows, etc., for this plan as outlined in Exercise 1. Exercise 5. Expenses of a Home 1. How many tons of coal would be needed to heat this home for a year? Get estimates from owners of houses of about the same size. 2. How much does coal cost in your community? Estimate the cost of the coal at that price. EFFICIENCY IN THE HOME 287 3. Compare the cost of burning hard coal and that of soft coal for a house of this size. 4. If the kitchen range were a coal stove, how many tons would be needed to supply the stove per year? Find the cost of the coal for cooking purposes for a year. 6. If gas is used in your community, find the cost per month for the average family. What is the total gas bill for a year? 6. If estimates for both coal and gas can be obtained, compare the costs to see which is the more economical. 7. Secure actual data from the homes in your community and estimate the cost of lighting a home for a year. 8. Estimate the table expenses 1 for a family of 4 to 8 persons per month? Campfire Girls In order to encourage girls to become efficient as home managers, honors are granted to Campfire Girls for the following achievements : 1. Save ten per cent of your allowance for 3 months. 2. Plan the expenditures of a family under heads of shelter, food, clothing, recreation and miscellaneous. 3. Have a party of ten with refreshments, costing not more than one dollar. 4. Market for one week on $2.00 per person. 6. Market for one week on $3.00 per person. 6. Give examples of 5 expensive and 5 inexpensive foods having high energy or tissue-forming value. Do the same for foods having little energy or tissue-forming value. Choose one of the above achievements to work out and report on it to the class at a later date. 'A review of the section on Food Values at this point will be of assistance in planning the food for the family use. A very elaborate and profitable treatment can be mad e of this topic. 288 EIGHTH YEAR Exercise 6. Keeping the Family Budget Efficiency in a business enterprise demands that the income and expenses of every department be known. Likewise effi- ciency in the home demands that the home managers apportion the family incomes in the most advantageous manner. A large business corporation made out a suggestive budget for the benefit of their employees. They suggested that the daily expenses be entered on an account sheet similar to the following: Budget Estimate for a Family of Five Date Food 30% Shelter 20% Operating Expenses 10% Clothing 15% Contingency 25% 1 2 3 4 5 6 7 8 9 10 etc. to the c ose of each r nonth. EFFICIENCY IN THE HOME 289 Under food they included meat, groceries, vegetables, bakery and dairy products, and any meals at hotels or restaurants. Shelter included rent or payments on owned home, interest on mortgage, taxes, fire insurance, and upkeep of the house. Operating expenses comprise heat, light, fuel for cooking, ice, hired help, laundry, telephone and replacement of home fur- nishings. Contingency includes savings, educational expenses, church dues, club dues, concerts, personal expenses and expenses for health and recreation. 1. If the family income is $75 per month, find the amounts that should be included under the various headings of the suggested family budget. 2. Find the amounts for family incomes of $100, $125 and $150 per month. 3. Keep a family budget at home for a month and see how the amounts expended for the various apportionments compare with the percentage of the suggested budget. 4. Another expert on home economy suggested the following classification: Rent, 25%; food, 25% ; clothing, 15%; education, 10%; luxuries, 5%; miscellaneous expenses, 10%; savings, 10%. Find the monthly apportionments of this budget for an income of $125. 6. Compare the apportionments for the two budgets. Which is the most suggestive and helpful to a home manager? 6. Bring to the class any other budgets for distributing the family income among various headings and compare these budgets with those presented in this chapter. 7. Does the location (in a large city, a small city, or the country) affect the per cents apportioned among the various items of a budget? Show why. 290 EIGHTH YEAR EFFICIENCY IN BUSINESS The boys and girls in the upper school grades are the coming business men and women. If you study the things that lead to efficiency in business, you will find that scientific planning and economy in management are the essential factors. The printing trade is here used for illustration only. The lessons will apply to other industries as well. Exercise 7 Mr. Franklin, with $5000 to invest in the printing business, rented floor space 50'x28'. The accompanying diagram will show how this space was laid out, by an expert, to insure the greatest working convenience, the proper proportion of expenditures in equipment and the highest utility of space. After a careful study of the floor plans, Mr. Franklin pur- chased the material and furniture listed on the following page, which it was found would give him a complete and well-pra- portioned working outfit. EFFICIENCY IN BUSINESS 291 Wood and Steel Equipment $ 850.00 Machinery, including Motors 1,830.00 Type, Spaces and Quads, Borders, Ornaments, Brass Rule, Iron Furniture, Quotation Quads, etc 1,435.00 Miscellaneous material such as Quoins, Mallets, Planers, Brushes, Benzine Cans, Ink, Knives, Roller Supporters, Composing Sticks, Galleys, and all the small tools necessary in a printing plant 110.00 1 Office Desk 55.00 1 Counter (built in) 42.00 1 Show Case 62.00 1 Typewriter 85.00 4 Chairs (average, $7.75) 31.00 Total What balance did he have remaining as working capital? There was still another necessary preparation for the safe conduct of the business, viz., the establishment of a cost system to include the overhead charges (see page 62) and a properly classified schedule of wages for the three separate departments of the work as below shown : l Composing Room wages $0.50 per hour Overhead charges Rent, Heat, Light, etc 1.00 per hour Net cost per working hour. $1.50 per hour Press Room wages (Gordons) 30 per hour Overhead charges Rent, Heat, Light, Power, Insurance, Taxes, etc 65 per hour Net cost per working hour $0.95 per hour Bindery wages Girls 21 per hour Overhead charges Rent, Heat, Light, Insurance, Taxes, etc 24 per hour Net cost per working hour $0.45 per hour J The "cost system" enabled Mr. Franklin, at the end of each week, auickly to determine whether the business of each department was con- ucted at a profit, or, if at a loss, to make the necessary correction and thus avoid further risk and loss. 292 EIGHTH YEAR Mr. Franklin ordered his paper from a wholesale paper house, by the ream, in sheets of various sizes, weights and grades, including the standard lines specified in the second column of the problems below. Let us now find the largest number of circulars 5"x7" that can be cut from a sheet 2l"x36" 1 . Solution : 3 7 = 21 0n x 7 Note that 5 is canceled into 36, 7 times, the fraction being discarded. Show the amount of waste in square inches. Find the number of circulars, or pieces of paper of the sizes given in the first column, that can be cut with the least waste from the sizes given in the second column, and show the amount of waste for each in square inches. from 26* x 29* from 28* x 42* from 32* x 44* from 35* x 45* 6. 6f x 9" from 25" x 38* 10. 9* x 12" from 38" x 50* Exercise 8 1. For a certain job of printing, 2 reams of book paper were needed, weighing 80 pounds to the ream, and costing 8 cents per pound. The composition (type setting) required 8 hours, the press work 6 hours and the bindery work 3 hours. What was the net cost based on the "working hour" rates given in the table on page 303? J In arriving at the amount of paper required for a job, printers by the use of cancellation are able to see at a glance the sized sheet they may have in stock from which they can cut with the least waste. EFFICIENCY IN BUSINESS 293 2. If the printing office added 20% for profit, what was the total cost of the job to the customer? 3. Mr. Howe, a merchant, ordered 6000 handbills, size 6j"x9", for his anniversary dry goods sale. How many reams of paper were required for this job if cut from sheets 25"x38"? 4. If the paper cost 6 cents per pound and weighed 60 pounds to the ream, what did the paper cost? 6 If the composition required 1^ hours and the press work 2 hours, what was the cost of these two items at the net prices given in the table? 6. If Mr. Franklin added 20% for his margin of profit on the job, what did the 6000 handbills cost Mr. Howe? 7. A High School Glee Club ordered 500 programs for their annual entertainment, size (before folding) 6f 'x9", printed on both sides from stock weighing 100 pounds to the ream. How many sheets 25"x38" were required, and what was the cost of the paper at 10 cents per pound? 8. If the composition required 5 hours and the press work 4 hours, what was the charge to the Glee Club, counting in the office charge of 20%? 9. A graduating class ordered 1500 programs, siz6 4"x6". What paper size given in the table cut to the best advantage, and how many sheets were required? 10. A School Board ordered 2000 letterheads, size 8|"xll". If these were cut from sheets 17"x22", of paper stock costing 9 cents per pound, and weighing 90 pounds to the ream, the composition requiring 1 hour, and the press work 2 hours, and 20% was added for profit, what was the total charge for the job? 11. Find some printed program, estimate its cost based on the tables given, submit your figures to your local printer, and see how near you have reached the correct amount. CHAPTER VI PRACTICAL MEASURING INSTRUMENTS The Thermometer The Fahrenheit thermometer is the standard measure of temperature in the United States. A thermometer consists of a small glass tube ending in either a spherical or a cylindrical bulb. At the temperature of your room, the bulb and part of the tube is filled with a liquid (usually mercury). Hold the bulb of a thermometer at your mouth and slowly blow on it. What happens to the mercury? The heat from your mouth has caused the mercury to expand. Hold the bulb for a few moments in some cold water. What change has taken place in the column of mercury in the tube? The thermometer can thus be used to measure the temperature of the air and certain liquids. There are two important points on a Fahrenheit thermometer: the freezing point of water, which is marked 32 above zero, and the boiling point of water, which is marked 212 above zero. Most scientists use the Centigrade thermometer, which has the freezing point marked and the boiling point marked 100. Exercise 1 1. Find from a physics book or the encyclopedia how a thermometer is made. Explain to the class how the freezing and boiling points are found. JO. @ A Standard Thermometer 294 PRACTICAL MEASURING INSTRUMENTS 295 2. How many degrees are there between the freezing and boiling points on a Fahrenheit thermometer? In order that temperatures above and below zero may be distinguished, the signs + and are usually used; +20 meaning 20 above zero and 20 meaning 20 below zero. 3. What is the difference in degrees between a temperature of +20 and a temperature of -20? 