i&Jii^ \ LIBRARY OF THE University of California. Mi-s. SARAH P. WALS;^ORTH. Received October, i8g4. Accessions No. ^C^- Class No. UNION READER, Number One. I uimiuix iM^MucrA, ,.u,..^^. ^. UNION READER, Number Two. ' ANALYSIS OF ENGLISH WORDS UNION SPEAKER. SMDEES' SERIES OF READERS, kc. Sanders' Primary Hand Cards. Sanders' German and English Primer. Sanders' Primary School Charts, Large, for Sanders' First Reader. the School Room, 8 Nos. on 4 Cards. Sanders' Second " Sanders' New Speller, Definer and Analyzer. Sanders' Third " Sanders' Test Speller. Sanders' Fourth " Sanders' Old Spelling Book. Sanders' Fifth " Sanders' Primary School Primer. Sanders' High School Reader. Sanders' Elocutionary Chart (on Rollers). Sanders' Young Ladies' Reader Sanders' Pictorial Primer. Sanders' School Speaker. ROBINSON'S FULL COURSE OF MATHEMATICS. G.raded to the -wants of Primary, Intermediate, Grammar, Normal and High Schools, Academies and Colleges. This Ski:tes has already acquired an Annual sale of nearly Half a Million, which ia rapidly increasing. Progressive Table Book. Progressive Primary Arithmetic. Progressive Intellectual Arithmetic, Rudiments of Written Arithmetic Progressive Practical Arithmetic. Progressive Higher Arithmetic, Arithmetical Examples. New Elementary Algebra. New University Algebra. New Geometry and Trigonometry.' Robinson's Geometry, separate. Robinscn's Trigonometry, separate. New Analytical Geometry and Conic Sections. New Surveying and Navigation. New Differential and Integral Calculus. Kiddle's New Elementary Astronomy. University Astronomy. Mark's First Lessons In Geometry. ^^° KEYS to the Arithmetics, Algebras, Geometries, and Surveying, arc published for the use of Teachers only, and will be furnished at Retail price, postage paid,^ r^ ET THE BEST. Vjt webster^s unabridged 80O0 Engravings ; 1840 Pages Quarto. Price $12. G. & 0. MERPwIAM, Publishers, Springfield, Mass. 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Parley's Universal History. Digitized by the Internet Archive in 2007 with funding from IVIicrosoft Corporation http://www.archive.org/details/arithmeticalexamOOfishrich ROBINSOX'S MATHEMATICAL SERIES. ARITHMETICAL EXAMPLES; OB, TEST EXERCISES FOR THE USE OP ADVANCED CLASSES. NEW YORK: TYISON, PHINNEY, BLAKEMAIsr & CO., 47 & 49 GREENE STREET, CHICAGO: S. C. GRIGGS & COMPANY, 1869. ROBIN SON'S The most Complete, most Practical, and most Scientific Series of Mathematical Text-Books ever issued in this country, mu Bobinson's Progressive Table Book, -----. Eobinson's Progressive Primary Arithmetic,- - - - Bobinson's Progressive Intellectual Arithmetic, - - . 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Bobinson's University Astronomy, •----, Bobinson's Mathematical Operations, Bobinson's Key to Geometry and Trigonometry, Conio Sections and Analytical Geometry, - - - - - Entered, according to Act of Congress, in the year 1864, by DANIEL W. FISH, A.M., In the Clerk's Office of the District Court of the United States, for the Northern District of New York. fUiriVEE:iTT)J c In the preparation of this work, it was not designed to make a book to take the place of any other, nor one to constitute a necessary part of the series to which it belongs, nor to adapt it to the use of beginners, or those commencing the study of Arithmetic ; but it was prepared to meet a demand in graded and advanced schools for a larger number of carefully pre- pared and practical examples for review and drill exercises than are furnished from ordinary text-books ; and it may be used in connection with any other series of Arithmetics. Of course, it is no substitute for a systematic treatise. On the contrary, its leading aim is to bring together promis- cuously a large number of practical examples, involving nearly all the principles and ordinary processes of common Arith- metic, and designed thoroughly to test the pupil's judgment ; to bring into use his knowledge of the theory and applications of numbers ; to cultivate a habit of patient investigation and self-reliance ; to test the truth and accuracy of his own pro- cesses by proof — the only test he will have to depend upon in all the computations in real business transactions in after life ; in a word, to make him independent of the text-book, and of written rules and analysis. Although the examples are promiscuous, yet there is a general classification of them, the work being divided into six chapters. The first chapter presents the Standards and IV PREFACE. Tables of Weights and Measures ; the second involves the applications of the Simple Rules of Arithmetic; the third embraces Common and Decimal Fractions ; the fourth takes in Compound and Denominate Numbers ; the fii'th involves Percentage, in all its varied applications ; and the sixth com- prehends all other subjects properly belonging to this science. The examples in each chapter involve the combination and application of the prmciples and processes contained in the preceding ones, but not to any extent those of the following chapters. Classes, therefore, that, in regular course, have gone over the Simple Rules of Arithmetic only, will find in the second chapter of this book all they need in the way of sup- plementary examples for drill and review. Those who have finished, in any systematic treatise, the study of Fractions, will here have in chapter third proper exercises to try their skill in this part of the science ; and so they may proceed by successive reviews, till the same searching test comes to be applied to every part of the subject. Two editions are printed ; one with answers at the close of the book, for the use of teachers, so that when different mem- bers of the same class obtain different results to the same example, he may decide which is correct, without being obliged to take the time nece ary to solve or verify it him- self. The othor edition is without answers, and designed for the use of classes, D. W. F. New York, July, 1864. - ^^j>> CHAPTER I. 1. Measure is that by which extent, dimension, capacity, or amount is ascertained, determined according to some fixed standard. Note.— The process by which the extent, dimension, capacity, or amount is ascer- tained, is called Measuring ; and consists in comparing the thing to be measured with some conventional standard. Measures are of seven kinds : 1. Length. 4. Weight, or Force of Gravity. 2. Surface or Area. 6. Time. '3. Solidity or Capacity. 6. Angles. 7. Money or Value. The first three kinds may be properly divided into two classes — Measures of Extension and Measures of Capacity. MEASURES OF EXTENSION. 2. Extension has three dimensions — length, breadth, and thickness. A Line has only one dimension — length. A Surface or Area has two dimensions — length and breadth, L Linear Measure. 3. Linear Measure, also called Long Measure, is used in measuring lines or distances. TABLE. 12 inches (in.) make 1 foot, ft. 3 feet " 1 yard, yd. 5i yards, or 16i feet, " 1 rod, rd. 40 rods " 1 furlong, fur. 8 furlongs, or 320 rods, " 1 statute mile, mi. MEASUEES OF EXTENSION". The following denominations are also in use 3 barleycorns make 1 inch, used by shoemakers in measuring the length of the foot. 4 inches " 9 " " 21.888 " « 3 feet " 6 " . " 1.15 statute miles " 3 geographic " " 60 " " or 69.16 statute " " 360 degrees " ( used in measuring the 1 hand, ■< heiglit of horses directly / over the fore-feet. 1 span, 1 sacred cubit. 1 pace. 1 fathom 1 used in measuring depths ' f at sea. iused in measur- ing distances at sea. 1 league. ) (of latitude on a meridian [ 1 degree i or of longitude on tho ) ( equator. the circumference of the earth. NoTEB. — 1. For the purpose of measuring cloth and other goods sold by the yard, the yard is divided into halves, fourths, eighths^ and sixteentlis. The. old table of Cloth Measure is practically obsolete. 2. A span is the distance that can be reached, spanned, or measured between the end of the middle finger and the end of the thumb. Among sailors 8 spans are equal to 1 fathom. 3. The geographic mile is ,-^5 of ^i^ or ^risoo of the distance round the center of the earth. It is a small fraction more than 1.15 statute miles. 4. The cubit was originally the length of a man's forearm and hand; or the dis- tance from the elbow to the end of the middle finger 6. The length of a degree of latitude varies, being 68.72 miles at the equator, 68.9 to 69.05 miles in middle latitudes, and 69.30 to 69.34 miles in the polar regions. The mean or average length, a^ stated in the table, is the standard recently adopted by the U. S. Coast Survey. A degree of longitude is greatest at the equator, where it is 69.16 miles, and it gradually decreases toward the poles, where it is 0. surveyor's LINEAR MEASURE. 4. A Gunter's Chain, used by land surveyors, is 4 rods, or 66 feet long, and consists of 100 links. TABLE. 7.92 inches (in.) make 1 link. 1. 25 links " 1 rod. rd. 4 rods, or Q^ feet, " 1 chain. ch. 80 chains " 1 mile. mi. Note. — The denomination, rods, is seldom used in chain measure, distances being taken in chains and links. MEASURES OF EXTENSION. 7 II. Square Measure. 5. Square Measure is used in computing areas or sur- faces ; as of Jand, boards, painting, plastering, paving, etc. TABLE. 144 square inches (sq. in.) make 1 square foot, sq. ft. 9 " feet u I u yard, sq. yd. 30| " yards " 1 " rod, sq. rd. 40 " rods " 1 " rood, R. 4 roods " 1 acre, A. 640 acres " 1 square mile, sq. mi. Artificers estimate their work as follows : By the square foot : glazing and stone-cutting. By the square yard : painting, plastering, paving, ceiling, and paper-hanging. By the square of 100 square feet : flooring, partitioning, roofing, slating, and tiling. Bricklaying is estimated by the thousand bricks, by the square yard, and by the square of 100 square feet. Notes — ^1. In estimating the painting of moldings, cornices, etc., the measuring- line is carried into all the moldings and cornices. 2. In estimating brick-laying by either the square yard or the square of 100 feet, the work is understood to be 12 inches or 1^^ bricks thick, 3. A thousand shingles are estimated to cover 1 square, being laid 5 inches to the weather. surveyors' square measure. 6. This measure is used by surveyors in computing the area or contents of land. TABLE. 625 square links (sq. 1.) make 1 pole, P. 16 poles " 1 square chain, sq. ch. 10 square chains " 1 acre, A, 640 acres " 1 square mile, sq. mi. 36 square miles (6 miles square) " 1 township, Tp. NoTEB. — 1. A square mile of land is also called a section. 2. Canal and railroad engineers commonly use an engineers' chain, which consists of 100 links, each 1 foot long. .3. The contents of land are commonly estimated in square miles, acres, and hun- dredths ; the denomination, rood^ is rapidly going into disuse. 8 MEASURES OF EXTENSION. IIT. Cubic Measure. 7. Cubic Measure; also called Solid Measure, is used in computing the contents of solids, or bodies; as timber, wood, stone, etc. TABLE. 1728 cubic inches (cu. in.) make 1 cubic foot, cu. ft. 27 cubic feet " 1 cubic yard, cu. yd. 40 cubic feet of round timber, or ) ,^ , , , ^ 50 " " hewn « } 1 ton or load, T. 16 cubic feet " 1 cord foot, cd. ft. 8 cord feet, or P c; 1 pipe. 126 wine " ) 2 pipes u 1 tun. Ipes of wine are of different < capacities, as follows : 110 wine gallons make 1 pipe of Madeira. ( Barcelona, 120 " " " ^ 1 " \ Vidonia, or ( Teneriffe. 130 " " " 1 Sherry. 138 " " '' 1 Port. 140 " " " 1 ^^ { Bucellas, or / Lisbon, 10 MEASURES OF CAPACITY. BEER MEASURE. 9. Beer Measure is a species of liquid measure used in measuring beer, ale, and milk. TABLE. 2 pints (pt.) make 1 quart. qt. 4 quarts "1 gallon. gal. 86 gallons " 1 barrel, bb] li barrels, or 54 gallons, " 1 hogshead. hhd. This measure is not a standard ; it is rapidly falling into disuse. II. Dry Measure. 10. Dry Measure is used in measuring articles, not liquid ; as grain, fruit, salt, roots, ashes, etc. TABLE. 2 pints (pt.) make 1 quart, qt. 8 quarts " 1 peck, pk. 4 pecks " 1 bushel, bu. or bush. The following are sometimes used : 8 bushels of 70 pounds each make 1 quarter of wheat. 36 " heaped measure, " 1 chaldron of coal. Note. — The quarter of wheat is 5G0 pounds, or ^ of a ton of 2240 pounds. 11. Comparative Table of Measures of Capacity. Cubic in. in one gaUon. Wine measure, 231 Dry measure Q pk.), 268 i Notes.— 1. Tlie beer gallon of 282 inches is retained in use only by custom. 2. Grain and some other commodities are sold by stricken measure, and in such cases the " measure is to be stricken with a round stick or roller, straight, and of the same diameter from end to end." 3. Coal, ashes, marl, manure, corn in the ear, fruit, and roots are sold by heap measiire. The bushel, heap measure, is the Winchester bushel heaped in the form of a cone, which cone must be 19^ inches in diameter (= to the outside diameter of the standard bushel measure), and at least six inches high. A bushel, heap mea- sure, contains 2747.7167 cubic inches, or 597.29(57 cubic inches more than a bushel stricken measure. Since 1 peck contains 11121L = 537.005 cubic inches, the bushel, heap measure, contains 59.6917 cubic inches more than 5 pecks. As this is about 1 bu. 1 pk. If pt, it is sufficiently accurate in practice, to call 5 pecks stricken measure a heap bushel. . . 4. A standard bushel, stricken measure, is commonly estimated at 2150.4 cubic in- ches. The old English standard bushel from which the United States standard bushel was derived, was kept at "Winchester, England ; hence the name. Cubic in. in Cubic in. in Cubic in. in one quart one pint. one gill. 57| 28| 73'2 671 33f 8| WEIGHTS. 11 WEIGHTS. I. Troy Weight. 12. Troy Weight is used in weighing gold, silver, and jewels. TABLE. 24 grains (gr.) make 1 pennyweight, pwt. or dwt. 20 pennyweights " 1 ounce, oz. 12 ounces " 1 pound, lb. Note. — Troy weight is sometimes called Goldsmith" s Weight II. Avoirdupois Weight. 13. Avoirdupois Weight is used for all the ordinary purposes of weighing. TABLE, 16 drams (dr.) make 1 ounce, oz. 16 ounces " 1 pound, lb. 100 lb. " 1 hundred weight, cwt. 20 cwt., or 2000 lbs., , " 1 ton, T. Note. — The long or gross ton, hundred weight, and quarter were formerly in com- mon use ; but they are now seldom used except in estimating English goods at the United States Custom-houses, in freighting and wholesaling coal from the Pennsyl- vania mines, and in the wholesale iron and plaster trade. LONG TON TABLE. 28 lb. make 1 quarter, marked qr. 4 qr. = 112 1b. " 1 hundredweight, " cwt. 20 cwt. = 2240 lb. " 1 ton, " T. The following denominations are also in use : 8 pounds of butchers' meat make 1 stone. 14 " other commodities " 1 " or | of a cwt. 2 stone, or 28 pounds " 1 todd of wool. 70 pounds of salt " 1 bushel. 56 " make 1 firkin of butter. 100 " " 1 quintal of dried salt fish. 100 " " 1 cask of raisins. 196 " " 1 barrel of flour. 200 " " 1 " " beef, pork, or fish. 280 " " 1 " " salt at tbe NT. State salt-works. 12 WEIGHTS. NoTFS.— The English quarter is 28 pounds, the hundred weight is 112 pounds, and the ton is 20 hundred weight, or 2240 pounds. 2. The weight of a barrel of flour is 7 quarters of old, or long ton weight 3. The weight of a bushel of Indian corn and rye, as adopted by most of the States, and of a bushel of salt is 2 quarters ; and of a barrel of salt 10 quarters, or i of a long ton. 4. The terms gross and net are used in this weight. Gross weight is the weight of the goods, together with the box, cask, or whatever contains them. Net weight is the weight of the goods alone. 14. The weight of the bushel of certain grains and roots has been fixed by statute in many of the States ; and these statute weights must govern in buying and selling, unless specific agreements to the contrary be made. TABLE OF AVOIRDUPOIS POUNDS IN A BUSHEL, As prescribed by statute in the several States named. «• t ci T1 rl Commodities. OS g 50 .2 1 o .15 *o .5 48 60 14 c c 48 60 14 83 O 48 60 14 3 C ^__ 48 60 14 •i '3 o 32 ++ 6 •S *s s i 46 1 S 48 1^ S 1 ^ i § 48 '48 60 |l4 S u 48 o >< t 48 62 48 O 46 t t 47 c ■a o 1 > 46 \ ei 45 Barley 48 Beans Blue Grass Seed rJuckwhoat 40 45 40 50 5.> 52 46 42 42 52 50 48 42 48 46 42 42 Castor lieauf 46 46 46 (46 Clover Seed 60 24 60 •25 60 24 60 60 •28 60,60 28|24 64 60 60 60 28 60 28 60 Dried Apple*'. •28 Pried Peache« 33 38 33 28 •28 33 28 28 8 Flax Seed 56 56 56 56 56 55 56 56 56 Hair 8 44 52 70 44 56 44 56 68 44 50 56 11 56 56 44 56 62 1 56 58 56 56 56 50 56 Hemp Seed Indian Corn 5'> 5fi 56 Indian Corn in ear... India i Corn Meal« . 48 50 50 60 50 50 Mineral Coal* 80 70 80 Oats 32 28 32 8> 35 33i 32 30 30 32 32 35 30 30 32 32 34 32 32 36 32 Onions 57 48 57 57 52 57 60 50 501 Peas 1 Potatoes 54 60 56 60 54 60 56 60 60 60 50 56 50 56 56 60 60 56 j 60 56 60 56 56 60 56 56 60, 50 60 60 '60 Rye 56,66 32 56 56 56 Rye Meal Baltt 45 50 45 50 50 45 46 50, 45 56 44 Timothy Seed 46 Wheat 00 56 GO 20 60 60'60 60 60 60 60 601 60 60 60 60 60 60 60 60 Whpat Bran 20 20 20 * In Kentucky 80 lbs. of bituminous coal, or 70 lbs. of cannel coal, make 1 bushel, t In Pennsylvania 80 lbs. coarse, 70 lbs. ground, or 62 lbs. fine salt make 1 bushel ; and in Illinois, 50 lbs. common or 55 lbs. fine salt make 1 bushel. % la Maine 64 lbs. of ruta baga turnips or beets make 1 bushel ^'^ /^^r\ A. WEIGHTS. -Vvv- 13 in. Apothecaries' Weight. 