4. At a certain city the temperature on a certain day at noon was 25. At midnight of the following day the tempera- ture was 4. How many degrees had the temperature fallen? Give the changes in the temperature indicated by the follow- ing readings: 6. +50 to +32 9. - 5 to +10 13. +40 to +101 6. +15 to- 2 10. +32 to +98 14. - 1 to - 16 7. +77 to +92 11. + 2 to +36 16. -15 to + 15 8. +60 to +43 12. -20 to +32 16. +98jto +10lJ At government observatories, the temperature is taken each hour. The following extract from a daily paper shows a portion of the weather record in a certain city on Feb. 9, 1917: 12 midnight 4 7 a. m 1 1 a. m 3 8 a. m 2 2 a. m 2 9 a. m 3 a. m 1 10 a. m 2 4 a. m 11 a. m 4 5 a. m 1 12 noon '. . 4 6 a. m 1 17. What was the maximum, or highest, temperature during the time indicated? 18. What was the minimum, or lowest, temperature? 19. What was the range or change in temperature during the 12 hours indicated? 296 EIGHTH YEAR 20. Keep a daily record of the outside temperature at the school house. Leave this for the pupils of next year's class. They will be able to make some interesting comparisons with the record that they are keeping. The Barometer A barometer is an instrument to measure the pressure of the air. A simple barometer may be made by inverting a tube, rilled with mercury, in a dish of mercury. If the tube is longer than 30 inches, the mercury will drop from the end of the tube, leaving a vacuum above it. The pressure of the air on the surface of the mercury in the dish will support a column of mercury 30 inches high at sea level. If one goes up in a balloon or climbs a mountain, the column of mercury in the tube will gradually fall because the higher above sea level one rises the less air there is to press down. The barometer is a very important instrument in predicting weather conditions. When the barometer is very low, stormy weather usually A Standard results, and when the barometer is extremely high, Barometer fair weather usually results. Exercise 2 1. Suppose the barometer tube has an area of 1 square inch at the base, and the air supports a column of mercury 30 inches high. How much is the pressure of the air per square inch, if mercury weighs .49 pound per cubic inch? Solution: A column of mercury 1 square inch at the base and 30 inches high contains 30 cubic inches. 30X.49 pounds = 14. 7 pounds. Since the column of mercury weighs 14.7 pounds, .the air pressure must be 14.7 pounds on each square inch of surface. PRACTICAL MEASURING INSTRUMENTS 297 2. Find the number of square inches on the top of your desk. How much pressure does the air exert on the top of this desk? 3. The area of an average person's body is 30 square feet. Find the total pressure which the air is exerting on our bodies. Our bodies are built to withstand this enormous pressure. If we go up a high mountain, the outside pressure becomes so much less that the pressure of the blood is apt to break the blood vessels, and bleeding at the nose and ears often results. The Hygrometer It is important not only to know whether the air is light or heavy as shown by the barometer, but also to know how much moisture it contains. The instrument for measuring the amount of moisture in the air is called a hygrometer. One of the common forms of hygrometers is the wet and dry bulb type. One of the thermometers is an ordinary thermometer; the other thermom- eter has its bulb covered with a wick which is dipping in a can of water. Evaporation of any liquid has a cooling effect. Drop some gasoline on the back of your hand and see how cool it feels when it is evaporating into the air. If there is a very little moisture in the air, the water will evaporate rapidly from the wick and cool it. The wet ther- mometer will then read lower than the dry thermometer. If there is a great deal of moisture in the air, the evaporation will not be so rapid and the difference in the readings of the two thermometers will not be so great. By the use of tables pre- pared for this hygrometer, the amount of moisture in the air can be found. The amount of moisture in the air is expressed in terms of its relative humidity. If we say that the relative humidity of the 298 EIGHTH YEAR air is 65%, that means that the air now contains 65% as much moisture as it is capable of holding. The relative humidity of a living room should be between 50% and 65%. If the air gets too dry, moisture will evaporate too rapidly from the body and chill the skin. The pores of the skin will then be closed, preventing the elimination of certain waste products through the glands of the skin. If the air of a room is too dry, an open vessel containing water should be placed on the stove or radiator to supply the necessary moisture. WEATHER REPORTS WEATHER FORECAST AN ANEROID BAROMETER' For City and vicinity Partly cloudy Wednes- day and Thursday, probably local thun- dershowers, continued warm Wednesday; not BO warm Thursday; fresh southerly winds Wednesday, becoming variable Thursday. For Central territory Partly cloudy Wed- nesday and Thursday, probably local thun- dershowers; not so warm Thursday in the northern portion; moderate, southwest winds. Sunrise. 4:19; sunset, 7:14; moonset, 10:17 p. m. TEMPERATURE During 24 hours Maximum, 2 p. m 91 Minimum, 5 a. m TB 3 a. m 4 a. m E a. m 6 a. m 7 a. m 8 a. ni 9 a. m 10 a. m .77 .76 .75 .75 .77 .80 .84 .84 11 a. m 85 Noon 88 1 p. m 2 p. m 3 p. m 4 p. m 5 p. m 6 p. m .90 .92 .92 .92 .92 .91 7 p. m 88 8 p. m 85 9 p. m 84 10 p. m. . .80.5 11 p. m . . Midnight 1 a. m. . 2 a. m.. ..80 .79 .79 .78 Mean temperature, 83.5; normal for the day, 60 Excess since Jan. 1, 363. Precipitation for 24 hours to 7 p. m., 0. Deficiency since Jan. 1, 2.17 inche.s. Wind, S. W.; max., 24 miles an hour, at 8:35 a. m. Relative humidity, 7 a m., 67%; 7 p. m., 52%. Barometer, sea level, 7. a. m., 30.02; 7 p. m., 30.01. A Daily Paper's Weather Record. One of the most beneficial depart- ments of our govern- ment is the weather bureau. By means of observations taken in various cities scat- tered all over the country, weather fore- casts can be made which save farmers and shippers thou- sands of dollars. The weather record of the preceding day is shown at the left as it appeared on a certain day in a large daily paper. We have now studied some of the instruments which are used in making these observations. PRACTICAL MEASURING INSTRUMENTS 299 Exercise 3 By reference to the above record answer the following ques- tions: 1. What was the mean temperature for the day? 2. Was this temperature warmer or cooler than is usually observed on this particular day of the year? 3. What was the difference between the maximum and the minimum temperature for the day? 4. Has the weather during this year since Jan. 1 been warmer or cooler than the average year's temperature? 5. Did any rain fall during the day? Has as much rain fallen during this year since Jan. 1 as is usually observed? (The amount of rainfall is measured each day by the amount of water falling in an open vessel with perpendicular sides.) 6. From what direction was the wind blowing? W T hat was its velocity? (The velocity of the wind is measured by an instrument called an anemometer, which may be described as a cup-shaped windmill so arranged that it shows the velocity of the wind by the rapidity with which the wind makes it revolve.) 7. What was the relative humidity of the air at 7 a. m.? At 7 p. m.? Explain what is meant by relative humidityf 8. What was the change in the pressure of the air, as measured by the barometer, between 7 a. m. and 7 p. m.? 9. From the preceding observations and other similar ones made in other cities scattered over the country, the weather forecaster makes predictions on what the weather will be. What was his forecast? 10. Bring in other daily records clipped from your daily papers and compare the records and forecasts with this one. 300 EIGHTH YEAR Uses of Weather Reports By taking observations over this country and Canada, forecasters are able to warn farmers and shippers of storms and cold waves. Rain storms usually sweep over the country from the southwest to the northeast, taking several days to travel across the country. Farmers can thus be warned of an approaching storm and make their plans accordingly. Shippers pack perishable produce in cars to withstand certain temperatures. If a cold wave is approaching, they must pack their cars to withstand the lower temperature. In the summer, more ice must be put in the refrigerator cars if a hot wave is approaching. The government issues bulletins to shippers telling them what temperatures they may expect. Exercise 4 1. A farmer had, in process of curing, five acres of new mown hay. Counting on fair weather and failing to profit by his daily paper's "Weather Forecast," he had his crop damaged to the extent of 35% during* an unexpected rainstorm. How much did he lose, on 11 tons of hay, counting the full market value at $11.40 per ton? 2. In a certain fruit belt the temperature dropped unex- pectedly, over night, from 51 degrees to 30 degrees above zero. The peach crop that year in a certain locality yielded 3768 baskets. In the season following, under normal conditions, the yield was 7348 baskets. What was this increased product worth at 55^ per basket? 3. In some localities the temperature of the air is kept higher by building fires all over an orchard. If the fruit growers in the locality described in the preceding problem had heeded the warning issued by the government and built suitable fires, how much loss might they have prevented? PRACTICAL MEASURING INSTRUMENTS 301 4. A farmer observed that the weather report said: "Con- tinued dry weather may be expected." He dragged an old mower wheel between the rows of his corn, thus forming a mulch and conserving the moisture in the ground by preventing its evaporation. His yield was 40 bushels per acre. Another farmer who paid no attention to the reports of the weather bureau and knew nothing of dry farming methods plowed his corn deep and his ground dried out so that his yield was only 25 bushels per acre. If both farmers had equally good land and prospects for corn, how much did the first farmer make per acre by dragging his corn, if it sold for 75^ per bushel? 5. The precipitation in a certain township in one season was 26.8 inches. The wheat yield that year in the township aggregated 137,540 bushels. 'In the succeeding year the pre- cipitation during the same period was 19.7 inches, and the wheat yield aggregated 68,430 bushels. What was the differ- ence in the value of the crops at 95^ per bushel? 6. A gallon contains 231 cubic inches. An acre of ground contains 43,560 square feet. What would be the weight, in tons, of a rainfall of one inch in depth over a quarter-section of land, estimating the weight of each gallon of water at 85 pounds? 7. A fruit grower in Georgia shipped a carload of peaches which were damaged by a hot wave striking the country while the car was on the way. Having insufficient ice to withstand the hot wave, the peaches were damaged 25 1 per bushel. If the car contained 420 bushels of peaches, what was the shipper's loss due to the change of weather? He might have prevented this loss if he had heeded the government's warning. 8. Tell of any instances in which you have heard of farmers or fruit growers profiting by the weather reports in the news- papers. 9. Bring to class newspapers containing weather reports. 302 EIGHTH YEAR THE ELECTRIC METER If we burn coal under a boiler, we generate steam. This steam may be used to run a steam engine which in turn may run a dynamo which generates an electrical current. This electric current supplies the power for electric lights, electric motors and runs our street cars and interurban lines. Steam engines and gas engines are generally rated by the horse power in this country. We say the engine in an automo- bile is 40 horse power or 60 horse power. Electric energy is measured in terms of kilowatts. A kilowatt is equal to 1^ horse power. Thus an engine rated at 40 horse power would be rated at 30 kilowatts. Electric light companies generally measure the current you use in terms of kilowatt-hours. A kilowatt-hour is equal to the use of 1 kilowatt of energy for 1 hour. For clearness we may say that a kilowatt-hour is equal to the energy which a good horse would supply in working steadily for if hours. Electric meters are instruments used to measure the amount of electrical energy which we use. How to Read an Electric Meter Integrating Type K. Beginning at the left indicator on the dial we see that the reading is some- where between 2000 and 3000 because over this dial we see that these figures are read in thousands. Going to the right we see hundreds, tens, ones, and tenths dials. We can easily read such a dial because it is just like writing numbers with figures in thousands, hun- dreds, tens, units and tenths. As we read the dial we take the figure that the dial is at or has just passed. The reading is 2438 kilowatt-hours. PRACTICAL MEASURING INSTRUMENTS 303 Kilowatt - Hours The dial at the right is the same as the preceding dial except that the tenths indi- cator is absent. Some meters have differ- ent dials on them. If the dial on your meter at school or at home is different, work out the method of reading it and then check your result by the reading on the light bill. If you can not read it, have the officer of the company, who calls each month to get the reading, explain how it is read. Exercise 5 1. What is the reading on the dial with 4 indicators on it? 2. The reading of the meter of Problem 1, for the previous month, was 1782. How many kilowatts has the family used during the past month? 3. If the local rate is 12^ per kilowatt, what was the light bill for last month? 4. Many light companies have a sliding scale for the use of electrical energy. The following shows a bill of a company which generates its energy by water power. Note the low rates for energy from water power. Meter Readings Dec. 13 2416 Nov. 13. ... 2368 Total consumption in k.w.hrs. 48 First 9 k.w. hrs. @ Second 9 k.w. hrs. @ 30 k. w. hrs. excess over 18 @ Gross Bill 10c= $0.90 6c= .54 3c = .90 Date: Dec. 22, 1916. Discount on first 18 hrs. if paid on or before Jan. 1, @ Ic per k. w. $2 .18 Net Bill $216 5. The reading on Jan. 13 of the meter described in Problem 4 was 2458. (Problem 4 gives the reading for Dec. 13.) Figure out the bill for this month according to the plan shown in Problem 4. 304 EIGHTH YEAR 6. A company in a small village charges 15^ per kilowatt hour for their electrical energy. How much will a family pay which uses 16 kilowatts during a certain month? 7. Draw a diagram, similar to the one shown in the book, of the dial of some electric meter which is convenient for you to read. What is the reading of the meter shown by your diagram? 8. Determine the system of computing charges for your community. Get some actual readings from bills in your community and make a problem. Present it to the class for solution. 9. Electric cars are run by storage batteries. They can be charged by running an electric current through them. After they are disconnected from the charging current they will give back the energy stored up on their plates. Find the cost of charging a storage battery. How many miles will this battery run the car in which it is used? Find the cost per mile for the current necessary to run this electric car. 10. Find the number of miles a gallon of gasoline will run an automobile of about the same weight. Find the cost per mile of the gasoline. Compare this cost per mile with that of the electric car. THE GAS METER Illuminating gas is made from soft coal by driving off the volatile gases by means of fires under closed retorts. This gas is then run through several processes to take out the impurities which are driven off with the gas. The purified illuminating gas is then pumped into large tanks where it is kept under a pressure which forces it through the pipes to the con- sumers. The consumption of illuminating gas is measured in terms of cubic feet. The gas meter records the number of thousand cubic feet used. The indicators on the dial at the left are PRACTICAL MEASURING INSTRUMENTS 305 Cubic Feet labeled 100 thousand, 10 thousand and 1 thousand. They really read in 10 thousands, thousands and hundreds. Hence the cor- rect reading is only one- tenth the reading as indi- cated on the dial. The reading on the dial at the right as above corrected is 87,300. Exercise 6 1. The reading on my gas meter on Oct. 27 was 83,800. On Nov. 27 it was 85,600. What was my gas bill for the month, gas selling at 90^ per 1000 cubic feet? Solution: Nov. 27 85600 Oct. 27 83800 1800 number of cubic feet consumed. 1800 cubic feet at 90f{ per thousand = 1.8X90j< = $1.62 (gross bill.) 2. If I am allowed a discount on this bill of 10(zf per 1000 cubic feet if I pay it within 10 days, what is my net bill? 3. Problem 1 gives the reading for Nov. 27. If my reading for Dec. 27 is 87,400, what is my gas bill for the month of Dec.? (Find both gross and net bill, using the same rates as given in Problems 1 and 2.) 4. If I use 2400 cubic feet of gas during the month of July, what is my gas bill at 90^ per thousand cubic feet and 1Q per thousand cubic feet discount if paid within 10 days? 5. If you live in a city where gas is used, find the cost per thousand cubic feet. Is there a discount for prompt payment? 306 EIGHTH YEAR 6. Get an old gas bill and make a problem similar to the ones given above and present it to the class for solution. Check their solution by the amount as stated on the bill. THE STEAM GAUGE The steam gauge is an instrument to measure the pressure of the ^team in a boiler. These gauges can also be used to indicate the pressure of compressed air in tanks. They are usually graduated to read pressure in so many pounds to the square inch. The gauge shown in the illustration shows no pressure, the pointer standing at zero. Exercise 7 1. How many pounds of pressure must be put in an auto- mobile tire to make it sufficiently hard? 2. A safety valve is placed in a boiler so that the pressure will not become too great and explode the boiler. Ask the janitor of your school building how many pounds of steam his boiler will carry before the steam forces its way out of the safety valve. 3. Most steam heating plants have low pressure boilers. Locomotives and engines have high pressure boilers. Ask an engineer how many pounds he aims to carry on his engine. 4. The pressure of the atmosphere is about 14.7 pounds per square inch. The steam gauge reads additional pressure above the pressure of the air. For example, if a steam gauge reads 14.7 pounds, we say the boiler is under two atmospheres of pressure inside and only one atmosphere of pressure on the outside. If the gauge reads 29.4 pounds, what would be the pressure on the inside and outside? MEASUREMENTS OF THE EARTH'S SURFACE Short distances on land are measured by means of the surveyor's chain, which is sixty-six feet long and has one hundred links. Surveyor's Chain Distances on the water, and long distances by land, are measured by observing the sun and other heavenly bodies, which seem to pass over the heavens and entirely around the world in twenty-four hours. Distance east and west measured in this way is called longi- tude. This old word meant length; and the ancient peoples who lived on the shores of the "long-east-and-west" Mediter- ranean Sea supposed that the length of the world was east and west. They did not know that the world is round and they gave us the word longitude. It is customary to measure longitude from some great observatory, where the heavenly bodies are observed through the best instruments. Since the one at Greenwich (grin nij) near London, England, is the best known in the world, longitude is generally reckoned from that one. To make the distances east and west, imaginary lines are drawn north and south from the North Pole to the South Pole. These imaginary lines are called meridians. All places between the poles along the same meridian have the same longitude. The Equator, which crosses every merid- ian at right angles half-way between the poles, is the line from which distance is measured in degrees north and south. Imaginary circles to indicate latitude, or distance north or south from the Equator, are called parallels of latitude. 308 EIGHTH YEAR THE MEASUREMENT OF TIME Suppose it is noon at the place where -you live and the sun is directly south of you. As the earth rotates from west to east, the sun seems to move westward and noon travels with the sun. Since the earth rotates on its axis once in 24 hours, the sun will seem to pass over 360 of longitude in 24 hours, or 15 of longitude in 1 hour. Exercise 8 1. If it is noon where you live, how long will it be before it is noon 15 west of you? 30 west of you? 45 west of you? 2. What time is it 15 west of you? 30 west of you? 45 west of you? 3. How long has it been since the sun was directly over the meridian 15 east of you? What time is it at a place 15 east of you? What time is it 30 east of you? For convenience, time must be reckoned from a certain meridian. This meridian has been chosen as that of Greenwich, England. All longitude west of this meridian to the 180th is called west longitude and all longitude east of this meridian to the 180th is called east longitude. STANDARD TIME 309 4. If it is noon at Greenwich, what time will it be 15 west of Greenwich? 30 west of Greenwich? 6. If I set my watch at Greenwich and carry it west with me to longitude 90 west without re-setting it, how much too fast will it be? 6. Philadelphia is in about 75 west longitude. When it is noon at Greenwich, what time is it in Philadelphia? 7. Since there are about 60 of longitude between the extreme east and west coasts of the United States, what is the difference in time between a city in Maine and a city in western Oregon? Standard Time All places on the same degree of longitude have the same local time, however far apart they may be north and south; but by far the greater amount of travel in the world is in an easterly or westerly direction, and to one traveling east or west the local time changes constantly. It is especially impor- 310 EIGHTH YEAR tant that railways shall have an unvarying standard of time for long distances. Hence a system of Standard Time has been adopted for this great country, by which its area has been divided into four great time sections, known as the Divi- sions of Eastern Time, Central Time, Mountain Time and Pacific Time. At all points in any one of these Divisions, the time is made artificially the same. When it is noon in the Eastern Division, it is 11 o'clock in the Central Division, 10 o'clock in the Moun- tain Division and 9 o'clock in the Pacific Division. Thus the Divisions are, successively, one hour apart. When travelers going east or west arrive at the boundary line of one of these divisions, they set their watches ahead or back, to correspond with the time in the next division. The Southern Pacific Railway makes no use of Mountain Time, but passes directly through from Pacific Time to Central Time. It will be noted that the Maritime Provinces of the Dominion of Canada make use of what is called Atlantic Time, which is the time of the meridian of Long. 60 W. This time is not employed in the United States. Exercise 9 1. When it is 12:15 a. m. at Chicago, what time is it in New York (Standard Time)? 