15. Apothecaries' Weight is used by apothecaries and physicians in compounding medicines ; but medicines are bought and sold by avoirdupois weight. ft grains (gr.) make 1 scruple, sc. or 3. 3 scruples " 1 dram, dr. or 3. 8 drams " 1 ounce, oz. or 5. 12 ounces " 1 pound, lb. or fc. apothecaries' fluid measure. 16. The measures for fluids, as adopted by apothecaries and physicians in the United States, to be used in compounding medicines, and putting them up for market, are given in the following TABLE. 60 minims (in.) make 1 fluidrachm, f5. 8 fluidrachms " 1 fluidounce, fg. 16 fluidounces " 1 pint, O. 8 pints " 1 gallon, Cong. 17. comparative TABLE OF WEIGHTS. Troy. Avoirdupois. Apothecaries*. 1 pound = 5760 grains, = 7000 grains-. = 5760 grains, 1 ounce — 480 " = 437.5 " = 480 " 175 pounds, = 144 pounds, = >75 pounds, 18. COMPARATIVE TABLE. United States. English. French. Extension, Yd. of 3 ft., or 36 in. Same as U. S. Metre, 39.3685 in. . j Wine gal., 231 cu. in. Imp'l gal., 277.274 en. in. Litre, 61.53294 cu. in. Capacity, ^ ^^^^1^,^ y^^ 2150.42 cu. in. Imp'l bu., 2218.192 cu.in. Weight, Troy lb., 5760 gr. Imperial lb., 57C0 gr. Gramme 15.433159 T. gr. Notes. — An Imperial gallon is eqnal to 1.2 wine gallons. 2. An old ale or beer gallon is very nearly equal to 1.221 wine gallons, or 1.017 Imperial gallons. 14 MEASURES OF TIME AND ANGLES. MEASURES OF TIME AND ANGLES. 19. Time is the measure of duration. 60 seconds (sec.]^ make 1 minute, 60 minutes 24 hours " 7 days " 365 days " 366 days " 12 calendar months " 100 years " mm. 1 hour, h. 1 day, , da. 1 week, wk. 1 common year, yr. 1 leap year, yr. 1 year, yr. 1 century, C. The calendar year is divided as follows : No. of month. Season. 2 3 4 5 6 7 8 9 10 11 12 i\ Names of months. Abreviations. No. of days. Winter. Spring, Summer, Autumn, Winter, j January, ( February, i March, ] April, (May, ( June, ] July, ( August, September, October, November, December, Jan. Feb. Mar. Apr. Jun. Aug. Sept. Oct. Nov. Dec. 31 28 or 29 31 30 31 30 31 31 30 31 30 31 Note, — In most business transactions 30 days are called 1 month. MEASURE OF ANGLES. 20. Circular Measure, or Circular Motion, is used prin» cipally ill surveying, navigation, astronomy, and geography, for reckoning latitude and longitude, determining locations of places and vessels, and computing difference of time. Every circle, great or small, is divisible into the same number of equal parts : as quarters, called quadrants ; twelfths, called signs ; 360ths, called degrees, etc. TABLE. 60 seconds {") make 1 minute, '. 60 minutes " 1 degree, ^ 30 degrees " 1 sign, S. 12 signs, or 360'\ " 1 circle, C. MISCELLANEOUS MEASURES. 15 Notes. — 1. Minutes of the earth's circumference are called geographic ornautical miles. 2. A Knot is a nautical or geographical mile. Thus, the expression, " ten knots an hour," denotes ten geographical miles per hour. 3. One English mile equals 5280 feet, and one nautical or geographical mile equals 6086 feet. 4. The denomination, signs, is confined exclusively to Astronomy. 5. A degree has no fixed linear extent. When applied to any circle it is always So o P^rt of the circumference, But, strictly speaking, it is not any part of a circle. 6. 90° make a quadrant or right angle ; 60° " a sextant or | of a circle. MISCELLANEOUS TABLES. 21. COUNTING. 12 units or things make 1 dozen. 12 dozen " 1 gross. 12 gross " 1 great gross. 20 units " 1 score. 22. PAPER. 24 sheets make 1 quire. 20 quires " 1 ream. 2 reams 1 bundle. 5 bundles 1 bale. 23. BOOKS. . The terms folio, quarto, octavo, duodecimo, etc., indicate the number of leaves into which a sheet of paper is folded. A sheet folded in 2 leaves is called a folio. A sheet folded in 4 leaves A sheet folded in 8 leaves A sheet folded in 12 leaves A sheet folded in 16 leaves A sheet folded in 18 leaves A sheet folded in 24 leaves A sheet folded in 32 leaves a quarto, or 4to. an octavo, or 8vo. a 12mo. a 16mo. an 18mo. a 24mo. a 32 mo. 24. COPYING. 72 words make 1 folio, or sheet of common law» 90 " " 1 " " " " chancery. 16 MONEY AND CURRENCIES. MONEY AND CURRENCIES. I. United States Money. 25. The currency of the United States is decimal currency, and is sometimes called Federal Money, TABLE. 10 mills (m.) make 1 cent, ct, 10 cents " 1 dime, d. 10 dimes ' " 1 dollar, $. 10 dollars " 1 eagle, E. Qoxs^.— The gold coins are the'double eagle, eagle, half eagle, quarter eagle, three dollar piece, and dollar. The silver coins are the half and quarter dollar, dime and half dime, and three cent piece. The nickel coin is the cent. STATE CURRENCIES. 26. United States money is reckoned in dollars, dimes, cents, and mills, one dollar being uniformly valued in all the States at 100 cents ; but in many of the States money is sometimes reckoned in dollars, shillings, and pence. Georgia Currency. Georgia, South Carolina, $l=4s. 8d.=56d. Canada Currency. Canada, Nova Scotia, $1 -5s. - 60d. JVew England Currency. New England States, Indiana, Illinois, \ Missouri, Virginia, Kentucky, Ten- V |l=26s.=72d. nessee, Mississippi, Texas, ) Pennsylvania Currency. New Jersey, Pennsylvania, Delaware, )^^ _r^^^ 6d. =90d. Maryland, ) JVew York Currency. New York, Ohio, Michigan, North ) |j_gg_^^^^ Carolina. ' MOWKY AISID CUKKENCIES. 17 II. Canada Money. 27. The currency of the Canadian provinces is decimal, and the table and denominations are the same as those of the United States money. Note.— The decimal currency was adopted by the Canadian Parliament in 1858, and the Act took effect in 1859. Previous to the latter year the money of Canada was reckoned in pounds, shillings, and pence, the same as in England. Coins. — The silver coins are the shilling, or 20-cent piece, the dime, and half dime. The copper coin is the cent. Notes.— The 20-cent piece represents the value of the shilling of the old Canada currency. 2. The value of the 20-cent piece in United States money is 18| cents, of the dime 9^ cents, and of the half dime 4| cents. 3. Every 3d. of the old coinage is equal to 5 cents of the new. III. English Money. 28. English or Sterling Money is the currency of Great Britain. TABLE. 4, farthings (far. or qr.) make 1 penny, d. 12 pence " 1 shilling, s. 20 shillings " 1 pound or sovereign, £ or sov. Notes. — 1. Farthings are generally expressed as fractions of a penny; thus, 1 far., sometimes called 1 quarter, (qr.) = jd. ; 3 far. = |d. 2. The gold coins are the sovereign (= £1) and the half sovereign (= 10s.) 8. The silver coins are the crown (= 5s.), the half crown (= 2s. 6d.), the shilling, and the 6 penny piece. 4. The copper coins are the penny, half penny, and farthing. 5. The guinea (= 21s.) and the half guinea (= 10s. 6d. sterling) are old gold coins, that are still in circulation, but are no longer coined. 6. In France accounts are kept in francs and decimes. A franc is equal to 18.6 cents United States money. 7. The pound (£) is not a coin, but stands for 20s. ; it is represented by the sove- reign, or the bank note of £\, The pound is so called, because its equivalent, 240d. or 20s., formerly contained a pound weight of siver, the pound then being smaller than at present. A pound of standard silver is now coined into 66s. The value of £1 in Canada and the United States is $4.84. Hence the value of an English shilling is 241 cents. 18 INTEREST. INTEREST. 29. Legal Interest is the rate per cent, established by law. It varies in different States, as follows : Alabama, 8 per cent. Minnesota, 7 per cent Arkansas, 6 (( u Mississippi, 8 (( u California, 10 u u Missouri, 6 (( (( Connecticut, 6 C( u New Hampshire, 6 u (( Delaware, 6 u (( New Jersey, C u u Dist. of Columbia, 6 u (( New York, 7 u i( Florida, 8 ii (( North Carolina, 6 (( (( Georgia, 7 (C u Ohio, 6 (( u Illinois, 6 (( (( Pennsylvania, 6 (( u Indiana, 6 (( u Rhode Island, 6 (( u Iowa, 6 (( u South Carolina, 7 (( u Kentucky, 6 (C u Tennessee, 6 (( u Louisiana, 5 (( u Texas, 8 u u Maine, 6 (( u U. States (debts), 6 (( « Maryland, 6 u u Vermont, G u n Massachusetts, 6 u u Virginia, 6 li u Michigan, 7 a u Wisconsin, 7 u u Notes. — I. The legal rate in Canada, Nova Scotia, and Ireland is 6 per cent., and in England and France 5 per cent. 2. When the rate per cent, is not specified in accounts, notes, mortgages, contracts, etc., the legal rate is always understood. TABLE. 30. Showing the number of days from any day of one month to the same day of any other month within one year. TO THE SAME DAY OF THE NEXT FROM ANY DAY OP Jan. 365 Feb. Mar. Apr. May. June July. Aug. 212 Sept. 243 Oct. Nov. 304 Dec. January 31 69 90 120 151 181 2T3 3.34 February.. . B34 365 28 59 89 120 150 181 212 242 273 3M3 March 30G 337 365 31 61 92 122 153 184 214 245 Tib April.- 275 306 335 365 30 61 91 122 153 183 214 244 Mny 945 276 304 335 365 31 61 92 l-.'3 153 184 214 June 214 -45 273 304 334 365 30 61 92 122 153 183 July 1S4 2!5 243 274 304 335 365 31 62 92 123 153 August \h'\ 1S4 212 243 273 304 834 865 31 61 92 122 September... V22 153 181 212 242 273 303 334 365 30 61 91 October 92 123 151 182 212 24:? 273 3(U 3:53 365 31 61 November.. 61 92 120 151 181 212 242 273 304 334 365 30 December . . 31 6'>. 90 121 151 182 212 243 274 304 335 365 ARITHMETICAL EXAMPLES. CHAPTEE II. 1. The total length of railroads in Massachusetts, Jan. 1st, 1864, was 1941 miles, and the total cost of the roads and equipments up to the same date, was $66809802. How much had been expended per mile ? 2. At the same date there were 112 miles of horse-rail- roads, costing for building and equipments $3979596. How much more had been expended per mile upon horse-railroads than upon steam railroads ? 3. A man bequeathed his estate as follows : to each of his three sons, $8500 ; to each of his four daughters, $4250 ; to his wife, $350 more than the sum of the shares of one son and three daughters; and the remainder, which was $2000 more than he gave to all his family, he left to benevolent in- stitutions. What was the value of his estate? S i. ^ 4. The national debt of Great Britain in 1861 was $183.55 for each person, and the population was 29334788. What was the national debt 1 5. At the same date, the annual interest of the national debt was $127665701. Required, the annual interest to each person. 6. The Finances of the State of Maine for the year 1862 were stated as follows : 20 ARITHMETICAL EXAMPLES. jReceipts,— Balance in Treasury, Jan. 1, 1862, $68434.63 ; receipts from Taxes, $439150.64 ; receipts from Loans and miscellaneous sources, $220661.39. Expenditures. — For war purposes, $124088.36 ; for soldiers' allotments, $109072.31 ; for civil services, $400732^45. Required the balance in Treasury, Jan. 1, 1863. 7. The area of Ireland is 32481 square miles, and 5023984 acres are uncultivated. How many more acres are cultivated than 3 times the number uncultivated, there being 640 acres in one square mile 1 8. In 1861 England paid the United States $132741160 for cotton ; Egypt, $6225330 ; and India, $31165565. In 1863 she paid the United States $2302290; Egypt, $32996465, and India, $110258560. How much less was paid for cotton by England in 1863 than in 1861 ? 9. Western Virginia embraces 51 counties, in which there were, Oct. 1, 1863, 368623 whites, 3981 free colored persons, and 20606 slaves. What was the average population in each county ? 10. During the six months ending March 1, 1864, 1020000 quarters of wheat were exported from the United States. How many vessels, each carrying 600 short tons, were re- quired to ship the same ? 11. The city of New York paid taxes from 1858 to 1864 amounting in the aggregate to $64445967.34. The proper- ty upon which these taxes were assessed amounted to $531194290 in 1858, and $594196863 in 1863. How much less than the taxes was the increase of property ? 12. The number of pupils in Girard College in 1857 was 295, and the expenses for the year were $88173 ; in 1862 the pupils numbered 400, and the expenses that year were $73247. How much less was the expense per pupil in 1862 than in 1857? 13. There were in operation, Jan. 1, 1862, in the Nev,^ ARITHMETICAL EXAMPLES. 21 England States 3641 miles of railroad ; in New York, 2769; in Pennsylvania, 2918 ; in Virginia, 1729 ; in Georgia, 1419 ; in Tennessee, 1253; in Ohio, 4232; in Indiana, 2169 ; and in Illinois, 3041. What was the aggregate number of miles in operation in all these States ? 14. The total length of railroad in operation in the United States, Jan. 1, 1862, being 33222 miles, what was the aggre- gate number of miles in all the other States not mentioned in the preceding Example ? 15. The total cost of the Atlantic Telegraph Cable, as originally made, was $1258250, of which 10 miles deep-sea cable was made at a cost of $1450 per mile, and 25 miles shore-ends at $1250 per mile ; the cost of the remainder was $485 per mile. How many miles of cable were made ? 16. If a house is worth $2500, and the farm on which it stands, 3 times as much, lacking $500, and the stock, one half as much as the house and farm, what is the value of the whole 1 17. The population of Boston in 1862 was 177812; of New York, 805651 ; of Philadelphia, 562529; of Baltimore, 212418; of New Orleans, 168675; of St. Louis, 160773; of Cincinnati, 161044, and of Chicago, 109260. What was the entire population of these cities ] 18. The product of three numbers is 535^500 ; one of the numbers is 68, and another 75. What is the third 1 19. Forty Michigan regiments, whose original strength was 35630 men, lost in 1861-'62, 771 men in battle, 1810 by disease, 370 missing, and 3791 were discharged. What was the total loss in two years, and, making no allowance for re- cruits, what was the entire strength of those regimentSj Jan, 1,1863? 20. The population of the New England States in 1860 was as follows :— Maine, 628279 ; New Hampshire, 326073 ; Vermont, 315098; Massachusetts, 1231066; Rhode Island, 22 ARITHMETICAL EXAMPLES. 174G20; Connecticut, 460147. Required the entire popula- tionc 21. The Pennsylvania Central Railway is 356 miles long, and cost $31450000 ; the New York Central Railway is 655 miles long, and cost 138825000 ; the Illinois Central is 708 miles long, and cost $31280000, and the Michigan Central is 329 miles long and cost $14000000. Required the aggregate length and cost of these four roads. 22. Of libraries containing 10000 volumes and upwards, Massachusetts has 20, containing an aggregate of 614415 vols.; Connecticut 6, containing 102373; Rhode Island 3, containing 69868 ; Maine 3, containing 40700 ; New Hamp- shire 2, containing 25679, and Vermont 1, containing 10000. What is the aggregate number of volumes in these libraries, and how many more in tho libraries of Massachusetts than in those of all of the other New England States ? 23. In Illinois in 1862 there were 9811 public schools, which were attended by 519983 scholars. What was the average number in each school ? 24. A man invests in trade at one time, $680 ; at another time, $820; at a third time, $1580, and on a fourth occasion $420. How much must he add to the sum of these that the amount may be increased three-fold ] 25. The Coast Survey issued a certain number of hydro- graphic maps and charts in 1863, of which 3000 were delivered to the marine transportation service, 4 times as many -f 300 to the military authorities, and the remainder, which was 650 less than one-half the whole number issued, to the naval service. What number of maps and charts were issued ? 26. What number is that which, being divided by 24, the quotient increased by 25 + 1, the sum diminished by the dif- ference between 40 and 27, the remainder multiplied by 4, and the product divided by 11, will give 12 for a quotient ? 27. France, with a population of 36000000 in 1861, had a national debt of $61.28 per capita. Required her national debt. ARITHMETICAL EXAMrLE^. 23 28. The annual interest upon the national debt of France was $110000000. How much was the annual interest to each person ? 29. Colorado Territory, organized Feb. 28, 1861, was formed of 47657000 acres formerly included in the territories of Utah and Kansas, 10262400 acres in that of Nebraska, and 8980600 acres formerly in New Mexican territory. Required, the number of acres and square miles in Colorado Territory. 30. There were 10869 miles of railway in Great Britain in 1862, the receipts from which were 28565355 pounds sterling. Reckoning a pound sterling worth $4.86, how many dollars were received per mile ? 31. A man worth $12750 received a legacy of $8000 ; he spent $456 in traveling, and gave $1000 to a college. How much money had he left ? 32. The number of 1 and 2 cent internal revenue stamps sold in 1863 was 70036697, the value of which was $1146- 738.69 ; the number of 3 to 20 cent stamps was 23065021, valued at $1520440.18, and of 25 to 40 cent stamps 3745355, worth $1009039.65. Required, the number and value of the stamps of these denominations. 