2. When it is 4:32 p. m. at San Francisco, what time is it in Chicago? 3. When it is 9:45 at New York, what time is it at Denver? 4. Detroit is now under Eastern Time. How much differ- ence is there between the time in Detroit and the time at Cincinnati, which is in the Central Time belt but has practically the same longitude? INTERNATIONAL DATE LINE 311 6. Buffalo, being at the line of division between Eastern Time and Central Time, makes use of both. How far apart are clocks and watches found to be in a city so situated? Men- tion some other cities on the dividing lines of Standard Time Divisions? 6. If El Paso should make use of Mountain Time it would have the time of what meridian? Would this be near the local time of the place? The International Date Line When Magellan's men returned to Spain from their voyage around the world, they found that they were a day behind in their time. There must be some place, then, where people travelling west or east can change a day in time. It would be very incon- venient for this change to be made in any thickly populated area of the world. The nations of the world have agreed upon such a line passing along the 180th meridian with a few variations as shown in the map. A person travelling west adds a day to his calendar when he crosses the international date line. If he travels east, he goes back a day on his calendar when he crosses this line. Exercise 10 1. If a ship crosses the international date line going west at 1 1 :50 p. m. Saturday, how long will it be Sunday on board the ship? 2. If a ship crosses the international date line going east at midnight Sunday, how long will it be Sunday on the ship? 312 EIGHTH YEAR Exercise 11. Review 1. The maximum temperature of a city during the summer of 1919 was 94 F. The minimum temperature for this city in the following winter was 20 F. What was the range in tem- perature in the city during that year? 2. An electric light company has the following system of rates: 12.8 cents per kilowatt for the first 18^ kilowatts, 5.8 cents per kilowatt for the next 18^ kilowatts, and 2.8 cents per kilowatt for all beyond the first 37 kilowatts. Find the light bill of a customer who used 53 kilowatts. 3. In a certain city gas is selling at $1.05 per 1000 cubic feet. What is a customer's gas bill who uses 2800 cubic feet during one month? 4. Show how to read a gas or electric meter. Make a draw- ing of the dial of your meter at home and use it to illustrate how a meter is read. 5. The reading of an electric meter was -346 on February 26 and 370 on March 26. How many kilowatts were used during that month? How much would the net bill for this month be if the electric ompany charged 12^ cents a kilowatt and allowed a discount of 10% for prompt payment. 6. The reading on a gas meter was 74,400 on March 1 and 76,800 on April 1. Find the gas bill for this month at $1.05 per 1000 cubic feet. 7. Washington, D. C., is approximately 75 of longitude west of London. When it is 12 o'clock in London, what time is it in Washington, D. C.? 8. If you set your watch at New York .City and carry it to San Francisco without resetting it, will it be too fast or too slow? How much? Why? 9. If you set your watch at Denver and carry it to Indian- apolis without resetting it, which way will you reset it and how much? CHAPTER VII GRAPHS Graphs are used so extensively to illustrate statistics that a knowledge of how to make them and how to read and interpret them should be obtained by every one. The Pictorial Graph Courtesy Office of Experiment Stations, U. S. Department of Agriculture The pictorial graph uses pictures of the things to be compared, showing dif- ferences in the numbers of the things by the relative sizes of the pictures. In the pictorial graph in the illustration a comparison is made of the eggs laid by a hen the first year (Fig. 1), the sec- ond year (Fig. 2) and the third year (Fig. 3). Which year was the most productive? How many eggs did the hen lay each year? The exact number of eggs can not be told by such a graph. Such a graph merely enables us to get a general impression of the numbers compared. Pictorial graphs are much improved when the num- bers represented by the pic- tures are also shown in the graph. The graph at the left shows an improved type of pictorial graph. ALFALFA BALANCES THE CORN RATION HANS EXP.-I4 PIGS- 180 DAYS CORN & WATER 75 IN DRY LOT ' --- 180 DAYS CORN __ ALFALFA PASTURE, 185 IB 80 DAYS LBS CORN 4 ALFALFA HAY 100 DAYS Courtesy International Harvester Co. 313 314 EIGHTH YEAR The Line Graph A line graph is a much more accurate way of representing certain kinds of statistics. Line graphs are also much more easily made than pictorial graphs. Suppose that the wholesale prices of eggs for a certain year are to be represented by a line graph. The prices averaged as follows for the different months: Jan. 30^f; Feb. 29 i; Mar. i; Apr. 18& May 17^; June 17& July 17^; Aug. 17fc Sept. I; Oct. 22^; Nov. 25; and Dec. 29 On the cross section paper let the vertical lines represent the different months and the horizontal lines represent the prices from to 36, increasing 4 cents from one horizontal line to another. 5-Sis > I-f?S"?s; On the January vertical line a ^U.y2Q dot is placed half-way between the 28^ line and the 32^ line, thus representing 30^ for January. On the February line a dot is placed one-fourth of the distance from the 28 f line to the 32^ line, representing 29 i for February. After the dots for all the months have been located in this manner, a broken line is drawn to connect them. This graph represents very clearly the fall and rise in the prices of eggs during that year. Exercise 1 1. From this graph give the wholesale prices of eggs for the following months: March, April, July, September, October, November and December. 2. During what four months did the average price of eggs remain the same? \ \ GRAPHS 315 3. How did the decline in price from February to April compare with the rise in price from August to December? 4. The production of coal in long tons for the United States for the years 1905 to 1914 was as follows: Year Anthracite Bituminous n 1905 69,405,958 281,239,252 ^^^ B 1900 1907 190B 1909 1910 1911 1912 1913 I9K 1906 63,698,803 306,084,481 WOOOMO / \ 1907 76,487,860 352,408,054 ^o^ / \ 1908 74,384,297 296,903,826 ^ooo^oo 1909 72,443,624 338,987,997 3^000,000 1910 75 514 296 372,339,703 azooooooo -v ' , ; ! \ / 1911 80 859 489 362 195 125 aoooooooo ' \ / 1Q19 7^ ^Q8 3fiQ 401 80** Q34 zsooooooo / 1Qio 01 7on OA7 4.97 1QO ^7^1 seooooooo i ni A QI nnn AQI Q77 A i A osn 210000000 HO.OOQOOO Suppose that we represent the aooo.ooo years on the vertical lines. The next 18aooo - cco step is to determine how many tons MO.OOO.OOO are to be represented by the distance KO 000.000 from one horizontal line to another. o,ooo,ooo Suppose that we decide on a graph t>0 - 000 - 00 60.00QOOO 19 squares high. The smallest num- ~~~, / ber of tons is 63,698,803 and the largest number is 427,190,573, the difference between these numbers being 363,491,770. Dividing the difference by 19, we find that the most convenient number to represent the distance from one horizontal line to another is 20,000,000. The numbers in the table can be plotted only approximately. 69,405,958, the first number of tons of anthracite coal, may be represented by a dot slightly less than half-way from the 60,000,000 line to the 80,000,000 line. Draw the graphs for both anthracite and bituminous, repre- senting the anthracite by a solid line and the bituminous by a dotted line. Compare your graph with the one in the book. In which one of these kinds of coal did the production increase more rapidly during this period? 316 EIGHTH YEAR 6. A pupil made the following grades on his practice exer- cises for two weeks: Feb. 1, 80; Feb. 2, 87; Feb. 5, 100; Feb. 6, 83; Feb. 7, 78; Feb. 8, 93; Feb. 9, 100; Feb. 12, 93; Feb. 13, 97; Feb. 14, 100. Draw a line graph to show his record. 6. The immigration into the United States each year since 1907 is shown in the table at the 1907 .......... 1,285,349 , f . ^ , 190g 782 870 Draw a line graph to show 1909.. 751 J86 * ne increases and decreases for the 1910 .......... 1,041,570 various years. In what year during 1911 .......... 878,587 this period was immigration largest? 1912 ........ 838,172 what year shows the least number 1913 ...... ....1,197,892 ,. . , TT j n * immigrants? How do you account .......... ,, 1915 .......... 326,700 * or * ne ra P!d drop for the years 1916 ......... 298,826 1915 and 1916? 7. The cost per pupil for education in the United States for the years 1901 to 1914 is 1901 ..... $21.23 1908 ..... $30.55 , . iono 01 iano QI n shown in the table. Make 1902 ..... zl.oo 19U9 ..... ol.bo 1903 ..... 22.75 1910 ..... 33.33 a une graph to show the 1904 ..... 24.14 1911 ..... 34.71 costs for the various years. 1905 ..... 25.40 1912 ..... 36.30 What does the graph show 1906 ..... 26 - 27 1913 ..... 38 - 31 about the cost per pupil for 1907 ..... 28.25 1914 ..... 39.04 ... . , 9 this period? 8. Keep a record of the temperature at 9:00 o'clock at the school house for a month and plot the graph for the temperature record for that month. The Bar Graph The bar graph is one of the easiest to construct and interpret. For comparative purposes it is superior to other forms of graphs because the size of a number is shown by the length of the bar. Thus only one dimension has to be considered, while in pictorial graphs two or three dimensions must be considered. GRAPHS 317 ALFALFA OUT-YIELDS OTHER HAY CROPS The illustration at the right shows a typical bar graph. The lengths of the bars are drawn to represent the numbers written at the right of each. In this graph the longest bar is one inch and represents 5.4 tons. The bar representing brome grass (1.3 tons) must then be drawn approximately j inch long, and the bars representing the yields Of Courtesy International Harvester Co. clover and timothy must be drawn to the same scale. Exercise 2 1. Draw a bar graph showing the comparative values of the products of the leading industries in the United States for a recent year as shown in the following table: Industry Value of Product 1. Slaughtering and packing $1,370,568,000 2. Foundries and machine shops 1,228,475,000 3. Lumber and timber 1,156,129,000 4. Iron and steel 985,723,000 5. Flour and grist mills 883,584,000 6. Printing and publishing 737,876,000 7. Cotton goods 628,392,000 8. Men's clothing 568,077,000 Suggestion: A suitable scale for determining the length of the bars in the above problem is 1 inch = $300,000,000. 2. In 1900, 40.5% of the inhabitants of the United States were living in cities of 2500 or more inhabitants. In 1910, 46.3% of the people were living in cities of this size. Show the comparison between these two years by a bar graph. 318 EIGHTH YEAR 3. Draw a bar graph representing the production for crude petroleum in the United States as shown in the table: 1904 4,916,663,682 1910 8,801,354,016 1905 5,658,138,360 1911 9,258,874,422 1906 5,312,745,312 1912 9,328,755,156 1907 6,976,004,070 1913 10,434,740,660 1908 7,498,148,910 1914 11,162,026,470 1909 7,649,639,508 1915 16,806,372,368 The Distribution Graph Another form of graph used extensively by the United States government in its reports is the distribution graph. The distribution graph in the illustration shows the distribution of poultry in the United States. Each dot in this graph repre- sents 1,000,000 fowls. The first step in the con- u. s. Census Report 1910 struction of such B. graph is to determine the number for each dot. Then determine the number of dots for each state and arrange them in some syste- matic order. From the distribution graph for poultry, name the chief poultry-producing states in our country. Exercise 3 1. Find the population for each county in your state and make a distribution graph showing the distribution of popula- tion in your state. 2. On a map of the United States draw a distribution graph showing the distribution of horses in the United States according to the census of 1910, which was as follows: GRAPHS 319 Iowa 1,449,652 Illinois 1,402,649 Texas 1,125,834 Kansas 1,099,738 Missouri .... 1,035,884 Nebraska... 971,279 Ohio 888,027 Indiana 785,954 Minnesota. . . 738,578 Oklahoma . S. Dakota. N. Dakota . Wisconsin. . Michigan . . New York . 708,848 645,639 625,984 608,657 602,410 587,393 Pennsylvania 542,793 California 445,849 Kentucky 425,884 Tennessee .... 333,025 Virginia 318,831 Montana 304,239 Colorado 284,647 Washington. . .269,501 Oregon 261,627 Arkansas 245,861 Mississippi.... 210,937 Idaho 189,322 West Virginia. 176,530 Louisiana 175,814 New Mexico . . 175,057 N. Carolina.. .162,783 Wyoming 150,984 Maryland 150,159 Alabama 132,611 Georgia 118,583 Utah 111,135 Maine 107,210 Arizona 93,803 New Jersey . . . 88,239 Vermont 80,556 South Carolina 79,105 Nevada 65,717 Massachusetts. 64,109 Connecticut... 46,248 N. H 46,154 Florida 45,029 Delaware 31,943 Rhode Island. 9,527 Plan your numbers so that you will get at least one dot for Rhode Island. Make your number per dot as large as possible, however, so that there will not be so many dots for the states containing large numbers. The Circle Graph The circle graph at the right rep- resents the approximate per cents of the different food substances in peanuts. The circumference of a circle is divided into 360 equal parts called degrees. The angle showing the pro- portion of fat cuts off 29.1% of 360 degrees (360) or 104.76. 1. Find the number of degrees in the angles for each of the other food substances in the peanut. 2. In alfalfa 65% of the food value is in the leaves and 35% in the stem. Draw a circle graph to show the relative proportions of each. Use a protractor to lay out the angles. A large amount of graphing can be done to advantage in connection with geography and thus broaden the practice work in arithmetic. CHAPTER VIII THE METRIC SYSTEM Weights and Measures Over a century ago, in the time of the French Revolution, a commission of able men was formed to devise a convenient system of weights and measures to replace the clumsy systems then in use in the countries of Europe. They proposed the metric system, a scheme so scientific in plan and so convenient in its use that it has grown in favor over the world, until now it is used around the globe, except among the English-speaking peoples. Even in the United States and in the British Empire it is in use in a limited way, being employed very generally in scientific laboratories and is recognized by law. The need for a more general knowledge of this system in this country is growing from day to day, in view of our increas- ing trade with the nations which use it exclusively. Without mastering it we cannot readily understand the trade catalogues of their business houses or the bills sent us for articles purchased ; nor can we make them readily understand our own price lists and bills of goods sold to them without writing these in terms of the metric system. No ambitious pupil of the present day can afford to slight the metric system in his study of arithmetic. This commission measured very carefully a portion of the meridian running through Paris and estimated, from this measurement, the distance from the North Pole to the Equator. They then took one ten-millionth of this distance as the stand- ard measure for length and named it the meter. Since they wished to base their scheme upon a decimal ratio, they selected the Greek prefixes deka, meaning ten; hekto, 320 THE METRIC SYSTEM 321 meaning hundred ; kilo, meaning thousand, and myria, meaning ten thousand, for the multiples of any unit of measure, and the Latin prefixes ded, meaning ^ ; centi , meaning YW > an( ^ mittit meaning 10 1 00 , for the fractions of any unit of measure. Instead of learning an entirely new set of names for each table as we have to do in our clumsy English system of weights and measures, all we have to do in the metric system is to learn one new unit for each table, and, by prefixing the roots, the new tables can be formed. Metric Table of Length 10 millimeters (mm) =1 centimeter (cm.) 10 centimeters =1 decimeter (dm.) 10 decimeters =1 meter (m.) 10 meters =1 dekameter (Dm.) 10 dekameters =1 hektometer (Hm.) 10 hektometers =1 kilometer (Km.) 10 kilometers =1 myriameter (Mm.) The following is an illustration of a decimeter divided into 10 equal parts called centimeters (cm.). Each of these centi- meters is also divided into 10 equal parts called millimeters (mm.). Along the base of the ruler is shown a scale in inches. This shows that a decimeter is slightly less than 4 inches. A meter = 39.37 inches. K)mm cm 3cm 4cm 5cm 6cm 7cm 8cm 9cm 10pm j i i Ocr lirx 2m 3m 4in Exercise 1 1. A meter stick is how many times as long as the decimeter shown above? 2. If you have access to a work shop, construct a meter stick from another as a model or use the scale in your book. 322 EIGHTH YEAR 3. A meter equals how many centimeters? 4. A dekameter is equal to how many meters? 6. A kilometer is equal to how many meters? 6. Change 355 millimeters to centimeters. Since 10 millimeters = 1 cm., 355 mm. =355 mm. ^-10 mm. =35.5, the number of cm. This shows the convenience of the metric system in chang- ing from one unit to another we merely move the decimal point to the right or left the required number of places. 7 Change 8750 mm. to meters. 8. Change .5 km. to Dm. 9. Change 345 meters to km. 10. A rod in our English system is equal to how many meters? 11. Find the length and width of your school room in meters. 12. Measure the length and width of your desk in centimeters. 13. Draw a line on the blackboard a meter in length without looking at a meter stick. Now measure it and see how many centimeters you have missed it. 14. Measure the lengths of objects in your school room after you have first estimated their length, using the different units meter, decimeter and centimeter in your estimates. 16. A kilometer is equal to what decimal fraction of a mile? In France they estimate the distance between two cities in kilometers instead of miles as we do here. Metric Table of Square Measure The square centimeter is one of the most common of the units of square measure in scientific work. As shown in the exact reproduction at the left, it is a square 1 cm. on each side. Find the number of square centimeters in a square inch. THE METRIC SYSTEM 323 100 sq. millimeters (sq. mm.) =1 sq. centimeter. 100 sq. centimeters (sq. cm.) =1 sq. decimeter. 100 sq. decimeters (sq. dm.) = l sq. meter (sq. m.). For measuring land the following units are used: 1 sq. meter = 1 centare (ca.). 100 centares =1 are (a.). 100 ares =1 hectare (Ha.). A hectare is equal to about 2.471 acres. Exercise 2 1. What is the area of the top of your desk in square centimeters? 2. Draw a square meter on the floor without using a meter stick. Use the meter stick to check your estimated square meter. 3. A friend of mine in Argentina writes that he has planted 20 hectares of wheat. How many acres of wheat has he planted? 4. What part of an acre is an are? 6. Reduce 45675 sq. mm. to square meters. (Remember that the multiplier is 100 in square measure instead of 10.) 6. Make 5 problems that involve square measure. Metric Table of Volume 1000 cu. millimeters (cu. mm.) = 1 cu. centimeter. 1000 cu. centimeters (cu. cm.) = 1 cu. decimeter. 1000 cu. decimeters (cu. dm.) = 1 cu. meter. In measuring wood a cubic meter is called a stere. A cubic centimeter is a cube 1 cm. long, 1 cm. wide and 1 cm. high. The exact size of a cubic cm. is shown in the illustration at the right. Find the number of cubic centimeters in a cubic inch. 1 cu. cm. is what part of 1 cu. in.? 324 EIGHTH YEAR Exercise 3 1. Make a cube 1 decimeter long, 1 decimeter' wide and 1 decimeter high. An open cubical box may be made by making each line in the pattern shown at the left 1 decimeter long. The four sides may be turned up at the dotted lines and the corners sewed or pasted together with some kind of gummed paper. 2. In a stere are how many cubic centimeters of wood? 3. A shipment of guanacaste wood from Central America forms a pile two meters high, 1 meter broad and 30 meters long. How many dekasteres does it contain? 4. How many cubic meters of earth are removed to make an excavation 12 meters long, 8 meters wide and 1.5 meters deep? 6. What will be the cost of teaming in the removal of 2500 cubic decimeters of gravel at $1 per cubic meter? 6. A cubic meter is equal to about 1.3 cubic yards. How many cubic yards would there be in the excavation described in Problem 4? Metric Table of Capacity The cubical box described in Problem 1 of the preceding exercise if made correctly will hold exactly 1 cubic decimeter. This is taken as the unit of capacity and called the liter (lee-ter). A liter is equal to about 1.057 quarts. lOmilliliters (ml.) =1 centiliter (cl.) lOcentiliters =1 deciliter (dl.) lOdeciliters =1 liter (1.) lOliters =1 dekaliter (Dl.) lOdekaliters =1 hektoliter (HI.) lOhektoliters =lkiloliter * (Kl.) THE METRIC SYSTEM 325 Exercise 4 1. How many cubic centimeters are there in a liter? 2. If milk costs 8 cents per liter, what is the cost of a deka- liter of milk? 3. Reduce 8 dekaliters to deciliters. 4. An aquarium 2 meters long, 1^ meters broad and 1 meter deep contains how many liters? 6. A bin in a certain granary is 4 meters long, 3 meters broad and 175 centimeters deep. How many hektoliters does it contain? 6. A hektoliter is equal to about 2.837 bushels. How many bushels of wheat will the bin described in Problem 5 hold? 7. Change 245 liters to hektoliters. 8. Make 4 problems involving the metric table of capacity. Metric Table of Weight If a cubic centimeter of distilled water be weighed at a temperature of 39 F. it will weigh exactly a gram. 1000 of these grams make a kilogram (or kilo for short). A kilogram, then, is the weight of a cubic decimeter or liter of distilled water at the temperature of 39 Fahrenheit. 