33. Connecticut made, during the year 1863, an aggregate monthly payment of $70636 to the families of 8333 soldiers. How much was the average amount paid to the family of each soldier ? 34. The population of the States in 1860 was 31224885, there being 241 representatives, how large a represen- tation should New York have, whose population was 3880735 1 35. Divide 900 +- (34 -h 2) X 5 by (75-4-5) + (4 x 12) -33. 36. In Vermont during the month of August, 1863, 7071 men were drafted ; 3583 of these were exempted, 557 failed to report, 145 cases were undecided, and 5 died ; the remain- der were held to military service ; of these 1833 paid com^ 24 ARITHMETICAL EXAMPLES. mutation, and 630 furnished substitutes. How many entered the service personally ? 37. There is an island 40 miles in circumference. A and B commence traveling around it at the same time and place, but in different directions, A at the rate of 4 miles an hour, and B, 5 miles. How far apart will they be at the end of 7 hours ? 38. The entire coinage of the U. S. Mint and branches from the commencement of their operations till June 30, 1863, was as follows : At Philadelphia, 768279944 pieces were coined, valued at $509602439.14; at San Francisco, 15136912 pieces, worth $165459288.20; at New Orleans, 94890695 pieces, worth $70271652.13; at Charlotte, 1206954 pieces, worth $5048641.50; at Dahlonega, 1381750 pieces, worth $6121^ 919.00 ; and at the Assay Office, New York, gold and silver in various forms worth $133131557.35. Eequired the whole number of pieces and their value. S9. A grocer bought 25 barrels of sugar at $25 a barrel, and 34 barrels at $22 a barrel. How much' would he gain by selling the whole at $27 a barrel ? 40. What is the area of New England, there being in Maine, 31766 square miles ; in Vermont, 9056; in New Hamp- shire, 9280 ; in Massachusetts, 7800 ; in Rhode Island, 1046 ; and in Connecticut, 4730 ? 41. The • cavalry and artillery furnished by Illinois up to Jan. 1, 1863, amounted to 20916 men, and the cavalry was 12918 more than the artillery; the infantry was 985 more than 7 times the cavalry. How many men had Illinois fur- nished for the war, Jan. 1, 1863 1 42. A drover bought cattle for $19800, and sold a certain number of them for $15360, at $96 per head, gaining thereby $960. How much did he gain per head, and how many cattle did he buy 1 43. The exports of flour and wheat from the United States to Great Britain were as follows: in 1861, 2561661 barrels AHITHMETICAL EXAMPLES. 25 of flour, and 25553970 bushels of wheat; in 1862, 2672515 barrels, and 25754709 bushels; in 1863, 1479413 barrels, and 23107190 bushels. How many more bushels of wheat than barrels of flour were exported in the three years ? 44. Bought 600 bushels of potatoes for $540, and sold 360 bushels at $1.25 per bushel, and the remainder at cost. How much was gained by the transaction ? 45. In 1862 Ohio sowed 69374 acres of barley, from which 763114 bushels were produced; 2266129 acres of corn were planted, which yielded 74782257 bushels. How much greater was the yield of corn than barley per acre ? 46. Jan. 1, 1863, there were 507 banks in the Eastern States, 491 in the Middle States, 167 in the Southern States, 307 in the Western States. How many more banks in the Eastern and Middle States than in th^. Southern and Western States ? 47. The sum of the killed and prisoners in the Union army at the battle of Stone River was 3496, and the prisoners were 548 more than the killed. The wounded were 747 more than three times the prisoners. The whole Union force en- gaged being 43500, how many were left for duty after the battle ? 48. In 1864 there were 237 members of Congress, and the salary of each member was $3000. How much did they all receive ? 49. The United States contain an area of 2819811 square miles, and in 1860 there were 11 inhabitants to the square mile. What was the entire population ? 50. The New England States have 35 libraries, containing 863035 vols. ; the Middle States, 28, containing 763733 ; the Southern States, 24, containing 503563, and the Western States, 17, containing 273109. What is the average number of volumes in these libraries ? 51. A mechanic earns $75 a month, but his necessary ex- 2 26 ARITHMETICAL EXAMPLES. penses are $50 per month. ITow long will it take him to pay for a farm of GO acres worth $40 an acre ? 52. A grocer wishes to put 1280 pounds of tea in 4 kinds of boxes, containing respectively 7, 9, 10 and 14 pounds, using the same number of boxes of each kind. How many boxes can he fill ? 53. In 1860 there were made in the United States 1860000 gallons of wine, valued at $2.50 per gallon. How many school houses, worth $T50 each, could be built with the pro- ceeds 1 54. The United States paid $61000 for the site of the Cus- tom House at Kichmond, Va., and contracted for the building for $110000; the total expense to the Government June 1, 1861, was $252016. How much did the cost exceed the price agreed upon? 55. The population of New Orleans in 1850 was 116375 ; in 1855, 139190, and in 1860, 168675. How much more was the increase in the last five years than in the previous five years ? 56. In 1861 the importation of specie into the United States was $46339611, and the exportation $29791080. What was the excess of importation over exportation 1 57. $16415052 specie was imported in 1862,and $86886956 was exported. How much more was the excess of exporta- tion in 1862 than the excess of importation in 1861 ? 58. In 1863, $9555648 specie was imported, and $64156610 was exported. What was the excess of exporta'tioti over im- portation for the three years ] 59. In 1862 there were sent out from the Dead Letter Office for delivery 10475 letters, containing $46538.90 ; of these 8766, containing $41068.48 were delivered, 1593, containing $5095.74 were returned to the office, and guerillas appropri- ated the remainder. What was the average amount in each letter lost ? ARITHMETICAL EXAMPLES. 27 60. Gunpowder was invented in the year 1330. Iron was discovered B. C. 1406. What period of time elapsed between these two events 1 61. Of the appropriation for the Custom House in Galveston, $1640.18 was unexpended, $6000 was paid for the site, and the building cost $17850.75 more than the contracted price, which was $90509.07. What was the appropriation 1 62. M. Smith rented a sugar orchard containing 1500 trees, agreeing to assume all the necessary expenses in making sugar, for one-half the quantity made ; he made on an average 3^ lbs. to each tree, and sold his part of the first 3000 lbs. made for 25 cents a pound, and the remainder at 20 cents; he paid $60 for labor, $30 for team work, and burned 25 cords of wood worth $2 a cord. How much was his gain 1 63. A horse dealer gave $8448 for a certain number of horses ; he sold a part of them for $7650 at $90 each, and by so doing lost $6 a head.^ For how much must he sell the re- mainder per head to gain $252 on the whole ? 64. The expenditures of the Post Office Department in 1860 were $14874772.89, and the gross revenue $9218067.40. How much greater than the revenue were the expenditures ? 65. In 1861 the expenses of the Post Office Department w^re $13006739.11, and the gross revenue, $9049296.40. How much more had the expenditures decreased than the revenue from the previous year 1 66. In 1062 the expenditures were $11125364.13, and the revenue $9012549.56. How much nearer self-supporting was the Post Office Department in 1862 than in 1861 ? 67. In Massachusetts 32079 men were drafted in 1863; of these 22343 were exempted, 3046 failed to report, and the remainder were held for service ; of these 743 served person- ally, 2325 furnished substitutes, and the remainder paid $300. How much commutation money did the Government receive? G8. Jan. 1, 1863, Rhode Inland had furnished 3147 men for 28 ARITHMETICAL EXAMPLES. three months, 2069 for nine months, and 9410 for three years ; during the year 18G3, 124G men were obtained by draft, 716 recruits were sent to regiments in the field, and two new regi- ments were formed, containing 1800 men; 425 enlisted in other States, and 1400 were in the navy. What was the aggregate number of men furnished by Rhode Island for the war up to Jan. 1, 1864? 69. What must the number be which divided by 453, will give the quotient 307, and the remainder 109 ? 70. A has $310; B, $558, and C, $744, with which they agree to purchase horses at the highest price per head that will allow each man to invest all his money. How many horses can each man buy ? 71. Of 3003 cases admitted into the retreat for the insane at Hartford, Connecticut, 574 were married males, and 728 were single, 704 were married females, and 730 single ; the remainder were widowed; the whole number of females ex- ceeded the whole number of males by 279. Required the number of widowed males and females, 72. The receipts of the U. S. Treasury for 1863 were as follows: Customs, $69059642; Public Lands, $167617; Direct Tax, $1485104: Internal Revenue, $37640788; Mis- cellaneous, $3046615; Loans, $776682362. Required the total receipts. 73. The expenditures for the same period were as follows : Civil List, $6350618.78; Foreign Intercourse, $1231413.06; Miscellaneous, $15671890.24 ; Interior Department, $4216- 520.79; War Department, $599298600.83 ; Navy, $63211- 105.28 ; on account of Public Debt, $205816482. Required the aggregate expenditures. 74. The balance in the Treasury at the beginning of the year was $13043547. What was the balance at the end of the year, the receipts and expenses being as is stated in the preceding examples'? 75. The State of Delaware received $60385.51 for general ARITHMETICAL EXAMPLES. 29 expenditures, in 1861, and $37424.99 for educational purposes; the expenditures for general purposes were $38989.05, and so much was expended for school purposes that the balance in Treasury Jan. 1, 1862, was $21396.46. Eequired the sum expended for education 1 76. The gold coin made at the U. S. Mint in Philadel- phia in 1863 was as follows: 152963 double eagles, 3658 eagles, 6902 half eagles, 39 three-dollar pieces, 20990 quar- ter-eagles, and 1950 dollar pieces. What was the whole number of pieces made and their value 1 77. The silver coin made at the mint in Philadelphia in 1863 was as follows: 31400 dollars, 425260 half-dollars, 412860 quarter-dollars, 49460 dimes, 64460 half-dimes, and 93460 three-cent pieces. Required the whole number of pieces and their value. 78. At the branch mint in San Francisco in 1863, 866423 double-eagles were coined, 9000 eagles, 16500 half eagles, and 4000 quarter-eagles. Required the number of pieces and their value. 79. During the year 1863 there were coined at the branch mint in San Francisco, 1542000 half-dollars, 43000 quarter- dollars, 291250 dimes, and 100000 half-dimes. How many pieces of silver were coined, and what was their value 1 80. In 1863, 47845000 cents were coined in the United States; $1949877.90 of gold and $390204.42 of silver were coined at the Assay Office, New York ; the coinage of the U. S. Mint and branches being as stated in the four preceding examples ; what was the value of the entire coinage of 1863 ? 81. A flour merchant bought 2000 barrels of flour at $9 a barrel, and sold 1200 barrels at $10, and the remainder at $8 a barrel. How much was his gain 1 82. What was the value of gold and silver of domestic production in 1863, if $2093590.69 was deposited at the mint in Philadelphia, $18207316.21 at San Francisco, and $1379448.60 at the Assay Office. New York ? 30 ARITHMETICAL EXAMPLES. 83. The sum of two numbers is 2487, and the greater is 553 more than the less. What are the numbers? 84. The Internal Revenue collected for the year ending June 30, 18G3, was $40993954.97. The total receipts to Aug. 31, 1863, were $47489473.03 ; to Sept. 30, $53625678.- 46. How much less was received in September, than in July and August ? 85. A cistern containing 1260 gallons has two pipes. By the first 48 gallons run into the cistern every half hour, and by the second 36 gallons run out in an hour. In how many hours will the cistern be filled 1 86. A man sold 600 bushels of wheat at $1.50 a bushel, and took his pay in sugar at 12 cents a pound ; he afterward sold one-half his sugar. How much had he left ? 87. The number of men sent by Vermont to the war was as follows : One regiment of 3-months men, numbering 782 ; 5 regiments of 9-months troops, containing 4833 men ; one regiment of cavalry, 966 strong ; 2 batteries, containing 286 men; 3 companies of sharpshooters, averaging 100 men each; 10 regiments of 3^years men; and 2740 recruits for regiments in the field ; making the total number of men fur- nished for the war, up to Oct. 1st, 1863, 19607. What was the average strength of the 3-years regiments ? 88. The quota of Vermont under the first call for 500000 S-years volunteers was 8950 ; under the second call for 300000 3-years volunteers, 4898, and the same under the call for 300000 9-months volunteers. To meet the first two requisi- tions the State furnished 13992 men, and under the last call 4834 9-months men. How much in excess of her quota was Vermont, 4 9-months men being equivalent to 1 3-years man ? 89. From 340 -f (20-4) x (8 + 2) take 36-h3 + (28 xQ)~ (19-5.) 90. A tailor made 2804 pairs of pants in four successive years, making each year 50 pairs more than during the pre- vious year. How many pairs did he make each year 1 ARITHMETICAL EXAMPLES. 31 91. The expenditures for educational purposes in New York for the year 1801, were $3842270.81 ; in New Jersey, |540- *283,80; in Pennsylvania, §2389383.00, and in Delaware, $85333.03. How much more was expended in New York than in the other three States ? 92. The State debt of Maine at the outbreak of the rebel- lion stood as follows : Debt incurred during the Aroostook war, $449000 ; debt due Massachusetts for lands, $250000, The war debt for 1861 was $800000 ; during 1862, $27000 of this debt was paid, and there was added to the war debt in 1863, 1950000. What wds the total debt of the State, Jan. 1, 1863, and Jan. 1, 18641 93. How many pounds of sugar at 20 cents per pound, must be given for 5 pieces of cotton cloth, containing 44 yards each, at 42 cents a yard ? 94. A man bought 750 acres of land at $20 per acre ; he sold at one time 325 acres at $23 per acre, at another time 260 acres at $25 per acre. At what price per atire must he sell the remainder to gain on his purchase $1945 1 95. According to the census of 1860, there were in the United. States 13869434 white males and 13133890 females; 234000 free colored males and 253996 free colored females ; 1982625 male slaves, and 1971135 female slaves. How many more males than females in the United States ? 96. 250 X 6-^(4 X 16)4-(8 x 2) + (25 x (8 -^ 4))= how many? 97. In 1860 New Jersey cultivated 1039086 acres, worth $180281421 ; Maryland cultivated the same year 1833306 acres, worth $145976990.25. How much were the farms of New Jersey worth per acre more than those of Maryland ? 98. Divide 16 x 72 x 45 x 21 by 27 x 32 x 12 x 35. 99. The rebel army in the battle of Stone River lost one- fourth of all its forces engaged ; 3500 were taken prisoners, and four times this number was 2000 more than the killed and wounded. Required the Confederate fjrce in the battle. 32 ARITHMETICAL EXAMPLES. 100. Bought 60 yards of cloth at the rate of 2 yards for $5, and 80 yards more at the rate of 4 yards for $9 ; I im- mediately sold the whole at the rate of 5 yards for .$14; how* much did I gain ? 101. The quota of New Jersey under the various calls for troops was as follows: 1st requisition, 3123 ; 2d, 3138; 3d, 5230; 4th, 5230; and 5th, (drafted militia,) 10478. Under the first call she furnished 3105 men ; 2d, 3120; 3d, 760 1; 4th, 4644; 5th, 10714, and 1030 recruits for old regiments in the field were enlisted. How much in excess of her quota was New Jersey, Jan. 1, 1863? 102. Connecticut cultivated in 1862, 1830800 acres, laid out in 22885 farms, the total value of which was $91540000. What was the average value of each farm? Average num- ber of acres in each farm ? 103. A farmer exchanged 40 bushels of corn and oats, mixed in equal quantities, at $\.2o and $.95 per bushel respectively, for wheat and rye in equal quantities, at $2.25 and $2.15 per bushel respectively. How many bushels of wheat and rye did he obtain ? 104. Arkansas Post surrendered to Gen. McClernand, Jan. 11, 1863. The rebel loss in killed and wounded was 550, which was twice the Union loss, and the number of prisoners was 230 less than 6 times the loss in killed and wounded of both armies. What w^as the number of prisoners ? 105. A farmer bought an equal number of horses, sheep and hogs for $9600. He gave $108, $9 and $11 per head for them respectively. What was the number of animals bought ? 106. The population of the five largest cities in England in 1861 was as follows : London, 2803034; Liverpool, 443874 ; Manchester, 338346 ; Birmingham, 295955; Leeds, 207153. How many more inhabitants in London than in the four other cities ? 