10 milligrams (mg.) =1 centigram (eg.) 10 centigrams =1 decigram (dg.) 10 decigrams =1 gram (g.) 10 grams =1 dekagram (Dg-) 10 dekagrams =1 hektogram (Hg.) 10 hektograms =1 kilogram (Kg.) 10 kilograms =1 myriagram (Mg.) 10 myriagrams =1 quintal (Q.) 10 quintals =1 Metric Ton (MT.) 326 EIGHTH YEAR Exercise 5 A kilogram is equal to about 2.204 pounds. 1. A gram is equal to how many centigrams? 2. A kilogram is equal to how many grams? 3. How many grams are there in a metric ton? 4. How many pounds are equal to a metric ton? 6. Linseed oil is only .935 as heavy as distilled water. How many grams will a liter of linseed oil weigh? 6. Gasoline is only .7 as heavy as distilled water. How much will a' liter of gasoline weigh? 7. I weighed myself on a standard metric scale in a phy- sician's office and found my weight 74 kilograms. Find my weight in pounds. 8. The average weight 1 of boys 13^ years old is 38.48 kilograms. Find their average weight in pounds. 9. The average weight of girls 13^ years old is 40.24 kilograms. Find their average weight in pounds. 10. How many pounds do you weigh? Express this weight in kilograms. 11. A farmer in Argentina measures his wheat by the hekto- liter. A hektoliter = 2.837 bushels. A bushel of wheat weighs 60 pounds. From these facts find the weight of a hektoliter of wheat in kilograms. 12. A cubic decimeter of gold weighs 19.3 kilograms. How many pounds avoirdupois weight does a cubic decimeter of gold weigh? 13. A cubic foot of water weighs 62.5 pounds. How many kilograms are there in the weight of a cubic foot of water? 14. Make three problems which involve the metric table of weights. 'From Table B, Rowe's "Physical Nature of the Child." THE METRIC SYSTEM 327 Exercise 6 From the information already given in connection with the metric system find the following equivalents : 1. A meter = ? feet? 6. A quart = ? cu. in.? 2. An inch = ? cm.? 7. A cu. meter = ? cu. ft.? 3. A mile = ? km.? 8. A pound = ? grams? 4. An acre = ? sq. yd.? 9. A cu. in. = ? cu. cm.? 6. A gallon = ? liters? 10. A rod = ? meters? Exercise 7 1. A book is 4 centimeters thick between the covers. It contains 400 pages. How many leaves are there in 1 millimeter of thickness? 2. Sound travels in the air at the rate of 1087 feet per sec- ond. Find the speed of sound in meters per second. 3. How many seconds would elapse between the flash and the report of a gun, if I were a kilometer away? 4. An American soldier bought 3 liters of milk of a French farmer. How many quarts of milk did he buy? 5. The German army advanced on one march until they were 5 kilometers from Amiens. How many miles were they from that city? 6. The French have a cannon called the "75." This means that the diameter of the bore is 75 mm. Express this diameter in inches. 7. Measure your height in inches. Find your height in cen- timeters. Express your height in meters. 8. The distance between two Belgian cities is 32 kilometers. What is the distance in miles between these cities. 328 EIGHTH YEAR Foreign Money The participation of our soldiers in the World War has made the subject of foreign money of a great deal of interest. Many of these soldiers have brought back foreign coins as souvenirs of the war. If you can get any foreign coins or bills, bring them to school and place them on exhibit for the class. During the war the value of many of these coins and bills became much lower in terms of U. S. money than their regular value. Find the present values of as many as possible. Country Money Unit . Regular Value in U. S. Money Present Value in U. S. Money Equiv. in Lower Coins Great Britian Germany .... France pound () mark franc $4.8665 .238 .193 ? ? ? 20 shillings 100 pfennigs 100 centimes Austria krone .203 ? 100 heller Italy lira .193 ? 100 centisimi Spain peseta .193 ? 100 centimes Holland Russia guilder ruble .402 .515 ? ? 100 gulden 100 kopeks Japan yen .498 ? 100 sen Portugal .... Brazil milreis milreis 1.08 .546 ? ? 1000 reis 1000 reis Greece drachma .193 ? 100 leptas Norway krone .268 ? 100 ore FOREIGN MONEY 329 Exercise 1 1. How many shillings are there in 3 pounds 4 shillings? 2. What is the value in U. S. money of 20? 3. What is the value in English money of $486.65? 4. What is the value in U. S. money of a shilling? 6. 12 pence = 1 shilling. What is the value in U. S. money of an English penny? 6. Reduce to U. S. money 2 francs 45 centimes. Solution: 1 franc = $.193. 2 francs 45 centimes = 2.45 X $.193 = $.47285 or 47 cents in U. S. money. 7. What is the sum of 4 francs 5 centimes; 6 francs 15 centimes; 25 francs 10 centimes; and 15 francs 75 centimes? What is the value of this sum in U. S. money? 8. What is the sum of 20 marks 15 pfennig; 42 marks 25 pfennig; 68 marks 40 pfennig; and 12 marks 20 pfennig? Express the value of this sum in U. S. money. 9. Add 14 pesetas 10 centimes; 16 pesetas 18 centimes; 25 pesetas 14 centimes; and 25 pesetas 58 centimes. Find the value of this sum in our money. 10. Add 60 yen 30 sen; 45 yen 15 sen; 26 yen 45 sen; and 14 yen 20 sen. What is their exact equivalent in our money? 11. If a friend in Rio de Janiero writes that he has invested 5000 milreis in a coffee plantation, how much do I know that he has invested in U. S. money? 12. If a "Jackie" bought a souvenir in Paris for 2 francs 50 centimes, another at Rome for 4 lira 10 centisimi, and one at Barcelona for 3 pesetas 50 centimes, what was the amount in U. S. money which he paid for the three souvenirs? (Use regular values.) 13. A traveler bought a set of Japanese dishes in Tokio for 96 yen. Find the cost of the dishes in U. S. money. 330 EIGHTH YEAR General Review Problems 1. A boy in a shop wishes to find the center of a board 16f inches long. How far from each end is the center? 2. How many pieces of ribbon 1^ feet long can be cut from a 10-yard bolt of ribbon? 3. Find the cost of 5^ yards of dress goods at $1.37^ a yard. 4. Mr. Johnson bought a house for $3200 and sold it for $3800. Find his per cent of gain. 5. What is the interest on $75 for 90 days at 6%? 6. A suit marked $56.50 is placed on sale at a reduction of 20%. What is the sale price on this suit? 7. A grocer bought eggs for 36 cents a dozen and retailed them at 39 cents a dozen. What was his per cent of profit 9 < 8. A four-room flat renting for $35 per month was increased to $45 a month. What was the yearly increase in rent? What was the per cent of increase in rent? 9. A corporation distributed a profit of $40,000 on a dividend of 8%. What was the value of the capital stock of this cor- poration? 10. A merchant was allowed a discount of 3% for a cash pay- ment on a bill of $32.40. Find the net amount of the bill. 11. A broker sold a carload of 95 hogs averaging 240 pounds at $10.00 per carload of 19,000 Ibs. and 5 cents per hundred in excess of that weight. What was his commission? 12. Mr. Coppins bought a piano listed at $650 at discounts of 25% and 10%. What was the net price of the piano? 13. Find the interest on $180 for 1 year 5 months and 12 days at 6%. 14. An agent received a commission of 25% for introducing an electric cleaner in a community. His sales amounted to $285. What was his commission? GENERAL REVIEW PROBLEMS 331 16. A real estate agent sold a farm for $28,750 on a commis- sion of 2%. How much did the owner receive? 16. Find the income tax of a married man with an income of $3750, allowing additional exemptions for 3 children , 17. A man 25 years of age takes out a 20-year endowment policy for $4000. What was his yearly premium on this policy? 18. Find the area of a triangular strip of land with a base of 20 rods and an altitude of 16 rods. 19. A boy raised corn on a rectangular piece of ground 132 feet long and 99 feet wide. He raised 24 bushels of corn on this plot. Compute his yield per acre at the same rate. 20. The area of the six New England States are as follows: Maine, 33,040 square miles; N. H., 9341; Vermont, 9504; Mass., 8266; Rhode Island, 1248; Conn., 4965. What is the total area of the New England States? 21. Find the cost of 2340 board feet of lumber at $85.00 a thousand. 22. Ellen missed 2 problems out of 25 on an arithmetic paper. Find her grade on the scale of 100 for a perfect paper and count- ing all of the problems of equal difficulty. 23. Explain the difference in a blank indorsement and an "indorsement in full" of a check. 24. What is the bank discount on a note for $350 for a period of 60 days at a rate of 6%? 26. What will 20 shares of stock quoted at 83^ cost if the broker charges \/ commission? 26. What will be the per cent of income on a bond bought at 90 (including brokerage) if the owner receives a dividend of $7.20? 27. Extract the square root of 43,296. 28. A rectangular field containing 20 acres is 80 rods long. How many rods of fence must a farmer buy to enclose it? SUPPLEMENT The purpose of this section is to provide additional work in simple equations to supplement Chapter III of Part I, and to give material for additional work in measurements in con- nection with Chapter IV of Part II. While this section is intended to be optional, it offers valuable training in preparation for algebra and geometry and should be used when time permits. I. SIMILAR FIGURES Similar figures are figures having the same shape. All squares are similar to each other because they all have the same shape. In the same way all circles are similar. All rectangles are not similar to each other. Rectangles A and B are similar to each other because they have the same shape, each being twice as long as wide. Rectangles B and C are not similar because C is 5 times as long as it is wide and B is only 2 times as long as it is wide. Exercise 1. Ratio and Proportion Ratio and proportion are very convenient tools to work with in discussing similar figures. It will be to our advantage, then, to master the uses of these tools before going further into the study of similar figures. The ratio of one number to another is the number of times the first contains the second. 332 SIMILAR FIGURES 333 The ratio of 15 to 3 is the number of times 15 contains 3, which equals 5. The ratio of 15 to 3 may be expressed as follows: 15 : 3 reads "the ratio of 15 to 3" or ^-. The fraction is an excellent way of expressing a ratio because it indicates the division idea of a ratio. -^-, the ratio of 15 to 3 = 15-i- 3 = 5. A statement that two ratios are equal is called a proportion as 15 : 5 = 24 : 8. The four numbers in this proportion are called the terms of the proportion. The first and last terms of a proportion are called the extremes and the second and third terms are called the means. 15 and 8 are the extremes of the above proportion and 5 and 24 are the means. What is the product of the extremes, 15 and 8? What is the product of the means, 5 and 24? How does the product of the means compare with the product of the extremes of the proportion? See if the same relation exists between the products of the means and extremes in the following proportions : 1. 10 : 5= 8 : 4. 6. 18 : 6 = 15 : 5. 2.60:15 = 12: 3. 6.30:6 = 25: 5. 3.48: 8 = 12: 2. 7.15:7=45:21. 4. 4 : 2 = 36 : 18. 8. 6 : 5 = 18 : 15. If we should try a very large number of these proportions, we should find that the same relation holds true. This relation may be expressed in the PRINCIPLE: In any proportion the product of the means is equal to the product of the extremes. If one term of a proportion is unknown, by means of this principle the unknown term can be found. Let X represent the unknown term. 1 'By putting the value of the unknown term in place of X after it has been found and then finding whether the product of the means equals the product of the extremes, a check upon the correctness of the work is shown. 334 EIGHTH YEAR 40 : X = 24 : 3 24 X X or 24X = product of the means. 40 X 3 = 120 = product of the extremes. Therefore: 24X = 120 (Check: 40 : 5= 24 : 3) 120 = 120 Exercise 2 Find the value of X in each proportion: 1. 27:12=X: 8. 2. 14: X = 26: 13. 6. 21 : 18= 56: X. 7. X : 28= 10: 7. 11. 9: 3=X: 6. 12. X: 12 = 20: 5. 3. 35: 7 = 15: X. 4. X: 7 = 36: 6. 6. 18:12=X: 6. 8. 3.5: 2.5 = .21: X. 9. 9 : 5= X:10. 10. 8 : X= 16: 8. 13. 16: 6=X:18. 14. 21:X = 14: 8. 1 R 3 2 "V 5 15 - 5 a; - A - T- PRINCIPLE: In similar figures the corresponding dimensions are proportional, c If the triangles ABC and M N O are similar (that is, the same shape), the corresponding dimensions are proportional: AB : MN = CD : OP Exercise 3 1. Suppose A B = 16 inches ; N M = 10 inches ; C D = 6 inches. Find O P. Solution: Put those values in the above proportion: 16 : 10 = 6 : X. 16X = 60 (the product of the extremes = product of means). X=fg- or 3j. Therefore: O P or X = 3f in. SIMILAR FIGURES 335 2. Two rectangles are similar. The base of the first is 12 inches, the base of the second is 8 inches and the altitude of the second is 6 inches. What is the altitude of the first? Caution: Be sure to keep the right order base of 1st : base of 2nd = alt. of 1st : alt. of 2nd. 3. In the above triangles A B = 16 inches, MN = 10 inches and A C = 7 inches. Find the side M O. Exercise 4. Similar Triangles 1. To measure the height of a tree. Method: Measure the shadow A B of the tree. Set up a stick F D whose length you have measured, so that it is perpendicular to the ^ surface of the ground. Measure the shadow of this stick. The triangles ABC and D E F are similar. The shadow of tree A B : shadow of stick D E = height of tree A C : height of stick F D. 2. If A B = 30 feet; D E = 22 inches and D F = 36 inches, find the height of the tree. Caution: Both expressions in the same ratio must be ex- pressed in the same unit of measure. 3. A tree casts a shadow 42 feet long. At the same time a stick 5 feet high casts a shadow 3 feet long. How high is the tree? 4. Another method of measuring the height of the tree is to construct a large right triangle out of strips of lumber. Make it so that the legs of the right triangle are 3 and 4 feet long. If equal legs are put on this triangle it is much easier to make the accurate measurements. 336 EIGHTH YEAR Move the triangle back and forth until a person with his eye at B can just see the top of the tree along the edge D B. Measure the distance from B to the tree. ABE and D C B are similar triangles. The length of the legs of the triangle measuring instrument must be added to A E to give the whole height A E. 6. Suppose AB = 50 feet, B C = 3 feet and DC = 4 feet, what is the height of the tree? Allow 3 feet for the legs. 6. To measure the distance across a pond. Measure B C, D C and E D. Triangles ABC and D C E are similar. ThenBC : DC = AB : ED. Suppose BC = 150 feet; D C = 90 feet; and E D = 50 feet. Find A B. 7. To measure the width of a stream. Select some object such as a tree on the opposite bank at B. Set a stake at A and lay off a line A D. Lay off D C as nearly par- allel to A B as possible, Set a stake at any point O in the line A D. Move, back along the line D C until the stake at O is in line with the tree at B. Set a stake at this point C. Measure A O, O D and D C. The triangles A O B and COD are similar. By means of this pair of similar triangles we get the pro- portion: AB : CD=AO : O D. 8. If CD = 100 feet, AO = 50 feet and O D = 25 feet, find A B, the width of the stream. . SIMILAR FIGURES 337 9. A boy desiring to measure the width of an impassable river flowing through level land drew on the edge of the bank, parallel with the stream, a base line, at each end of which he drove a stake to which he attached the end of a ball of twine. At one end of the base line, with an instrument, he sighted a small spot in a rock on the opposite bank, and noted the angle made by the line of sight with the base line. He then turned his instrument to an equal angle on the other side of the base line, and had an assistant carry the twine a long way along the line of sight. At the other end of the base line he sighted the same spot in the rock, then turned his instrument to an equal angle on the other side of the base line, and had his assistant carry the second ball of twine along the line of sight. From the point where the strings crossed, he measured straight to the base line, and announced the measure as being that of the width of the stream. Was this correct? Explain your answer. 10. By placing a mirror on the ground and moving up or back measured is seen in the mirror, the height of any object can be found. ABC and B D E are similar triangles and C A distance from the eye to the ground; A B, the distance from one's feet to the mirror = D E, the height of the object : B D the distance of the mirror from the object. If AB = 10 feet; CA = 5 feet; B D = 25 feet, find D E. Have pupils find other methods of measurements involving the use of similar triangles. 338 EIGHTH YEAR II. CONES AND PYRAMIDS A pyramid is a solid having for its base a triangle, rectangle or other polygon, and having for its lateral faces triangles meeting at a point called the vertex. Triangular Pyramid Quadrangular Pyramid Cone A cone is a solid having for its base a circle, and bounded by a curved surface tapering uniformly to a point called the apex. Construct a hollow quadrangular prism out of cardboard. Construct a hollow quadrangular pyramid with a base and altitude equal to the base and altitude of the prism. Fill the pyramid with sand and see how many times it must be emptied into the prism to fill it. You will find that it takes 3 pyramids full of sand to fill the prism. The volume of the prism is equal to the product of the area of the base times the altitude. The volume of a pyramid is ^ of the product of the area of the base times the altitude. In the same way it can be shown that the volumes of a cone is one-third of the volume of a cylinder of the same base and altitude. PRINCIPLE : The volume of a pyramid or of a cone is equal to one-third of the product of the area of the base times its altitude. Exercise 5 1. What is the volume of a cone having a base 7 inches in diameter and a height of 9 inches? Solution: 3.5X3.5X9X3.1416 Volume = 3 SPHERES 339 2. Find the volume of a pyramid having a base of 64 square feet and an altitude of 6 feet. 3. A marble cylindrical shaft 1 foot in diameter and 10 feet high is capped by a marble cone having tne same diameter at the base. The altitude of the cone is equal to its diameter. Find the volume of the shaft and cone. 4. The Pyramid of Khufu, in Egypt, has a square base, measuring 750 feet on each side, and its height was originally 482 feet. Find in cubic yards its contents as originally com- pleted, according to these figures. A globe or sphere is a solid bounded by an evenly curved surface every point of which is equally distant from a point within called the center. HI. SPHERES A cubical block of wood may be made into a sphere having its diameter equal to the width of the cube. The wood that is removed lies chiefly at the corners and along the edges of the cube. If very exact weights are made of the cube and of the sphere, the sphere will be found to weigh .5236 as much as the cube. Since the volume of the cube is equal to the cube of its edge and the diameter of the sphere is equal to the edge of the cube. PRINCIPLE: The volume of a sphere is equal to .6236 times the cube of its diameter. [See page 243.] Exercise 6 1. Find the volume of a sphere 4 inches in diameter. Solution: .5236 X (4X4X4) = 33.5104, number of cubic inches in volume of sphere. 340 EIGHTH YEAR 2. Find the volume of a sphere 6 inches in diameter. 3. If the earth were a perfect sphere exactly 8000 miles in diameter, what would be its volume in cubic miles? 4. A globe 3 feet in diameter is how many times the size of a globe 1 foot in diameter? 6. A wood turner makes a wooden ball 3 inches in diameter from a 3-inch cube. What part of the wood is wasted in making the ball? 6. Measure the circumference of a regulation baseball. Find its diameter. How many cubic inches are there in the volume of the baseball? Surface of a Sphere If a croquet ball be sawed into two equal parts and cord be wrapped around the curved surface and then around one of the flat circular surfaces where the ball was sawed, it is found that it requires twice as much twine for the curved surface of one of the halves as for the circle. It therefore requires four times as much cord for the whole surface of the sphere as a circle of the same diameter. Since the area of a circle = ?rr 2 , the area of the surface of a sphere =47rr 2 . 7. Find the surface of a sphere 8 inches in diameter. Solution: Area of surface of a sphere =47Tr 2 . 47Tr2=4X3.1416X(4X4) =201.0624. The area of the surface of this sphere =201. 0624 sq. in. 8. Find the surface of a sphere 5 inches in diameter; 6 inches in diameter; 10 inches in diameter. 9. The radius of the earth is approximately 4000 miles. Find the approximate number of square miles in the earth's surface. 10. Find the number of square inches of leather in a regu- ation baseball cover. (Use measurements found for Problem 6.) EQUATIONS 341 IV. SIMPLE EQUATIONS Exercise 1 An equation is a statement of the equality of two quantities. For convenience in writing equations, letters are generally used to stand for the unknown numbers. For example, if we wish to solve the following problem, we will find it convenient to use an equation: 1. A newsboy sold twice as many papers today as he did yesterday. During the two days he sold 96 papers. How many did he sell each day? We may let the letter X stand for the unknown number of papers sold yesterday. Then 2X stands for the number of papers sold today. X+2X =the total number sold. But 96 = the total number sold Therefore X+2X=96. or3X=96. The expression 3X =96 is an equation because it is a statement of the equality of 3X and the number 96. If 3X = 96, X= 96-!- 3, or 32. and 2X= 2X32, or 64. Solve the following problems by using equations: 2. A farmer bought 20 rods of chicken wire fencing. He wished to make a lot twice as long as it was wide. Find the number of rods in the length and width of the chicken lot. Suggestion: Let X= the number of rods in the width. Remember that there are four sides to be considered in getting the perimeter of the lot. 3. Mary is twice as old as her brother. The sum of their ages is 21 years. Find the age of each. 4. A real estate dealer bought a lot on which he built a house costing three times as much as the lot. If the total cost of *-he house and lot was $5200, what was the cost of each? 342 EIGHTH YEAR 6. The sum of three numbers is 84. The second is twice as large as the first and the third is twice as large as the second. Find the three numbers. 