107. A and B invested $120 in lottery tickets, A paying $3 as often as B $5. C and D invested an equal sum, C paying ARITHMETICAL EXAMPLES. 33 $4 as often as D paid $6. They purchased tickets together agreeing to share the prizes in proportion to the sums invested by each. The prizes amounted to $7200. How much ought each to receive ? 108. The aggregate receipts of the Post Office Depart- ment for 1863 were $11163789.59, while the expenditures during the same time were $11314206.84. What was the net expense'? 109. A company in a fort numbering 75 men have provi- sions for 30 days. How many men must depart, that the same may last the remainder 45 days 1 110. The rebel loss at Gettysburg was reported 40121; the prisoners were 371 more than half the loss in killed and wounded, and 4 times the killed was 1000 more than the wounded. What were the respective losses in killed, wounded and prisoners 1 111. A merchant expended for cloth $7850. He sold a certain number of yards for $5580, at $15 per yard, and gained on those sold $1860. How many yards did he buy at first, and how much did he gain per yard on the cloth sold ? 112. A horse worth $120, and 4 cows at $28 each, were exchanged for 31 sheep and $46' in money. What were the sheep valued at per head ? 113. The quotient of one number divided by another is 74, the divisor is 321, and the remainder 95. What is the dividend 1 114. The mails of the United States in 1862 were carried 2001500 miles by steamboat, at an expense of $300225 ; by coaches 7268400 miles, for $1744416, and by railroad 22777- 200, for which $2505492 were paid. How much was . the rate per mile by each mode of transportation ? 115. General Meade reported the losses of the Union army at Gettysburg 23186. The number killed was 290 more than one-eighth of the sum of the losses in prisoners and 2* 34 ARITHMETICAL EXAMPLES. wounded, and twice the prisoners was 423 less than the wounded. How many were the killed, wounded and pris- oners? 116. Bought 17 cwt. of prunes at |15 per cwt., and gave in exchange for them 250 lbs. of butter at 25 cents per pound, 48 dozen eggs at 15 cents per dozen, and the remain- der in salt at $1.70 per bushel. How many bushels of salt were required ? . 117. The population of the seven largest cities in France in 1861 was as follows: Paris, 1696141 ; Lyons, 318803; Marseilles, 260910; Bordeaux, 162750; Lille, 131827; Nantes, 112625; Toulouse, 113229. How much did the population of Paris exceed that of the other six cities 1 118. What is the value of 16 x 3125— (49 x 7) + (125 x 27)— (9 X 32) +43264— 16 x 9 1 119. A trader purchased a lot of horses and oxen for $2000, paying twice as much for a horse as for an ox. There were three times as many oxen as horses, and the horses cost him |80 a head. Required the number of each. 120. Required the area of North America, if the United States contain 2988892 square miles; British America, 2914318; Danish America, 800000; Russian America, 394- 000; Mexico, 645822 ; and Central America, 219000. 121. S. J. Eaton bought 75 hhds. molasses at $18 per hhd. How much must he charge per hhd. to gain $300, and what will be the gain on each ? 122. What were the respective losses in the Union army in the battle of Chickamauga, 3 times the killed being 13 less than the missing, and twice the missing being 628 more than the wounded, and the whole loss 15851 ? 123. If the President of the United States expends daily $60, how much will he be able to save at the end of four years, his salary being $25000 per annum ? 124. The army pension rolls stood as follows, June 30, ARITHMETICAL EXAMPLES. 35 1863 : Invalid pensioners 7248, to whom $570048 was pay- able annually; Revolutionary soldiers, 18, to whom $1045 was payable ; widows of Revolutionary soldiers, 1573, amount payable to them $129684; widows, mothers, sisters and orphans, in wars since the Revolution, 4820, annual payment to the same $526266. What was the whole number of pen- sioners and the sum paid them ? 125. I exchanged 5 barrels of vinegar, each containing 32 gallons, at 25 cents a gallon, for 5 pieces of sheeting, each containing 40 yards. How much did it cost me per yard ? 126. In 1860 Virginia contained 19578964 acres of im- proved land, worth $371608736.72; Pennsylvania, 6548847 acres, worth $662022943.23. How much more were the farms worth per acre in the latter State than in the former 1 127. Required the actual value of my farm if $25344 is 6 times the sum I paid for it, and it cost me $776 less than its real value. 128. According to the census of 1860, 20875 of the popu- lation of New York city were born in the Eastern States, 397980 in the Middle States, 1941 in the Western States, 4881 in the Border States, 1353 in the Seaboard Slave States, 882 in the Southwest Slave States, and 2130 in the territo- ries. How many of the inhabitants of the city were natives of the United States ? 129. The foreign born in New York city in 1860 were as follows: natives of Germany, 119984; of Great Britain, 244- 826 ; of Contmental Europe, 17235, and of various other countries 1672. Required the total foreign born. 130. The population of the city was 629904 in 1855. How much was the increase in 5 years, the population in 1860 being as stated in Examples 128 and 129? 131. Ten men agreed to gather 1000 bushels of cranberries, and to receive for their labor one-half the quantity gathered. After 400 bushels were gathered 4 men withdrew, leaving the 3G ARITHMETICAL EXAMPLES. . Others to complete the job. How many bushels should each man receive ] 132. F. Harriman purchased 318 acres of wild land for $6996, and sold 253 acres at $17 per acre, and the remainder at cost. Did he gain or lose, and how much 1 133. Durmg the year 1863 $2876983 was paid to post- masters, and $6541580 for mail transportation. The expen- ditures bemg $150417 in excess of the revenue, which was $11163789. How much was expended for miscellaneous purposes ? 134. Having money to invest I buy 2 farms worth $4550 each, 20 shares railroad stock at $106 per share, and have $250 left. How much had I at first ? 135. The navy pension rolls for 1863 showed that 545 navy invalids were paid $35019; 577 widows or children were paid $107886, and 10 privateer pensioners were paid $622. How many pensioners were there, and what was the amount paid? 136. How many barrels of apples at $4 per barrel must be given in exchange for 10 bags of wheat, each containing 3 bushels at $2 per bushel ? 137. During the first three months of 1864 there were 27 gold mining companies organized in New York city, with an average capital of $2350000 ; 4 silver companies, with an average capital of $3625000 ; 8 coal and iron companies, whose average capital was $1250000, and 4 copper companies, with an average capital of $625000. How much capital was invested in mining companies during the three months ? 138. What is the number of subjects belonging to the Russian Government, there being 66891493 in Europe, 8203- 197 in Asia, and 54000 in America? 139. How many sheep at $3,621 must be given in exchange for 58 cows at $40 each ? 140. The first settlement in the United States was made ARITHMETICAL EXAMPLES. 37 in 1565. America was discovered by Columbus in 1492. How many more years from the first settlement to the Dec- laration of Independence in 1776, than from the discovery to the first settlement 1 141. A groc«r in packing 6 dozen dozen eggs, broke half a dozen dozen, and sold the remainder at 20 cents a dozen. How much did he receive for the eggs 1 142. What are 30 hogsheads of molasses worth at $.75 a gallon, if each hogshead contains 68 gallons ? 143. A speculator paid $6569.64 for a quantity of wheat ; he sold 1480 bushels at $2 a bushel, and the remainder stood him in $1.42 a bushel. How many bushels did he purchase ? 144. During the year 1862, 60021250 l-cent, 183740250 3.cent, 1029300 5-cent, 4058450 lO-cent, 1046750 12-cent, 984125 24.cent, 396040 30-cent, and 30940 90-cent stamps were issued by the Post Office Department. Eequired the whole number of stamps and their value. 145. During the same year the following number of stamped envelopes were issued: 1-cent, 3084400; 3-cent, 20963050 ;4-cent, 35000; 6-cent, 131850; lO-cent, 520050; 12- cent, 8400; 20-cent, 7850; 24-cent, 8800; 40.cent, 4100, and 195800 letter sheets and stamped envelopes combined ; the total value of all was $733265.50. What was the value of the combined letter sheets and envelopes ? 146. During the same time 2364850 1-cent newspaper wrappers were issued. What were the total receipts from stamps, stamped envelopes and wrappers ? 147. The receipts from stamps in 1861 were $5908522.60, and from envelopes, $781711.13. The receipts in 1862 from the same sources being as stated in previous examples, how much more was received in 1862 than in 1861 ? 148. A grocer gave 153 barrels of flour worth $9 a barrel for 81 barrels of sugar containing 1*^0 pounds each. What was the cost of the sugar per pound ? 149. In 1861, 10631 vessels, tonnage 1024726, arrived in 38 ARITHMETICAL EXAMPLES. the ports of Russia ; 10739 vessels, tonnage 1026794, departed from the same ports. What was the average tonnage of the vessels ? 150. If 850 men require 25500 rations of bread for a month, how many rations will a garrison of ^l 250 naen re- quire for the same time ] 151. In the month of Sept. 1863, on account of the Indian massacre, 6588 fugitives fled from the St. Peters district in Minnesota, one-ninth as many from the Minneapolis district, and in other districts 127 more than from Minneapolis. How many were made homeless by this massacre ? 152. From Jan. 1, to April 15, 1864, 27 gold mining companies were organized in New York with an aggregate capital of $63450000. What was the average capital of each company ? 153. Two persons, starting from the same place and travel- ing in opposite directions, are 20 miles apart at the end of one hour, but traveling in the same direction they are 6 miles apart at the end of an hour. How far does each travel per hour] 154. The population of France in 1861 was 37472732; of Algeria, 2999124; and of French colonies, 3062389. How many subjects had the French government ? 155. Three men rented a farm and raised 960 bushels of grain, which was divided in proportion to the rent paid by each ; the first was to have one-half of the whole, the second two-thirds of the remainder, and the third what was left. How much did each receive, the grain being worth $2 a bushel 1 156. During the year ending July 1, 1862, 9763 letters containing papers of value other than money, were sent to the dead letter office, and the following reasons were assigned for their non-delivery : Held for postage, 1050 ; misdirected, 1466 ; mails suspended, 326 ; refused, 26 ; name of post ARITHMETICAL EXAMPLES. 39 office omitted, 86 3 person addressed dead, 27 ; and the others were micalled for. IIow many of this last number were there ? 157. Gen. Grant reported the losses of the Union army in the series of battles connected with the taking of Vick^burg as follows: Port Gibson, 130 killed, 718 wounded, and 5 missing ; Eaymond, 73 killed, 365 wounded, and 32 missing ; Jackson, 40 killed, 240 wounded, 6 missing ; Champion's Hill, 426 killed, 1842 wounded, 189 missing; Big Black Bridge, 29 killed, 242 w^ounded, 2 missing, and the losses before Vicksburg made the entire loss 8875. This was so distributed that the total missing were 706 less than the killed, and the wounded were 25 less than 4 times the sum of the killed and missing. Required the number of killed, wounded and missing before Vicksburg. 158. The forward wheels of a carriage are 7 feet in circum- ference, and the hind wheels 10. How many times will each revolve in passing over 42 miles, there being 5280 feet in a mile 1 159. A man paid 11024 for a farm, 1250 for drainage, $50 for fencing, and for hired labor, $376. The gross proceeds of one year amounted to $2100 ; with the profits he purchased an equal number of sheep at $3 each, and horses at $77 a piece. How many of each did he buy 1 160. The population of Great Britain and Ireland in 1863 was estimated at 30000000, and the value of real and per- sonal property, $33402600000 ; at the same time the estimated population of the loyal States was 24000000, and the value of property, $13929840000. How much more property to each person in the United Kingdom than in the loyal States ? 161. The products of Great Britain and Ireland in 1863, amounted to $3340200000, and in the Loyal States to $3720- 000000. How much more was the value of the annual pro- ducts to each person in the loyal States than in Great Britain and Ireland ? 40 ARITHMETICAL EXAMPLES. 1G2. Suppose two locomotives start from the same place and move in the same direction, the first at the rate of 30 miles an hour, and the second 20 miles ; after the first has gone 150 miles it commences a backward movement with the same velocity till it meets the second engme. IIow far from the point of starting, and in how many hours do they meet 1 103. The Internal Revenue collected upon advertisements in 1863, at the rate of 3 cents upon a dollar, amounted to $40629. What was paid for advertising during the year 1 164. What number is that which being divided by 72, the quotient increased by 25, the sum diminished by the differ- ence between 25 and 18, the remainder multiplied by 7, and the product increased by (9 x 8) ^(3 x 4) the sum will be 167 ? 165. In Dec. 1862, the United States Navy numbered 427 vessels, carrying 3268 guns, tonnage 340036 ; in Dec, 1863, there were 588 vessels, carrying 4443 guns, tonnage, 467967. What was the increase in vessels, guns and tonnage ? 166. IIow many subjects are claimed by the British government, there being 29458442 in Europe, 4496741 in America, 1020525 in Africa, 173738866 in Asia, and 3423- 996 in Australia 1 167. In 1862 New Hampshire reported 2352 school dis- tricts, and 84672 children who attended school. Required the average attendance in each district. 168. Bought 25 sheep fur $56; how much less per head should I have paid, had I purchased 7 more sheep with the same money ? 169. According to the census of 1860, the population of Maine was 628279; New Hampshire, 326073; Vermont, 315098; Massachusetts, 1231066; Connecticut, 460147; Rhode Island, 174620 ; New York, 3880735. How many more inhabitants in New York than in New England ? 170. A and B pay $2.25 f )r a barrel of apples, and 20 cents for the barrel ; A contributes $1.25 and B the remain- ARITHMETICAL EXAMPLES, if J^ t^ 'v41 der. They divide the apples equally, and A ta^R^lhe Which owes the other, and how much ] V'^?^'^ 171. How many melodeons at ^QQ'l are worth a^^ifi'uch as 4 pianos at $333 i 1 172. It is estimated that the public lands of the United States amount to 2265625 square miles ; if cne-half of thi^ was donated to various purposes, and the remanider was sold at $1.25 per acre, w^hat would be the net income 1 173. It is estimated that the annual loss to the United States by intemperance is $98400000. How many school houses could be built, and schools sustained each year with this sum, provided that the cost of a school house and the yearly expenses of che school, were each $1200 1 174. At a certain election 5000 votes were cast for three candidates, A, B and C. B had 400 more than A, and C 300 more than B. How many votes did A receive ? 175. The income fi'om the various shops in Wethersfield State Prison for the year 1863, w^as $13026.80, the expendi- tures, $12065.30. What was the net income ? 176. The number of vessels belonging to the U. S. Navy which were captured by the rebels during 1863 was 12, car- rying 48 guns, tonnage, 5947 ; the number destroyed to pre- vent falling into the enemy's hands was 3, carrying 29 guns, tonnage 2983 ; sunk in battle, 4, with 28 guns, tonnage 2201 ; lost by shipwreck, 13, with 61 guns, tonnage 4854. Required the total naval loss during the year. 177.The revenue collected from railroads is 3 cents for every dollar of fare ; from this source $1029288 revenue was collected in 1863. What amount was received for passengers' fare? 178. In Rhode Island there are 400 school districts, and 29600 children attend schools. Required the average atten- dance in each district. 179. One-half the sum of two numbers is 500, and onQ-half their difference is 300. What are the numbers 1 % 42 ARITHMETICAL EXAMPLES. 180. The whole number of pupils attending the four normal schools of Massachusetts in 18G2, and the expenses of the schools were as follows: Frammgham, 104 pupils, expenses, ^3519; Salem, 140 pupils, expenses, $4020; Westfield, 179 pupils, expenses, 13119; and Bridgevvater, 141 pupils, expen- ses, $3977. What w^as the average expense per scholar? 181. The condition of the banks of New York city, April IG, 1864, was as follows: Loans, $198703099; specie, $2168700; circulation, $5779650; and deposits, $168350790. How much were the assets in excess of the liabilities ? 182. During the year ending June 30, 1862, the number of letters exchanged between the United States and Great Britain was 1485970 received, 1391386 sent; between the United States and France, 403275 received. 506461 sent. How many letters did the exchange with Great Britain exceed the exchange with France 1 183. The postage on mails sent to Europe in 1862 amount- ed to $573533.45; on mails received, $570562.37. The postage collected in Europe was $465744.23, and the remain- der was collected In the United States. How much more was collected in the United States than in Europe ? 184. The postage on mails transported by the Cunard line in 1862 amounted to $521854.78. What was the amount of postage on mails carried by other lines, the whole amount being as stated in Example 183 ] 185. There were in the State of New York in 1862, 11750 public schools, attended by 893000 pupils. Required the average attendance iil each school. 186. In 1862 there were 554 stone school houses in the State of New York, 964 brick, 10004 frame, and a number of log school houses, making the whole number 11750. How many less than one-fiftieth of the school housed were built of logs? 18X. In 1862 there were 21145212 acres of land in Ken- tucky, valued at $174187983. How much had the land de- ARITHMETICAL EXAMPLES. 43 creased in value per acre since 1861, when the average value was $10.34? 188. Wisconsin sent into the army before Nov. 1, 1863^ 34 infantry regiments, averaging 1001 men each ; 3 regi- ments cavalry, averaging 1290; 13 batteries, averaging IGl ; one company sharpshooters, numbering 147 ; and 2441 re- cruits for old regiments. The quota under all calls up to that date was 44661. How much did the State lack of filling its quota 1 189. Russia exported gold and silver coin and bullion, in 1861, amounting to 5790355 roubles. The imports for the same time were 7138395 roubles. How much did the im- ports exceed the exports, one rouble being worth 80 cents *? 190. A teacher having a school of 144 ladies and 128 gen- tlemen, divided it into the largest possible equal classes, so that each .class of ladies should number the same as each class of gentlemen. What was the number of classes ? 191. Ohio produced in 1862, 35442858 pounds of butter, worth on an average 20 cents a pound, and 20637235 pounds of cheese, worth 14 cents a pound. What was their aggre- gate value? 192. A farmer sold 34 bushels of oats and 26 bushels of corn for $63.10. He received for the corn 35 cents more per bushel than for the oats. What was the price of each per bushel 1 193. The value of all the exports of Russia in 1861, by maritime commerce, was 137702143 roubles; by overland commerce, 30473888 roubles. The value of the imports for the same year was, by maritime commerce, 115651243 rou- bles; by overland commerce, 44028013 roubles. How much did the value of the exports exceed the imports, a rou- ble being worth 80 cents ] 194. The number of letters exchangred between the United States and Europe, in 1862, was 2644039 sent, and 2556624 received, being a decrease of 945158 from the number re- 44 ARITHMETICAL EXAMPLES. ported the previous year. How many letters were exchanged in 1861 1 195. The Treasurer of Vermont made the fol'i owing report Sept. 1, 1863 : Balance in treasury, Sept. 1, 1862, $224250.- 41 ; receipts from ordinary sources during the year, $774- 327.30 ; on account of the war, $1853874.28. The disburse- ments were, for civil purposes, $281666.34 ; for war pur- poses, $2358682.69 ; interest, $89669.21. What balance did the Treasurer report ? 196. In New York, in 1863, 77862 men were drafted; 53109 were exempted, 14073 paid commutation, 6619 fur- nished substitutes, 1504 failed to report. How many entered the military service ? 197. Jan. 1, 1863, Pennsylvania had furnished men for the war as follows : 20979 3-months men ; Reserve Corps, 15- 856; under .call of July 22, 1861,93759; under requisition of July 7, 1862, 40383; under call of Aug, 4, 1862, 15100; recruits for old regiments, 9259. The Adjutant General, allowing for enlistments in other States, reported the whole number 200336. How many did he estimate enlisted out of the State 1 198. There were 476203 votes cast for two candidates for governor in Ohio, in 1863. The majority of the successful candidate was 101079. How many votes were cast for each ? 199. A speculator had 210 acres of land, which he might have sold at $220 an acre, and gained $6300, but after holding for a time, he sold it at a loss of $3150 ; how much per acre did it cost him, and for how much per acre did he sell it 1 200. A merchant bought 3 pieces of cloth of equal lengths at $5 a yard ; he gained $35 on the whole cost, by selling 2 pieces for $350 ; how many yards in each piece 1 CIIAPTEE III. 1. If 5| yards of calico cost 11.17, how much must be paid for 43 1 yards 1 2. Change y\ of j| of f f to an equivalent fraction, hav- ing 75 for its denominator. 3. If cloth 1.875 yards in breadth require 18.75 yards in length to make a certain number of garments, how many yards in length will it require if the cloth be .625 yards wide ? 4. In a certain school room, 1 of the desks are occupied ; I of the scholars study grammar; i study physiology; ^ study book-keeping ; and the remaining scholars are equally divided into 3 algebra classes. ^ of the most advanced alge- bra class study geometry, and there are 5 in the geometry class. What is the number of scholars in the school-room, and how many desks are unoccupied 1 5. j\ of a certain number exceeds ^ of the same by 156. What is the number ? 6. A certain sum of money is divided among 4 persons. A has I ; B, i ; C, | ; and D the remainder, which is $39. How much more has A than D1 7. A book publisher sold 2 dozen Webster's Unabridged Dictionary at $60 a do!zen, 15 dozen Robinson's Arithmetic at $9, and 10 dozen Testaments at $2; the actual cost of the books was $250. How much was his gain ? 8. I exchanged 14| cords of wood at $4^ per cord, for flour at $9 1 per barrel. How much flour did I receive ? 9. The product of 3 numbers is 112 ; one of them is 5|; another is 61. What is the third ? 46 ARITHMETICAL EXAMPLES. 10. Divide ±^Lili5_^ bv -"— - -5". I of 2^x31 ""y 7«gof3- 11. A can do a piece of work in | of a day ; B can do it in i of a day, and C can do it in 1 J days. In what time can all do it, working together ? 12. If 5i lbs. of coffee cost ll^g, what will 27i lbs. cost? 13. A merchant had $9000 with which to purchase goods. He bought 20 pieces of sheeting, each containing 44 yds., at $.12 per yard ; 400 pieces of calico of 31 yds. each, at $.17^- per yard ; 25 pieces of cassimere, each containing 38.75 yds., at $2,375 per yard ; 100 pieces of silk, each containing 29| yds., at $.95 a yard. How much money had he left ? 14. In 1864 Illinois packed 1273400 hogs, of an average weight of 200 pounds. How many car-loads would these make, 10 tons of 2000 pounds each loading a car? 15. How long a train would all the cars necessary to ship the pork mentioned in the preceding example make, allowing 25 feet for each car, there being 5280 feet in one mile 1 16. A and B engage in trade. A furnished ^q of the cap- ital, and B /g. If B should transfer $379| of his capital to A, their shares would be equal. How much did each furnish? 17. How many times can a vessel containing | of a gallon be filled from | of a barrel containing 31;^ gallons? 18. Add the following fractions : ^ of f , 2J, | of | of 5, I of f of 3i. 19. Bought a cord of wood for $4,625, a cheese for $7.- 56^, and 14^^^ lbs. butter at $.25 per lb. What was the cost of the whole ? 20. A man purchased a number of lemons at 2 cents each, and I as many at 3 cents each; he sold them all at the rate of 2 for 5 cents, and gained 25 cents. How many of each kind did he purchase ? 21. A can do a piece of work in 2| days, B can do it in 3 1 days. In what time can both, working together, do it ? ARITHMETICAL EXAMPLES. 47 22. What number is that from which, if 7^. be taken, the remainder will be 9| ? 23. Find the sum of forty -nine and three-tenths, four hun- dred, and three millionths, subtract from it two hundred forty-six, and three thousandths, multiply the remainder by five thousand, and divide the product by four ten-thousandths. 24. In New Jersey 137578 children attended the public schools in 1861, and the total expenditures for school purpo- ses were $510283; in 1862,132590 children were in the public schools, at an expense of $562259. How much more w^as the expense per scholar the latter year than the former ? 25. Peter can do a piece of work in 1| days, Martin in j^^j of a day, and Jacob in 2 days. They commence the work together, btit Martin ceases to labor after working | of a day, and Jacob quits after having performed J of the task, when Peter completes the work. How long does Peter work ? 26. If 3 horses eat 2^ bushels of oats in 2 days, how many horses will eat 34| bushels in 8 days ? 27. From one take two ten-millionths. 2- X - 28. Reduce ~-f-kt to a decimal fraction. I of 3} 29. In the Massachusetts State Prison, for one year, $30958 was paid for salaries, $18468 for provisions, $7489 for cloth- ing, and $26432 for miscellaneous purposes ; $53655 was received for the labor of the convicts. How much were the net expenses of the prison ? 30. If a family of 9 persons consume 0S^\ lbs. butter in 41 weeks, how many pounds will each person consume per week 1 31. If I of a bushel of corn be worth ^ of a bushel of wheat, and wheat be worth $1.40 a bushel, how many bushels of corn will $27 buy ? 32. After spending ^, | of f , and j\ of my money, I had $484 left. How much had I at first ? 48 ARITHMETICAL EXAMPLES. 83. What is the continued product of 9_ 174^ 44f 40j^ 381 ^ 1 96T ^ 101 ^ 'm}^ 34. What number is that from which, if 1 1 be subtracted, J of the remainder will be 42 ? 35. How many yards of carpeting li yds. wide would be required to carpet a room 6i yds. long and 5| yds. wide? 36. Bought 12 yds. of cloth at $.371 per yard, and agreed to pay 1 of the cost in butter, at I.16| per pound ; } in money, and the remainder in eggs, at $.121 per dozen. How many pounds of butter and dozens of eggs were required ? 37. If 21.65 tons of hay are sold for $10821, what will 1 ton cost ? 38. What will 42.875 yards of cloth cost at $5i per yard 1 39. What is the profit upon one million spelling books, at $.006 per book ? 40. If fy of a tub of butter cost $3.55, what will 9 tubs cost? 41. Samuel Smith has 99.875 acres of land in one field, 163.625 acres in another, and 243.1678 acres in a third. How much land must he purchase to have 640 acres ? 42. A farmer sold at one time 7 tons and 375 thousandths of a ton of hay, at another time 12 tons and 3125 ten-thou- sandths of a ton, and at a third time 13 tons and 3125 hun- dred-thousandths of a ton, at an average price of $8 per ton. How much did he receive for the whole ? 43. What is the sum of 2i decimal units of the first order, 4f of the second order, 7 Jg of the third order, and 92^5 of the fourth order ? 44. How many pairs of pants can be made from 48.6 yds. of cloth, allowing 1.8 yds per pair? 45. I purchased a quantity of grain, f of it being oats, at $.75 a bushel ; j\ wheat, at $1.50 a bushel, and the remahi- ARITHMETICAL EXAMPLES. 49 der barley, at $.90 a bushel, to the amount of $7,425. How- much did I pay for the whole ? 46. A owns f of a ship ; he sells | of his share for $1800. What is the value of the ship ? 47. A can perform a piece of work in 9 days ; A and B together can do the same in 6 days ; A, B and C working to- gether can do it in 4 days. In how many days can B and C, working together, perform the whole ? 48. What is the sum of 5^\ decimal units of the first order, 6/3 of the second order, 7y9g of the third order, 8f of the fourth order, 9| of the fifth order, and 3^ of the sixth order ? 49. Multiply the sum of the quotients of 270-^-4000; 1807-^.008; .0103-^.04 ; 70.306-^.5; 3.78-^200; .04735 -^.0005; 30^.004; 903^30000 by 25.25. 50. There are two numbers whose sum is l^^,^ and whose difierence is 4^. What are the numbers ? 51. A, B and C own a furnace ; A owns /_7j of it ; B owns ^3- of it more than C. What parts of the fiirnace do B and C own respectively ? 52. X and Y traded in company. X put in merchandise valued at $8000, and Y put in $20000 cash. They agreed to share the gains or losses equally. At the end of two years, the business proving unsuccessful, they dissolved partnership, and found the losses amounted to $11500. Wliat was each partner's share of the remaining property ? 53. In the thirty-eighth Congress, 1864, the House of Rep- resentatives was divided into two parties, so that J of the number in one was equal to |-f the number in the other, and there were 177 members. Required the number of each party. 54. What is the sum of the continued products of f x 4| x 2i f xf Xx\ and 3|xf x^^ 50 ARITHMETICAL EXAMPLES. 55. A man having $06, gave A $5 more than J of the whole; B $2 less than | of the remainder; C $12 more than I of the remainder, and the rest he gave to D. How much did each receive ] 50. The transactions of the Treasury of the State of New York, in 1863, were as follows: Balance in Treasury at the hecrinning of the year, $5750621.19; receipts during the year, $18656285.17; payments, $20703585.84. How much less in Treasury, Jan. 1, 1864, than Jan. 1, 1863? 57. Multiply 1 of/, of 11 by j% of jf of A|. 58. A teacher spends | of his salary in board for himself and family, -^L jn clothmg himself, his wife's clothing costs f as much as his own, his daughter's, l as much as his wife's ;. his son's, | as much as his daughter's, and he lays by $115. What is his salary ? 59. The marble used in the Capitol extension, Washington, had cost, Jan. 1, 1863, $1029041, and the cutting and the set- ting of the same, $1373749 more; 19403800 bricks had been used, worth $7.50 per thousand, and the new iron dome cost $900000. Required the sum of these expenditures. 60. Divide 172170063 by .0000009. 61. What will 15}-} doz. eggs cost at 18i cents per doz. ? 62. Add nine ten-thousandths, 1000 and six-million ths, 3 and forty-seven ten mill ion ths, 246 and twenty -five-thousandths. 63. John Brown killed an ox, which, when dressed, weighed 1178f lbs., he kept | of it for his own use, and sold | of the remainder to Hiram Jones. What was the value of the re- mainder at 11^ cents per pound? 64. A merchant purchased 17 bales of cotton goods con- taining 587A yds., at 8| cents per yard ; he sold | of it at 11^ cts. per yard, and | of the remainder at 12 i cts. per yard. How much would he receive for what still remained at 1 3 cents per yard and what profit would the merchant make on his bargain ] ARITHMETiCAL EXAMPLES. 51 65. Fanny Church disposed of $38.88f as follows : She gave ^ of it to the Sanitary Commission, | of the remainder to the Christian Commission, and the remainder she divided equally among 7 poor women. How much did each woman receive ? 66. What number must be multiplied by 9^ x Si, that the product may be 100? 67. A boy in flying his kite lost | of the string, then added 65 feet and found that it was just | of the original length. What was the length at first ? 68. A and B, being 133 miles apart, travel towards each other, both starting at the same time. They meet at the end of 10 hours, and find that A has traveled 1| miles more than B each hour. How many miles did each travel 1 69. California cultivated, in 1861, 361350 acres, of wheat, which produced 8816940 bushels, and 20780 acres of potatoes, from which 1298750 bushels were harvested. Allowing the expense of cultivating an acre of each to be the same, the wheat worth $1.75 per bushel, and the potatoes $.60, how much more profitable per acre was the wheat than the potato crop? 70. A barrel holding 31^ gallons is J full ; 9 J gallons being drawn off, what part of the contents remain ? 71. Reduce to their lowest terms H|f|; |f}; |H^ and 1389 3 7 4* 72. Three men. A, B and C, start from the same point to travel around an island 100 miles in circumference ; A travels 22| miles each day; B, llf miles, and C, 12^ miles. Re- quired the least number of days in which all will be together at the point of starting, and how many times each will have t-'^veled around the island. 73. If at each stroke of the piston rod of a locomotive engine a distance of 15.625 feet be passed over, how many strokes must be made in passing from New York to Washing- 52 ARITHMETICAL EXAMPLES. ton, the distance being 225.25 miles, allowing 5280 feet in each mile? 74. If the circumference of the truck wheels of an engine be 8.8 feet, and of the drivers 21.3 feet, how many more times will the one revolve than the other, in running from New York to Albany, the distance being 150 miles? 75. The enumeration of youths of school age in Ohio in 1857 was 8-]8037; the enrollment of those in attendance was 003347, and the average attendance, 350867. In 1862 the enumeration was 920890; enrollment, 723669, and average attendance, 433343. Required the-> respective increase in enumeration, enrollment and average attendance. 76. If I of J of an acre of land sell for |16yVo5 what is 5 times i of i^ of an acre worth at the same rate? 77. S. Smith being asked how many sheep he had, replied that he Tiad them in 4 fields ; in the first there were 5 less than ^ of the whole number of sheep ; in the second i as many as in the first ; in the third | as many ; and in the fourth there were 30 sheep. How many sheep had he ? 78. A. wifiM spent ll$.81 f#re^u«rf qiimitities of butter and lard; for the butter he paid $.18 per lb., and for the lard, $.15 per lb. How much of each did he buy ? 79. A had $576, which was $156 more than | of 2i times B's money. How much money had'B ? 80. If i of John's marbles equals | of James', and both to- gether have 44 ; how many marbles has each 1 81. If one yard of sheeting cost 18| cents, how many yards may be bought for $1.31 1 ? 82. The State of Kansas paid $14009.67 for teachers' sala- ries in 1862, and $1747.23 for incidentals. The district taxes amounted to $10381.81, and the school fund, $4148.45. How large a school debt remained to be provided for the next year? 83. It is 116,-'^^- miles from New York to Hudson, and 74 Jf ARITHMETICAL EXAMPLES. 53 miles from New York to Poughkeepsie ; how many miles from Poughkeepsie to Hudson ? 84. 41 1 is the f part of what number? 85. A owns j\ pf a cargo worth |23426i ; B owns f of a steamboat worth 1174251. They exchange stocks. How much money must A pay to B ? 86. A father divided $3000 among his 6 sons so that each elder brother had $100 more than his next younger brother. Required the share of the youngest. 87. Bought S3 baskets of peaches, each basket containing J of a bushel, at $1.37i per bushel. What was the cost? 88. From 23| bushels, subtract the sum of f and 4| bushels. 89. If a man earns $56 in j\ of a month, how much does he earn in one week, allowing 4 weeks to a month ? 90. A merchant in selling lOf lbs. sugar at the rate of 8 lbs. for $1, gains 17 cents; what was the cost of the sugar per pound. 91. When potatoes are worth $.87| per bushel, and corn $1.16|, how many bushels of corn will a farmer receive in exchange for 28 bushels of potatoes ? 92. If 9 horses eat | of 7^ bushels of oats in a day, how much does each horse eat ? 93. Bought i of 3]f cords of wood for f of $17^. How much did one cord cost ? 94. If 1.75 acres produce 6.51 tons of hay, how many tons will 7.625 acres produce ? 95. A man bought 43f yds. of carpeting for $58i ; he sold I of the piece, gaining $.16| on each yard sold. How much did he receive for it ? 96. If 28 men build a bridge in 4| days, how many men could build the same in 2| days ? 72_4i 73 97. Reduce 7^-^^ x ^r— to its simplest form. iofSf 31| J 54 AIlITHxMETICAL EXAMPLES. 98. The distance from Boston to Worcester is 44 miles ; A, starting from Boston, travels jSj of the distance ; B, start- ing from Worcester, travels y\ of the distance in the same time. How far apart are they ? 99. A merchant has 3 pieces of cloth, containing respec- tively 28f yds., 351 yds. and 41f yds.; after selling several yards from each piece, he finds he has left in the 3 pieces B51 yds. How many yards has he sold ? 100. What number is that to which, if you add ^ of j\ of itself, ^ of the sum will be 101 ? 101. Bought 2.125 yards of cloth, 1.375 yards wide, for $4,675; what will 27.625 yards, 1| yards wide, cost, at the same price per square yard ? 102. A and B traded with equal sums of money ; A gained a sum equal to ^ of his stock ; B lost $220, and then had ^ as much as A. What was the original stock of each ] 103. James can do a piece of work in | of a day ; Henry can do it in 1| days, and John can do it in j of a day. How much longer will it take John to do the work alone than it does James and Henry working together ? 104. From a piece of calico containing 33J yds. there have been sold, at different times, 11 J yds., 7f yds., 2y^g yds. and 1 1 yds. How many yards remain ? 2^ 105. What number must be multiplied by -j, that the product may equal 1 ? 106. The report from the Army of the Potomac, Feb. 1, 1862, was as follows : There were present for duty 1002 men less than ^ of the whole army ; 1621 men less than y^^ were in hospitals; 107 less than ^y were in confinement; 124 more than y\ were on furlough, and 1580 were unaccounted for. How many men were reported for duty, in hospital, in confinement, and on furlough, respectively, and what was the aggregate strength of the army ? ARITHMETICAL EXAMPLES. 55 107.. If j\ of a yard cost $10, what quantity will |17^ purchase ? 108. A merchant sold a piece of cloth for $24, and thereby lost I of his purchase money. What part of his purchase money would he have gained had he sold it for $34? 109. George Hawkins leased 100 acres of land in Missis- sippi, of the U. S. Government, for one year ; his cotton crop, raised upon J of the land, averaged 1 bale of 400 lbs. per acre ; he planted corn upon the remaining land, raising 45f bushels per acre. He sold the cotton at 50 cents per pound, and the corn at 75 cents per bushel ; his expenses for farming implements, labor, and Government tax, were just i the gross receipts. What were the net profits for the year 1 110. Bought a horse and saddle for $150, and paid for a buggy I of what I paid for the horse ; the saddle cost f the value of the horse. What was the price of each ] 111. A company, whose capital stock is divided into 1000 equal shares, consolidate the stock into 300 equal shares. How much larger would a share of the latter be than one of the former size ? 112. If 22 boarders consume a barrel of beef in 63 days, how long would it last if 6 more were added to their number ? 113. If a man, by laboring 14 hours a day, can perform a certain piece of work in 6 days, how many days would it re- quire to do the same work, by laboring 12 hours a day 1 114. In 1856, 4056471 votes were cast for three presiden- tial candidates. Buchanan received 497573 votes more, and Fillmore 467309 votes less, than Fremont. How many votes did each receive ? 115. If a horse eat 19^ bushels of oats in 87| days, how many bushels would 14 horses eat in 30 days ? 116. James Stow can mow a field in 6 days, by working 10 hours a day ; his son George can mow the same field in 9 days, by working 8 hours a day. How long will it take them 56 ARITHMETICAL EXAMPLES. both to mow the field, provided they each work G hours a day ? 117. An Illmois farmer sold 212f bushels of wheat for $201 1 ; 328^2 bushels of corn for $1781 ; 187y\ bushels of oats for 184 1^. How many bushels of grain did he sell, and how much did he receive for the whole] 118. Tlie total expenses of public schools in Pennsylvania, in 1862, were $1955315, and 385463 scholars attended school. The same year there were 68954 scholars in the public schools of Philadelphia, educated at an expense of $604100. How much were the expenses per scholar in the city more than in the State at large 1 119. Bought I of a ten-acre lot, and sold | of what I pur- chased. How much did I sell ? 120. Bought 8 lbs. hyson tea and 12 lbs. black tea. The price per pound of the latter was f the price of the former, which was $y9-. What did the whole cost? 121. What is the difference between -^l^- yards, and 159 whole yards 1 122. A lady spent ^ of the day in sleep, | in visiting, I at her toilet, ^ in reading, and 2 hours each day in receiving calls. How much of her time remained for other occupations ? 123. A gentleman bequeathed ^ of his estate to his w^ife, I of the remainder to his oldest son, and i of the residue to his oldest daughter, whose share was $684.66|. What was the value of the estate ? 124. The estimated value of all the gold throughout the world in 1863, was $4860000000; of the silver, $5700000000. What part of this sum was produced the same year, the annual product of gold behig $180000000, and of silver, $60000000? 125. A having 104^ bushels of wheat, sold f of it to B, who sold I of what he bought to C, who sold } of what he bought to D. How many bushels did each purchase ? 126. A boy can do a certain piece of work in 3| days, and ARITHMETICAL EXAMrLES. 57 a man can cIo the same in ^ of the time. How many days will both working together require to do the work ? 127. A grocer has 74}| gallons of beer, which he wishes to put into bottles, each holding j\ of a gallon. How many dozen bottles must he obtain ? 128. A garrison of 5000 men were besieged in a town, with provisions for three weeks, allowing each man 16 ounces per day. Being reinforced by 3000 men, upon what allow- ance per day must the garrison be put, that the same provi- sions may last four weeks 1 129. What will 12.75 bales of cotton cost, each bale weigh- ing 7.75 cwt., at 128.625 per cwt. ? 130. What is the greatest common 'divisor of 408, 1190 1445 and 4012? 131. How many limes does the sum of 21^ and 121 co ^ tain their difference ? 132. In a certain school, .375 of the pupils study arithm, > tic, .3 study grammar, .25 study geography, and the remaiuv der, which is 21, learn to read. What is the whole numbu of pupils ? 133. The public debt of Austria in 1863 was 253909083C florins, and her population was 34714326. What was the debt per capita, a florin being worth 50 cents in United States money 1 134. Divide $1000 among 7 boys and 9 girls, giving to each girl J as much as to each boy. How much does each boy and girl respectively receive ? 135. If 7 men or 11 boys can perform a piece of work in 28 days, in what time can 1 1 men and 7 boys do the same ? 136. Four persons bought a house together for $8250 ; B paid twice as much as A, C paid as much as A and B, and D paid as much as A and C. How much did each pay '' 137. In Belgium, the budget for 1863 gives the total re- ceipts at 155946790 francs, and the expenditures at 150120345 58 ARITHMETICAL EXAMPLES. francs. How many more dollars were the receipts than the expenditures, 5 francs being worth 98 cents U. S. money ] 138. A man, going a journey of 418 miles, finds at the end of 5 days that the distance he has traveled is i| of the re- maining distance. How many miles does he travel per day ? 139. A regiment of soldiers, consisting of 1025 men, is to be furnished with coats, each to contain 2| yards. If yards wide. How many yards of cloth, |f yards wide, will line them 1 140. How many times is .75 of 2.625 contained in .375 of 261. 141. A man having a cow and horse found that 4 loads of hay would keep them both 6 months ; having disposed of his horse he found that the same quantity of hay would keep his cow 14 months. In what time did each consume 1 load ] 142. Bought a hogshead of molasses containing 128 gallons at $.65 a gallon ; paid $.80 for cartage, and lost 16 gallons by leakage. At what price per gallon must the remainder be sold to gain } of the entire cost ? 143. Jan. 20th, 1864, Gen. B. F. Butler seized at Norfolk, Va., 48 barrels of whiskey, each containing 31.5 gallons; this was sold for the U. S. Government, ^ at $7.50 per gallon, and the remainder at $8.75 per gallon ; the parties violating the laws of trade were also fined $1000. How much did the Government receive ? 144. The number of the Union army killed in the battle of Gettysburg was 515 more than y'^- of the whole loss; the number of wounded was 956 more than 4| times the number killed ; there were 6647 missing. What was the whole loss ] 145. A boy bought a slate, a book and a pen for 80 cents ; the pen cost 10 cents, and the book cost If times as much as the slate and pen. How much did each cost ? 146. Divide $870 among A, B and C, so that i of A's money shall be equal to | of B's, or | of C's. ARITHMETICAL EXAMPLES. 59 147. Bought a horse for $115. At what price must it be sold so that the gain shall be f of the cost ? 148. By selling a house for $2175, my gain was y\ of the cost of the house. What did I pay for the house ? 149. A grocer bought a cask of sugar, containing 400 pounds, for $32; a part of it being damaged he sold the re- mainder for I the cost per pound, and thereby gained a sum equal to | of his purchase money. How many pounds were damaged ? 150. A merchant bought a bag of coffee, containing 80 pounds, at 15 cents per pound ; he also paid $.54 for roasting it. For what must it be sold per pound to yield a profit of I the cost of the coffee, allowing to each pound ^^ of a pound for waste ? 151. The entire population of Denmark and the two Duchies of Holstein and Schleswig, is 2554870; Denmark contains 3 times as many inhabitants as Holstein — 32706, and Schleswig contains 134519 less than Holstein. What is the population of Denmark and the Duchies respectively 1 152. Bought a cask of nails containing 100 pounds at 4?- cents per pound, and, after reserving 15 pounds for myself, I sold the remainder at 5| cents per pound. How much did I gain ? 153. A can do | of a piece of work in 4 days ; B can do I of it in 5 days ; C can do ^ of it in 3 days, and D can do } of it in 1^ days. How long will it take them all to do it? 154. Divide — - of --^-^by -^^ of — • 155. A man owned scAenty -five- thousandths of the stock in a bank, and sold three hundred and twenty-five ten-thou- sandths of the whole stock. How much did he still own ? 156. A mast stands J in the ground, I in the water, and 83 feet above the water. What is its length ? 157. I sold an article for J more than it cost me, to A, who 60 ARITHMETICAL EXAMPLES. sold it to B for $10, which was -J- less than it cost him. What did it cost me 1 158. The number of postage stamps sold in one year was as follows: 53893792 one-cent stamps; 151223056 three-cent; 677200 five cent; 3925690 ten-cent; 1053900 twelve-cent; 650600 twenty-four-cent ; 340000 thirty-cent; and 24280 ninety -cent stamps. What was the whole number of stamps and their value ? 159. Seven men engage to do a piece of work in a given time, but three of them failing to come, the work was pro- longed 7i days. In what time would the seven men have done it ? 160. The report of the Normal School at Albany, N. Y., for the year 1863, showed that the number of males was 1 less than I of the whole number in attendance ; the number of fe- males was 32 more than | of the whole number, and 22 less than 4 times the number of graduates ; and three-fourths of the entire number of graduates were females. What was tho whole number of graduates, and how many were males '? 161. A man bought 3 barrels of molasses, containing re- spectively 30.375, 33.675, and 28.6625 gallons, at an average price of $.375 per gallon. What was the whole cost ? 162. A person proposes to sell his horse by lottery; if the price of the tickets be $3 each, he will lose $20 on his horse, but if he sell them at $4 each he will gain $20. What was the value of the horse and the number of tickets ? 163. There is an island 27 miles in circumference; A, B and C start from the same point, and travel in the same di-^ rection around it ; A goes at the rate of 4 miles ; B, 7 miles, and C, 10 miles per hour. In what time will they all be to- gether ? 164. What are all the exact divisors of 560? 165. A person after spending $40 more than | of his money, had $60 less than ^ of it left. How much money had he ? ARITHMETICAL EXAMPLES. 61 1C)6. In 1860 Georgia cultivated 14321 farms and planta- tions, containing an average of 563 acres each, at an average value of $20 per acre. New Jersey cultivated 18518 farms, containing an average of 105 acres each, at an average value of $94 per acre. Of tow much greater value were the farm- ing lands of the latter State considered, than those of the former ? 167. From a cask of rum there were drawn off 26 gallons; i of the remainder leaked out; the cask was then found to be 4 gallons more than i full. How many gallons did the cask at first contain ? 168. A man being asked his age, replied, " If ^ of my age be multiplied by 11, and f of it be multiplied by 15, and I of it be added to the sum of these products, the sum will be 381. What was his age? 169. The Illinois Central Eailroad sold, in one month, 16461 acres construction land, at $11^ per acre; 242 acres interest fund land at $9 J per acre; 2781 acres free lands at $10f per acre ; and 4 town lots at $425.50 each. How much were the total receipts, from the sale of lands 1 170. The receipts of the same railroad for the same month were, from passengers, $138615.83 ; from freight, $164226.20 ; from mails, $6358.33 ; from rent of road, $4000, and from other sources, $5000. How much did the receipts from run- ning the road exceed those from sale of lands ? 171. A and B have the same income ; A saves } of his, but B spends l^ times as much as A, and finds himself $98.56 in debt at the end of the year. What is their income ? 172. The third satellite of Jupiter is .0000885 of the mass of the planet, and .02947 of the mass of the earth. The mass of Jupiter is how many times that of the earth ? 173. If 8| ounces of bread are bought for $.06i, when wheat is $li per bushel, how much bread may be bought for $.25 when wheat is $ J per bushel ? C2 ARITHMETICAL EXAMPLES. 174. What is the sum of 45 millionths, 45 thousandths, 45 hundredths, 45 tenths, and 45 units? 175. In 1861, the revenue of the Post Office Department was $9049296.40, from 28586 offices; in 1862, it was $10388- 934.60, from 199"'3 offices. How much more was received, on an average, from each office, the latter year than the former ? 176. A market woman wished to sell a basket of oranges ; her first customer bought ^ of what she had, and gave her back 5 ; the second bought ] of what she then had, and gave her back 10; the third bought } of the remainder, and gave her back 15; the fourth bought | of the residue, and gave her back 20 ; after which she found she had 60 oranges left. How many had she at first ? 177. If 5 of a yard of cloth cost $^^^ what will | of a yard costi 178. The exterior semi-diameter of the exterior ring of . Saturn is 88209 miles, and of the interior ring 75845 miles ; the width of the interval between the rings is 1791 miles, and the space between the planet and interior ring is 19089 miles. What is the width of the rings, the semi-diameter of the planet being 39580 miles ? 179. A and B can perform a piece of work in 1 | days; A and C in two days ; C and B in 2| days. In what time would each perform the work alone, and how long would it take them to do the work together ? ■ 180. Bought 7640 brick, at $4.75 per 1000; 26789 feet of lumber, at $2.75 per 100; and 986 feet of pine boards, at $20 per 1000; I paid $.35 per 1000 for planing 23463 feet of boards. What was the whole bill ? 181. There were 193 applications for admission into the Normal School, at Albany, in 1864 ; the number that passed examination was 2 less than 4 times the number that failed. How many failed, and how many were admitted ? 182. A speculator gave $19550 for horses, and sold a cer- AEITHMETICAL EXAMPLES. 63 tain number of them for $8925, at $105 each; by so doing he lost $10 apiece. For how much must he sell the remain- ing horses each, to gain $425 by the operation ? 183. A and B together have $600 ; I of what A has, added to ^ of what B has, amounts to $135. What have they each ? 184. In 1862, the export of petroleum from four ports was as follows, viz. : from New-York, 6783563 gallons, valued at $2037413 ; from Philadelphia, 2607203 gallons, worth $529- 575; from Boston, 891616 gallons, worth $457859; from Baltimore, 1120000 gallons, worth $500000. How many gallons w^re exported, and of what value ? 185. What is the smallest sum of money with which I can purchase either sheep at $3.50 a head, calves at $10.50, cows at $35, oxen at $70, or horses at $105 ? 186. A and B, traveling together, started with such sums of money that i of A's was equal to j'3 of B's ; each spent $12, when I of A's money was equal to I of B's. How much did each start with ? 187. The point in the earth's orbit farthest from the sun is 90600000 miles ; the point nearest, 93400000 miles ; of the moon from the earth the farthest, 3»^ ^^760 miles ; the near- est, 221290 miles. W^hat are the grtsatest and least possible distances between the sun and the moon ? 188. From a cistern containing 3465 gallons, 62.75 barrels, of 31.5 gallons each, were drawn off. How many gallons remained 1 189. A has $647, which lacks $33 of being 4 times what B has ; C is worth twice as much as A and B together, lack- ing $72. How much money have B and C respectively ? 190. A merchant bought a number of bushels of corn ; having sold 6 bushels more than | of it to W. Smith, and 8 bushels more than | of the remainder to J. Acker, he had 20 bushels remaining. How many bushels did he buy ? 191. The number of stamped envelopes sold in one year 64 ARITHMETICAL EXAMPLES. were as follows: three-cent envelopes, 22940100; one-cent, 2845000; four-cent, 70000; six cent, 40450; ten-cent, 131- 750 ; allowing 5 cents as the cost of paper and manufacturing every package of 25 envelopes, what was the whole number sold and their value ? 192. Reduce f? /a, Is, /^ and 41 to their least common denominator. 198. A, B and C, who can respectively travel 3, 4 and 5 miles an hour, propose to walk from Springfield to Hartford, the distance being 26 miles. How many hours after A starts must B and C each set out, that all may reach Hartford at the same time ? 194. In the battle of Chickamauga, the number killed was 485 more than ^ the wounded ; the missing were 13 more than 3 times the number killed ; the total loss being 15861, how many were killed, wounded and missing ? 195. A farmer exchanged 50 loads of wood, each containing I of a cord, at $4.40 per cord, for an equal number of bushels of corn worth $.75 a bushel, and of oats worth $.57 a bushel. How many bushels of each did he receive ? 196. A has 6.4 acres in one lot, and 8.75 in another; B has 4.375 acres less than 3 times as much as A ; C has 7.2875 acres less than ^ as much as A and B together. How many acres had B and C 1 197. The entire population of Connecticut in 1860, was 460146, and the products of industry were $83056353 ; allow- ing I of the entire population to be engaged in industrial pur- suits, what was the average value of the labor of each during the year ? 198. How many bushels of corn must a farmer carry to mill that he may Jbring back 3| bushels, provided the miller takes y^g for toll ? 199. Reduce H^Hi ^o its lowest terms. 200. John, Henry and Charles have respectively. 65, 91 ARITHMETICAL EXAMPLES. 65 and 117 cents, with which they agree to purchase tops at the highest price that will allow each one to spend all his money. How many tops can each buy? 201. Bought a quantity of lumber for 1785/^, and of wood for 13471; sold the lumber for $649 1, and the wood for 15895. How much did I gain 1 202. Hudson County, New Jersey, appropriated $3723.08 for the education of 17501 children for one year. How much was appropriated for each child ? 203. Two men, 84.675 miles apart, traveled till they met each other, when' they found that one had traveled 8.425 miles farther than the other. How far did each travel ? 204. How many bushels of potatoes at $| per bushel, will pay for 6| bushels of wheat at $1.40 per bushel ? 205. The N. Y. Central R. R. Company owned, in 1862, 556 miles in length of railroad, which cost for construction and equipment, $31524226. The New York and Erie R. R. Company owned 446 miles in length, which cost $35796902. How much was the average cost per mile of the one more than of the other ? 206. The discharging pipe of a cistern has | the capacity of the receiving pipe, which will fill the cistern in 9.8 hours ; the receiving pipe has been open 4| hoiirs, when the discharging pipe is opened. In how many hours after will the cistern be full ? 207. There were 2187480 pieces of gold, silver and copper coined at the U. S. Mint in one month, valued at $168908 ; 2170000 were copper coins, and there were 12002 silver coins, valued at $6606. What was the average value of the gold coins ? 208. If I of I of I of I of a ship be worth | of 14 of t| of f^ of her cargo, how many times the value of the ship is her cargo worth? 209. I exchanged 30 barrels of molasses, each containing 34 gallons, at $.56 a gallon, for 17 chests of tea of 24 pounds each. How much did the tea cost me per pound? 66 ARITHMETICAL EXAMPLES. 210. A coal dealer sold 5 tons of coal for $57.50, which was g as much as he received for all he had left at $7.66 1 per ton. How many tons did he sell ? 211. A farmer sold, in one year, 150 bushels of oats at 1.45 per bushel ; 250.25 bushels of corn at $.875 per bushel ; 75.75 cords of wood at $3,625 a cord ; 645 1 pounds of wool at $.78 per pound ; 23 head of cattle at an average price of $50.75 per head. How much did he receive for the whole 1 212. The number of railroad accidents, in the U. States, in 1862, was I of the number of persons killed by the accidents; and the injured, which were 877, were 30 more than 2| times the number of accidents and killed together. What was the "number of accidents, and how many were killed ? 213. Six boys divided some chestnuts among themselves; James took i of them wanting 6 ; Thomas took 6 less than I of the remainder ; John took 5 less than i of what still re- mained ; Henry took 2 less than J of what then remained ; William took 5 less than | of the residue, and George took the remainder, which was 25. How many chestnuts were di- vided ? 214. In 1858, 9061504 bushels of wheat were sent out of the country; in 1859,2849192 bushels; in 1860,4076704 bushels; and in 1861, 38313624 bushels. How many more bushels were exported in 1861, than during the three previous years ? 215. What number is that whose sixth part exceeds its eighth part by 20 less than its ninth part 1 216. A speculator sold a quantity of grain for $96, and gained 4 of what it cost him. What part of the cost would his gain have been had he sold it for $100? 217. A, B and C can perform a certain piece of work in 26]^ days; A, B and D in 29fi days; A, C and D in 33| days, and B, C and D in 42 days. How long would it take each to do it alone '? ARITHMETICAL EXAMPLES. G7 218. If a mason, in constructing a sewer, 650.25 feet in length, begin with a diameter of 32 inches, and increase .1 of an inch in every foot in length. How many times the diam- eter of the beginning will the end be? 219. The sales of sperm oil for export and home use, at New Bedford, for the week ending Jan. 23, 18G4, were 3488 barrels, of 31.5 gallons each, at $1.65 per gallon; 5.6 times the quantity for home use, was equal to 1| times the quanti- ty for export. What was the value of the exported oil ? 220. If 3y\ tons of coal will last as long as 4]f cords of wood, how many tons of coal will last as long as ISy'j cords of wood ? 221. A merchant expended 1384 for an equal number of yards of six different kinds of broadcloth, costing respectively $2.00, $3.00, $3.50, $4.00, $4.50, $7.00 per yard. How many yards of each kind did he buy ? 222. How many rails, of the longest possible equal lengthy will inclose a rectangular field 9893 feet long by 8047 feet wide, w^ith a straight fence six rails high 1 223. In 1863 the school houses built of brick in the State of New York were -j\^ the whole number + 16; the framed school houses were 10 more than 10 times the brick; the stone, 3 less than ^\ the brick, and the log school houses were 33 less than | the brick. Required the number of each kind. 224. What number is that whose I part being subtracted from its ^, the remainder will be 4 less than | the number ? 225. A man dying, left to his oldest son -] of the estate, in- creased by j^0 his daughter's share ; to his youngest son .] of the estate plus | of his daughter's share ; and to his daughter the remainder, which was $700 less than the younger son's share. What was the value of the estate 1 226. A grocer has forgotten the weight and first cost of a box of coffee; he only recollects that if he had sold it at 28 cents a pound he would have gained $2.00, but if he had sold 68 ARITHMETICAL EXAMPLES. it at 21 cents a pound he would have lost $5.00. Required the number of pounds in the box and the first cost per pound. 3 Qf 5 4 Qf _7_ 227. The sum of ^—r^~ and -^—pr—-: is equal to how many • D -y 01 /C.iZO times their difference ? 228. During the year 1861, of the letters exchanged be- tween the United States and Great Britain, 1707439 were re- ceived, 1591644 were sent; between the United States and France, 679184 were received, 680577 sent. How many letters did the exchange with Great Britain exceed that with France 1 229. The rate of postage between the United States and Great Britain w^as $.24 for each i ounce ; between the United States and France, $.30 ; allowing the letters to weigh A ounce each, how much greater wxre the receipts for postage, between the United States and Great Britain than between the United States and France ? 230. A and B can do a piece of work in 6| days ; B and C in 12 days; and A and C in 10 days. In how many days could all working together do it ? 231. A trader bought corn at $.63 per bushel, and sold it for $.56. How much did he lose on every dollar he paid out? 232. A boat which could move 14 miles an hour in still water, was accelerated 2^ miles per hour in going down stream, and retarded the same in coming up ; it was 10 hours longer in coming up a certain distance than in going down the same. What was the distance ? 233. The difference between two numbers is 8, and j^y of the larger is equal to | of the smaller. What are the numbers? 234. J. Burke engaged to work a year for $180 and a suit of clothes; at the end of 8 months he was disabled, and re- ceived for his w^ages the suit of clothes and $110. What was the cost of the suit of clothes ] ARITHMETICAL EXAMPLES. 69 235. ITow long will it take a man to walk 480 miles, if he walk 3 1 miles an hour, and 7i hours each day ? 236. The population of the United States in 1840, was 17069453; in 1850,23191870; in 1800, 31445080. IIow much more was the increase for every hundred, from 1840 to 1850, than from 1850 to 1860 1 237. A grocer exchanged 112.5 lb. of coffee, for tea at 1.875 per lb., the price of 3| lb. of coffee being equal to that of 2 lb. of tea. How many pounds of tea did he receive, and what w^as the price of his coffee per pound 1 238. A tree, by falling, was broken into 3 pieces; the top part was 15 feet long; the bottom, as long as the top and ^ the middle piece, and the middle part as long as the top and bottom. What was the height of the tree 1 239. How far may a person ride in a coach, which goes 10 miles an hour, so that he may be gone 3 hours, provided he walk back at the rate of 4 miles an houi ? 240. If it is worth $.80 to saw a cord of wood consisting of sticks 4 feet long, into pieces 1^ feet in length, how much is it worth to saw a cord consisting of sticks 8 feet long, into pieces of the same length ? 241. What number is that which being increased by | of 1^2 ^^ if J ^^ itself, will amount to 247| ? 242. The forward wheels of a carriage are 10.5 feet in cir- cumference, and the hind wheels 15 feet. The places where the tires are welded together in each wheel were up together when the carriage started, and when it stopped the same places were up together for the 352nd time. Required the number of miles the carriage had traveled, allowing 5280 feet to a mile? 243. A and B set out from the same place, and in the same direction; A traveled 10 miles a day, and after traveling 7i days turned and went back as far as B had traveled in 7S days ; he then turned again, and pursuing his journey, over- 70 ARITHMETICAL EXAMPLES. took B 25 days after they first set out. How far did B travel each day 1 244. If 10 oxen, or 14 cows, eat 4f\ tons of hay in 58 days, in what time will 4 oxen and 6 cows eat the same quantity of hay? 245. In the State of New York 72104 children attended school more than 10 months of a certain year; 65161, more than 8 months; 115450, more than 6 months; 176221, more than 4 months ; 240328, more than 2 months, and 217551, less than 2 months. How many children of school age did no-t attend school at all, the whole number being 1357047 ] 246. Six men can do a piece of work in 7| days. How soon after beginning must they be joined by 2 more, so as to complete it in 5| days ? 247. Bought a western farm for $11180, and after expend-* ing $871 in improvements, I sold one half of it for $7740, at $18 per acre. How many acres of land did I purchase, and at what price ? 248. How many times is the greatest common divisor of 4 J, 6J, 7| and 7,T> contained in the least common multiple of the same numbers ? 249. When one dollar of gold is worth 1594 cents, how many whole dollars in gold ought a broker to pay for a ten- dollar U. S. note, and how much fractional currency ? 250. A hound ran 200 rods before he caught a fox ; | the distance the fox ran before being caught was equal to the dis- tance he was in advance when they started. How far in ad- vance was the fox, and how far did he run ? 251. The State Superintendent of Schools in Pennsylvania reported, in 1862, that 98 more than 1- the whole number of school houses in the State were wholly unfit for use ; that 25 more than twice this number were improvable, so as to an- swer for school purposes ; and the remainder, 4133, were suitable in all respects. How many school houses in the State 1 ARITHMETICAL EXAMPLES. 71 252. Twelve men can do a piece of work in 8| days; how many days may 3 remain away, and yet finish the work in the same time, by bringing 7 more with them ? 253. In 1860, Virginia produced 12396775 lbs. of tobacco, at an average value of $.10 per lb. IIow many school houses, at a cost of §1150, and how many churches, at a cost of $8550, of each an equal number, could be built with the proceeds of the tobacco crop 1 254. A boy spent one-third of his money for apples, and 20 cents for nuts ; he then gave 10 cents more than one-fourth of the remainder for oranges, when he found he had but 50 cents left. How many cents had he at first ? 255. Divide $14500 between A and B, so that A shall have I as much as B, increased by $2500. 256. In a lot of silver change, worth $13.50, | of the value is in 50-cent pieces, | of the remainder in 25-cent pieces, and the rest is made up of 10-cent, 5-cent and 3-cent pieces, of each an equal number. How many pieces of each coin are there ] 257. If a cubic foot of granite weigh 168.48 pounds, what will be the weight of a block of granite 1 0.75 feet long, 4.5 feet wide, and 3.8 feet thick ? 258. The United States has an area of 2819811 square miles, and a population of 31445080. Europe has an area of 3757209 square miles, and a population of 268851381. What is the difference in area and population ? 259. 3 fj .^01 Divide the sum of I of 4 of 28 -4 and 3 '^ by the, ^ 105 .' ;x A . p34i 98 1 2} , 128 contniued product of — — ?, — ^, -^ and ^.— :-• 27 8/g J 81f,- 260. John and James started together and ran a race ; when James had run 80 rods, y^^ the distance John had run was equal to the distance he was ahead of James. How much did John gain on James in running 80 rod^ ? 72 ARITHMETICAL EXAMPLES. 2G1. A school house which cost $980 is to be paid for by four men, A, B, C and D. It is agreed that each shall pay according to his nearness to the school house. A is twice as near as B, and B is |- as near as C, who is | as near as D. How much ought each to pay 1 362. If 14 men can perform a job in 27 days, in how many days can they perform the same labor with the assistance of 7 more men? 263. The value of books printed in New York, in 1860, was $6920102; of job work, $2574529; of newspapers, $13422254. The aggregate value of printing in the United States for the same period was $39678043. How much more than one-half the value of the whole printing was done in New York ? 264. A can travel around a certain island in 2 f - days, B in 31 days, and C ni 3] days. If they all set out from the same point, and travel the same way, in how many days will they all meet at the point from which they started ? 265. The total cost of maintaining schools in the State of New York, in 1863, was $3859159.21. The rural districts raised by taxation $503181.28, by rate bills, $363741.05 ; the cities raised by taxation $1595728.80; the remaining cost was paid by the State School Fund ? What amount of money was received from the State? 266. A man *laid out | of his fortune in speculation, and put out on interest the remaining $6800 ; at the end of the year he had gained j^^ as much by speculation as he laid out, and his interest was ^ of the principal. What was his for- tune, and how much did he gain during the year ? 267. A man bought 2400 bushels of corn, at $.90 a bushel, but in measuring it he found that he had more bushels than he paid for, and that he had gained 2.25 bushels for every hundred. He sold the same without delay at $1.05 a busheL How nmch did he make by the transaction ? ARITHMETICAL EXAMPLES. ^ ,|^ Q -73 268. A man has 2 horses and a saddle ; if the saddle be placed upon the first horse, valued at $60, it will make him 1| times the value of the second horse, but if it be put on the second horse, it will make his value twice that of the first horse. Required the value of the saddle and the second horse. 269. In 1861, there were 2819811 square miles, of 640 acres each, in the United States; and there were 1155510 farms, of 215 acres each, under cultivation. How many- acres were still uncultivated 1 270. The above farms were each valued at an average of $5756, and upon each farm there was an average of $213 in machinery and implements. What was the aggregate value of the firms and implements ? 271. Bought a bale of cloth for $96.75, and disposed of it for I the cost, by which I lost $1.00 on a yard. How many yards were there in the bale 1 272. There is a cask containing brandy and water ; | of the whole -|- 4 gallons, is brandy, and i of the whole + 2 gallons is water. How many gallons of each ? 273. A had | of | of 3| times $31448, and paid | of | of ^0 of it for a farm. How much money had he remaining ? 274. Bought 7.5 lb. of sugar for $.37]. For how much must I sell 5.25 lb., to gain the cost of .25 of a lb. ? 275. The New England States had sent into the army, Jan. 1, 1863, 183732 men ; the Middle States, 453386 ; the West- ern States, 103887 more than the Middle States; the Border States 101877 less than the New England States. Of the whole number, 91561 were three-months men, 67335 nine- months men, and 48571 were enlisted for irregular periods; the remainder enlisted for three years. How many of thia class were there 1 276. A man divided $670 among his 3 sons, so that | the share of the first was equal to | the share of the second, and to 4 the share of the third. Required the several shares. 4 74 AKITHMETICAL EXAMPLES. 277. Bought 24 tons of hay, at $16.50 per ton, for | of which I paid sheep, at $3^ each, and for the remainder I paid butter, at $.19i per pound. How many sheep and how many pounds of butter did it require to pay the debt ? 278. Bought 17 chests of tea, each containing 59 pounds, at $.07 a pound, and gave m exchange 118 bags of wheat, each containing 3.4 bushels. What was the value of the wheat per bushel '? 279. The value of the flour and meal produced in the United States, in 1860, was $224000000; of cotton goods, three million of dollars more than one-half the value of the corn and meal ; of boots and shoes, I f the value of cotton goods ; of clothing, | the value of the boots and shoes ; of printing, | the value of the clothing. How much did the sum of the values of the printing, and boots, and shoes, exceed in value the cotton goods ? 280. The circumference of a circle is always 3.141592 times the diameter. How many revolutions will a carriage wheel, which is 3^ feet in diameter, make in going a distance of 5.73 miles ? 281. A father divided a piece of land among his three sons. To the first he gave 16.25 acres; to the second, ~\ of the whole; and to the third, as much as to the other two. How many acres had the third ? 282. The British army in India, in 1863, consisted of 7062 cavalry; twice as many artillery, lacking 124; and 4 times as many infantry as artillery, lacking 1163. The cavalry in the home army were 66 more than the artillery in the India army, and the infantry 2968 more than 9 times the home cav- alry. What was the aggregate strength of the home and of the India army ? 283. A market woman bought a number of peaches at the rate of 2 for 1 cent, and as many more at the rate of 3 for 2 cents, and sold them all at the rate of 5 for 3 cents, gaining 4 cents. How many peaches did she buy ] ARITHMETICAL EXAMPLES. 75 284. A tree 164 feet high, in falling was broken into two pieces, of such lengths that | of one piece equaled ^ of the other. Required the length of the pieces. 285. In Wisconsin, the number of stone and brick school houses, in 1861, was 376; of framed, 2478; of log, 1357; the average cost of these buildings was $309.50. What was the cost of all the school houses ? 286. If ^ yds. of cloth. If yds. wide, cost $3.46;j, what will be the cost of 42} yds., 1 1 yds. wide ? 287. A piece of land was divided into two parts, so that ^ the first was equal to J the second. The difference between the two parts was 10.7534 acres. What was the whole amount, and what were the parts ] 288. What is the value of the following expression : § of 5 ^3.7 • ' ^ '' 2.15+ I ^ 4/3^39 289. A garden whose breadth is 9 rods, and whose length is 1| its breadth, has a wall 3| feet thick around it. What was the cost of digging a trench 2| feet deep, in which to lay this wall, at 1 1 cents per cubic foot ? 290. There were 38068 children attending school in 614 districts in California, in 1861. The whole cost of schools for the year was $470115.24. What was the average number attending in each district, and what the average expense per scholar 1 291. Three horses start from the same point, and at the same time, upon a race-course 300 rods in circuit ; the first horse passing over i the circuit, the second |, the third J, in a minute. In how many minutes will they all be together again, and how far will each have traveled ? 292. Bought 4 bushels of wheat, and 3| times as many bushels of corn ; for the former I paid | as many dollars per bushel as there were bushels of the latter, and for the latter I as much per bushel as for the former. Required the price of each per bushel, and the whole cost I OHAPTEE IV. 1. The source of the river Volga is 550 feet above the level of the sea ; after a course of 2000 miles it empties into the Caspian sea, which is 83 feet below the surface of the ocean. How much is the average fall, per mile, of the river ? 2. A physician bought by Avoirdupois Weight, 15 lb. opium at 4 cents a dram, and sold the same by Apothecaries' AVeight, in doses of 10 grains each, for 25 cents per dose. How much did he gain ? 3. The amount of money in the Sub-Treasury in New York, Jan. 1st, 1864, was $12898926.89; the amount received in January, on account of Customs, was $6179605.51 ; of Loans, $37463895.94; of Internal Revenue, $2275409.67; of Transfers, $300000.00; of Patent Fees, $6613.65; of Miscel- laneous, $4164352.27; of Post Office Department, $108982.- 51 ; and the amount paid out in Treasury Drafts w^as $48343- 806.66 ; in Post Office Drafts, $82663.06. How much re- mained in the Treasury, Peb. 1st, 1864? 4. How much land in New York at $2.25 per square foot will $200000 buy ? 5. The population of London, in 1860, was 2800000 ; the number of deaths during the year was 63644 ; the population of New York, at the same time, was 805600, and the number of deaths, 18126. How many more deaths per million in London than in New York ? 6. A man and his son walk from Hartford to New Haven, a distance of 36 miles ; allowing that the man passes over a distance of 2 ft. 9 in. at each step, and the boy a distance of 1 ft. 10 in., how many more steps does the boy take than the man. ARITHMETICAL EXAMPLES. 77 7. A school room, which is 36 ft. long, 30 ft. wide, and 12 ft. high, is occupied by 80 pupils, each breathing 10 cu. ft. of air in one minute. In how long a time will they breathe as much air as the room contains ? QWV..-.>. P .5X.006 .iof|fx(|)% 8. Whatisthesumof ^,^^^,^^^^. and-^^-yi 9. A man having a hogshead of molasses, sold ji^ of it to A, I of the remainder to B, and I of the residue to C. How many gallons remained ? 9_T_ 10. What is the value of j^ of a dollar? 11. Bought 78 A. 3 R. 15 P. 7 sq. yd. 5 sq. ft. 9 sq. in. of land at $80 per acre ; I sold | of it to A at $120 per acre ; | of the remainder to B at SI. 00 per sq. rd., and the residue to C at $.005 per sq. ft. What was my whole gain 1 12. A fruit dealer bought 4 barrels of cranberries, each containing 2^ bushels at $8.00 per barrel ; he retailed the same at 12^ cents per quart, wine measure. How much was his profit ? 13. ^ of the muskets captured at the battle of Gettysburg by the U. S. army were loaded ; 4 of these contained one charge each; i, two charges each; |, from three to ten each; f^j^Q^ from ten to fifteen each, and the remainder, which was 40, from fifteen to twenty-three each. How many muskets were captured ? 14. The distance from Albany to Buffalo is 298 miles ; an express train from Albany, and a mail train from Buffalo, start at the same time ; the express runs at the rate of 24 miles per hour, and the mail train, 20 miles ; for each hour of running time the express stops 6 minutes, and the mail train, 12 minutes. How many hours before they meet, and how far from each city ? 15. The total yield of nine copper mines in 1862, was 3942 T. 12 cwt. 1 qr. 1 lb. ; in 1863, the same mines yielded 78 ARITHMETICAL EXAMPLES. 4101 T. 8 cwt. 3 qr. 3 lb. ; if copper was worth 20 cents per pound, of how much greater value was the amount produced in 1863, than in 1862? 16. In the Maine House of Representatives in 1863, the number of lawyers was 5 more than the editors ; the clergy- men, 2 more than the lawyers ; the merchants 17 more than the clergymen, and 17 less than the farmers, who were 1 more than ^ the whole number. What was the number of each class ? 17. A man took 5 loads of turnips to market, each load containing 16 bags, and each bag 3 bushels ; he sold them for 20 cents a bushel, and received in payment 4 boxes of sugar, each box containing 8 papers, and each paper 15 lbs. What was the price of the sugar per pound 1 18. Sold 72 yds. carpeting at 11.371 a yd., and gained thereby $18. How much did it cost me per yard ? 19. A merchant carried on business three years ; the first year he gained a sum equal to j\ of his original capital ; the second year he lost | of what he had at the end of the first year ; the third year he gained /^ of what he had at the end of the second year; he then had $14625. How much had he gained in the three years 1 20. A farmer exchanged 26 bu. 1 pk. 6 qts. of oats for 22 bu. 4 qts. of salt. What quantity of oats must be brought to the same market by a farmer who wishes to get 73 bu. 3 pks. of salt? 21. Divide 637 A. 3 R. 8 P. 11 sq. yds. 4 sq, ft. 16 sq. in. by 16. 22. A pedestrian, in training for a foot race, traveled 75 mi. 3 fur. 37 rd. 5 yd. 2 ft. 10 in. the first week ; the second week, 89 mi. 3 fur. 9 rd. 2 yd. 1 ft. 10 in. ; the third week, 127 mi. 6 fur. 9 rd. 1 yd. 3 ft. 10 in. IIow far did he travel in the three weeks ] 23. If a person count 90 a minute for 10 hours each day, how long will it take him to count a million'? ARITHMETICAL EXAMPLES. 79 24. Bought a lot 25 rods long and 20 rods wide for $10- 000, and sold the same at 25 cents per square foot. How much was my gain ] 25. Simplify the following fractions : I 7| ?' 207 I 1_ .003] 500 .0| 25 26. A cellar is 26 feet long, 18 feet wide, and 7 feet deep. How much earth must be removed to make it 28 feet long, 21 feet wide, and 8 feet deep ? ^ 27. How many square yards in the walls of a room 40 feet long, 3H feet wide and 12 feet high 1 28. A person, being asked the time of day, replied : " llf times the time past noon is equal to 4] times the time till midnight." What was the time 1 29. I purchased some pens at two for a cent, and 1.5 times as many at 3 for 2 cents ; I sold them all at the rate of one- half a cent each, and lost 15 cents by the transaction. How many of each kind did I buy ? 30. The market value being the same in both States, a farmer from New Jersey exchanged 50 bushels of buckwheat, worth $1] a bushel, with a farmer in New York, for oats, worth $.40 a bushel, which he sold in his own State for cash. The exchange being made by weight, in whose favor was the difference, and how much in cash value ? 31. What will 4| bales of cloth cost, each bale containing 43.75 yards, at $.75 a yard ] 32. A man worked 3 months, 25 days each month, 10 hours each day, for $.08 an hour, and received in payment 2 loads of grain, each containing 15 bags of 2^ bushels each. What was the price of the grain per bushel ? 33. I bought 397 barrels of flour, at $9,625 per barrel ; 290 bushels of corn, at $.93 per bushel ; 48 barrels of beef, 80 ARITHMETICAL EXAMPLES. at $.00 per lb. ; 170 barrels of pork, at $.08^ per lb. ; and 225 cords of wood, at $.87 i per cord foot. What was the difference in value between the sum of the cost of the flour and the corn, and the sum of the cost of the other articles ? 34. How many tons of hay, at $.75 per cwt, must be given for 35 cords of wood, at $.60 per cord foot ? 35. It is estimated that the Falls of Niagara have receded 50 yards within the last 40 years. How long at this rate has it taken them to recede from Lewiston, 6 miles below their present site ? 36. The amount expended in work upon the canals in New York, in 1863, was as follows, viz. : Champlain Canal, $48- 195.95; Black River, $3261.77 ; Erie, $151435.42 ; Oswego, $15456.02; Cayuga, $19755.58; Baldwinsville, $25615.88; Chemung, $15083.20; Crooked Lake, $28895.62 ; Chenango, $16935.21; Genesee Valley, $88292.75; for work done by Canal Superintendents, $107626.51. What was the whole amount ] 37. The total cost of engineering upon the above men- tioned canals was $31223.11. How much was expended in work for $1 in engineering] 38. What part of 5 da. 23 h. 58 min. is 4 da. 6 h. 50 min. ? 39. Bought 7000 bushels of corn in Chicago at $.80 a bushel. I shipped the same to Buffalo, and sold it at an ad- vance of 20 cents per bushel ; the expenses for freight and handling the grain were $500 : the corn being bought and sold by weight, how much did I gain or lose 1 40. Nineteen lots of equal size contain 159 A. 2 R. 17 sq. rd. 25 sq. yd. 8 sq. ft. 130 sq. in. What is the value of one lot, the land being worth half a dollar per square foot ? 41. A spent i his money and gave away $20; he then spent I the remainder and gave away $10 less than | of what then remained, and found he had $48 left. How much had he at first ? ARITHMETICAL EXAMPLES. 81 42. The amount of cheese made in the State of New York, in 1860, was 48548288 lbs. Suppose each cheese to weigh 64 lbs., and to be 20 in. in diameter, how many miles in length would they extend if placed in a line? 43. Thirty-two men agree to build 14 mi. 5 fur. 34 rd. 6 ft. of road ; when the work is ^ done they employ 8 more men. What distance does each man construct ? 44. The total vote for Governor in Kentucky, in 1863, was 85695, of which Bramlette, the successful candidate, received 50917 more than WicklifTe, his