6. A farmer has a farm of 80 acres. He has a certain number of acres in oats; twice as many acres in pasture and hay as in oats; and five times as many acres in corn as in oats. How many acres has he in each? 7. The area of a rectangle is 56 square inches and the width is 4 inches. Find the length. Let X = the length. Then 4 times X or 4X=the area. 8. The area of a field is 80 square rods. The length is 32 rods. Find the width, using an equation as shown in Prob- lem 7. Exercise 2 As shown on page 49, an equation may be represented by a balance. The two sides will therefore balance or remain equal if we take the same quantity or number from both sides or if we add the same numbers to both sides. Suppose we wish to find the value of X in the equation X+6 = 19. If we take away 6 from the left side, we shall have left merely the un- known number X. But if we take 6 from the left side, we must also subtract it from the right side to keep both sides of the equation equal to each other. X+6 = 19 Subtracting: 6 = 6 X = 13 If we wish to find the value of X in the equation X 3 = 5, we must add 3 to the expression X 3 to make it equal to X because X 3 means three less than X, the unknown number. If we add 3 to the left side of the equation, we must also add 3 to the right side to keep both sides of the equation equal. EQUATIONS 343 X-3=5 Adding: 3=3 X =8 Find the value of X in the following equations: 1. X+5 = 12. 11. X+ll = 15. 2. X-4= 9. 12. 3X- 5=13. 3. 2X+3 = 17. 13. 5X+ 2 = 27. 4. 3X+ 1 = 10. 14. 2X- 6 = 12. 6. 2X-2= 8. 16. X-13 = 19. 6. 5X+4 = 19. 16. 9X+ 4 = 49. 7. 2X-5 = 11. 17. 3X- 2 = 13. 8. X+7 = 15. 18. 4X+ 3 = 21. 9. 4X+3 = 19. 19. 7X- 5=16. 10. 7X-3 = 11. 20. 5X+ 6 = 26. Exercise 3 1. The sum of two consecutive numbers is 27. What are the numbers? Suggestions: Let X = one number. Then the next (consecutive) num- ber is X+l. The two numbers X+X+1 =27 or 2X+1 =27. Solve the equation 2X+1 =27 for the value of X. 2. John is 4 years older than Louise. The sum of their ages is 24 years. Find their ages. 3. Two newsboys made 45 cents selling papers. One made 7 cents more than the other. How much did each make? 4. A farmer bought a horse and a cow for $185. The horse cost $55 more than the cow. How much did each cost? 5. The sum of two numbers is 80. One is 20 larger than the other. Find the two numbers. 6. A lawyer received $26.60 for collecting a debt on a commission of 5%. Find the amount of the debt. Equation: $26.60= .05 XX. 344 EIGHTH YEAR Per Cents of Food Substances in the Various American Food Products Protein Fat Carbo- hydrates Ash (mineral) Water Refuse White bread Q 2 1 3 53 1 1 1 35 3 Graham bread 8 9 1 8 52 1 1 5 35 7 Soda crackers 9 8 9 1 73 1 2 1 5 9 Corn meal 9 2 1 9 75 4 1 12 5 Oat meal-. 16 7 7 3 66 .2 2 1 7 7 Buckwheat 6 4 1 2 77 9 9 13 6 Butter.... 1 85 3 11 Cheese.. . 26 8 35 3 3 3 3 8 30 8 Milk 3 3 4 5 7 87 Buttermilk . 3 5 4 8 7 91 2 5 18 5 4 5 5 74 Beef 16 7 16 1 8 51 7 16 4 Veal .... 16 5 7 8 7 58 2 17" 5 Pork 14 5 23 2 8 50 3 14 3 Mutton.. . 13 7 25 5 7 44 16 6 Sausage 16 9 27.5 1 1 3 1 50 7 3.3 Soups 3 2 2 1 4 3 1 3 89 Chicken 13 7 6.8 7 45 4 33 7 Turkey 16 1 18 4 8 42 4 22 7 Fish 14 9 3.0 4 9 52 9 35.5 Oysters 6 1 3 3 3 1 i 88 3 Potatoes 1 8 1 14 7 8 62 6 20.0 Sweet potatoes 1 4 0.6 21.9 0.9 55.2 20.0 Beans 7 1 0.7 22 1 7 68 5 Peas 7 0.5 16.9 1.0 74.6 Beets 1 3 0.1 7.7 9 70 20 Cabbage 1.4 0.2 4.8 9 77.7 15.0 1 4 0.3 8 9 5 78 9 10.0 Turnips 0.9 0.1 5.7 0.6 62.7 30.0 Parsnips 1.3 0.4 10.8 1.1 66.4 20.0 Squash 7 0.2 4.5 0.4 44.2 50.0 Tomatoes.. 0.9 0.4 3.9 0.5 94.3 Cucumbers 7 0.2 2.6 0.4 81.1 15.0 Lettuce 1.0 0.2 2.5 0.8 80.5 15.0 Rhubarb 4 0.4 2.2 0.4 56.6 40.0 Rice 8.0 0.3 79.0 0.4 12.3 0.4 0.1 88.0 0.1 11.4 100.0 70.0 Honey . 81.0 96.0 Apples . _ . 0.3 0.3 10.8 0.3 63.3 25.6 8 0.4 14.3 0.6 48.9 35.0 Grapes ... . 1.0 1.2 14.4 0.4 58.0 25.0 7 0.5 5.9 0.3 62.5 30.0 Oranges ... 0.6 0.1 8.5 0.4 63.4 27.0 Pears 5 0.4 12.7 0.4 76.0 10.0 Strawberries .. . 0.9 0.6 7.0 0.6 85.9 5.0 Watermelon 0.2 0.1 2.7 0.1 37.5 59.4 3 4.6 3 44 8 50.0 Dates dried 1.9 2.5 70.6 1.2 13.8 10.0 Figs dried 4.3 0.3 74.2 2.4 18.8 2.3 3.0 68.5 3.1 13.1 10.0 Almonds . 11.5 30 2 9.5 1.1 2.7 45.0 Brazilnuts 8.6 33.7 3.5 2.0 2.6 49.6 Butternuts 3.8 8.3 0.5 0.4 .6 86.4 6.6 4.9 45.9 1.4 21.1 15.0 Cocoanuts 4.6 41.6 22.9 1.1 5.4 25.0 5.8 25.5 4.3 0.8 1.4 62.2 Filberts 7.5 31.3 6.2 1.1 1.8 52.4 5.2 33.3 6.2 0.7 1.4 53.2 19 5 29.1 18.5 1.5 6.9 24.5 6.9 26.6 6.8 .6 1.0 58.1 INDEX Addition 5, 6, 8, 9, 11, 18, 20-1 Angles and lines 149, 150 Applied fraction problems . 42, 45-8 Applied insurance problems 121 Applied measurement problems . 154 Applied percentage problems. . 75-88 Approximation problems 196-8 Banks and Banking 199-215 Bank checks 201-3, 234-5 checking account 201 deposit slip 200 discount 208 drafts 210-12,233 federal reserve 214-5 organizing a 213 sight and time drafts. . . .210, 212 issuing notes 214 review problems 229-30 savings accounts 204 Borrowing money at bank .... 207-8 Bonds 221-4 Book making 168 Boy scouts 154 Boys' cash account 136 Business forms 129-144 invoices bills 131 monthly statement 133 cash account 135-6 daybook and journal 137 personal account 138-9 inventory 140 payroll 144 cashiers' memorandum 142 receipts 134 review exercises 143, 146 Business transactions 89, 90 By-products 79 Calories 85-8 Campfire girls 287 Clearance sales 92 Commissions 104-6, 192 Cones and pyramids 338 Coupons 223 Cotton industry 81-2 Custom duties .. ..112 Dairy products 75-7 Decimal fractions 38-44 Indorsing checks Discounts 91-5, 193, 208 ^Interest PAGES Efficiency in the home 282-9 budget ..288-9 cost of the house 283-4 expenses of the home 286-7 furnishing the home 284-6 Electric meter 302 Equations 52-9, 241-3 Equivalent percents 50-3 Exchange 209, 235 Federal reserve banks 214 Food values 84-8, 344 Foreign money and travel .... 328-9 Fractions Common 27-48 addition of 29, 30 division of 34 multiplication of 33 subtraction of 29, 30 cancellation of 33 common denominators 30 mixed numbers 31, 34, 184 drills 37,45-48 reviews 183 Fractions Decimals 38-44 addition of 40 division of 43 multiplication of 41 subtraction of 40 review and test problems . . 185-7 Freight and express rates 146 Gardening 155 Good roads 272-6 Graphs 313-19 pictorial 313 line 314 bar 316 distribution 318 circle 319 Insurance 118-124 accident 124 casualty 119 fidelity 119 fire 119 life 122 marine 119 review 195 Income tax 116 202 95-107 Division drills. 6 ; 7, 8, 10, 11, 18-38^ compound 205-6 Efficiency in business 290-3 notes 96 345 PAGES partial payments 101-3 six percent method 98 table 100 reviews 191 Internal revenue 115 International date line 311 International money orders 235 Investments 225-8 Irrigation 270-2 Loaning money 96, 207-8 Longitude and Time 308-11 Lumber problems 278-9 Making change 26 Measuring instruments .... 294-307 barometer 296 hygrometer 297 thermometer 294 electric meter 302 gas meter 304-5 steam gauge 306 surveyors chain 307 Metric system 320-6 table of capacity 324 table of length 321 table of square measure 322 table of volume 323 table of weights 325 Mixed numbers 31, 35, 184 Multiplication drills 5, 7, 8, 10, 18-25 Meat industry 78-80 National expenses. . Ill National revenues 112 Paper and printing 165-170 Parcel post 144 Percentage .49-88 application of 89-90 clearance sales 92 discounts 91-3 equations 52, 61-65 equivalent percents 50 factor and product 53-4 problems by pupils 73 reviews 71, 188, 193 time test exercises 67-70 "pi" 253 Practical measurements . 147-53, 239-307 circles 253, 256-9 cylinders 268 hexagons 260 parallelograms, , . . . 156 rAGES prisms 262 quadrilaterals 151, 239 rectangles 151, 240 solids 261 squares 141 trapezoids 158 triangles. . . . 159-62, 240, 246, 335 reviews 147, 240, 280-1 volume 263-4 Problems by a farmer 277 Pupils own problems 73 Radiation 265-6 Ratio and proportion 332 Reading and writing numbers. .2, 3 Reading the meter 302-3 Remitting money 231-8 cabling 237 checks 234-5 drafts 233 emergency .236 express money order 232 foreign remittance 235 postal money order 231 telegraphing 236 wireless 238 Roman notation 3 Sales slip 129 Savings accounts 204 Shop problems 255 Short methods in division 180 Shortmethodsinmultiplication 1 76-8 Signatures and seals 221 Silos 269 Speed and accuracy 5-11, 18-25 tests 175-182 Spheres 339 Square root 241-5 Standard time 309-11 Stocks and bonds 216-230 Subtraction drills 174 Tariffs 113-5 Taxes 107-10, 116-8 special assessments 110 surtax rates 117 reviews 194 Training for Efficiency 1, 171 Trust companies 215 Type sizes 167 U. S. money 26 Weather reports 298-301 Supplement 332-43 106 C34eb Chadsey - Efficiency 1920 arithmetic cop.l QA 106 C34eb 1920 oop.l Substanci Qua: Peck For Measuring Liquids: Gallon For Weighing: Scales quarts ^ 3ji gallons: = 1 barrel 63 gallons = 1 hogshead (hhd.) Avoirdupois Weight 16 ounces (oz.) = 1 pound.. ...... ...(ft.) 100 pounds = 1 hundredweight (cwt.) 2000 pounds = 1 ton.... One pound Avoirdupois =7000 grains. Troy Weight 24 grains (gr.) ==1 pennyweight ....(pwt.) 20 pennyweights = 1 ounce. (oz.) 12 ounces = 1 pound Ub.) One Pound Troy =5760 grains. Apothecaries' Weight 60 grains (gr.) = 1 dram _.(dr.or5) 8 drams - = 1 ounce (oz. or 3 ) 12 ounces = 1 pound.... One Pound Apothecaries' weight = 5760 grains Apothecaries* Liquid Measure 60 minims (m.) =1 fluid dram (3) 8 fluid drams = 1 fluid ounce. 16 fluid ounces = 1 pint (fl. oz. or 8 pints = 1 gallon (cong.) Measure of Time 60 seconds (sec.) = 1 minute (nata.) 60 minutes = 1 hour (jr.) 24 hours =1 day -(da.) 7 days = 1 week - ( 7 k '( 365 days! = 1 common year (yr.) 366 days = 1 leap year *A11 schools are not fully equipped witt the various measures and instruments required in the ^ study o Denominate Numbers. For this reason suitable illustrations eccompany these tables, but necessarily reduced In size. TABLES OF DENOMINATE NUMBERS I 1 1 1 1- 1 I/I 1 1 1 1 1. 1 1 1 1 1 L 1 1 i 1 i Qli^45^789 ^10 1 1 Surveyor's Chain* For Surface Measuring: l n . Foot Rule, reduced to one third of its true length. For Measuring Lengths: Linear Measure 12 inches (in.) =1 foot (ft.) 3 feet = 1 yard (yd.) 5 yards, or 16| feet.. = 1 rod (rd.) 40 rods = 1 furlong. (fur.) 320 rods, or 5280 feet.. = 1 mile (mi.) Imi. =320rd. = 1760yd. =5280ft. = 63,360in. Surveyors' Linear Measure 7.92 inches (in.) =1 link (1.) 25 links = 1 rod (rd.) 100 links = 1 chain (ch.) 80 chains =1 mile (mi.) Square Measure 144 square in. (sq. in.)..=l square foot (sq.ft.) 9 square feet (sq.ft.) =1 square yard (sq.yd.) 30J sq. yd.,or272isq.ft = l square rod..(sq.rd.) 160 square xods =1 acre (A.) 640 acres =1 square mile (sq.mi.) 1 A. = l<50sq.rd. =4840 Sq.yd. =43,560 sq.ft. Surveyors' Square Measure 16 square rods =1 square chain (sq.ch.) 10 square chains = 1 acre (A.) 640 acres = 1 square mile (sq.mi.) 1 square mile = 1 section (sec.) 36 sections = 1 Cong, township (T.) Cubic Measure 1728 cubic inches (cu.in) =1 cubic foot.... (cu.ft.) 27 cubic feet = 1 cubic yard., (cu.yd.) 128 cubic feet = 1 cord (cd.) 16 cubic feet = 1 cord foot (cd.ft.) 8 cord feet = 1 cord (cd.) ^Instead of the standard (Gunter's) chain, some sur- veyors use a steel tape 50 feet long, divided into foot Cube lengths, each of these being marked off into tenths. Carpenter's Square Illustrating Solids: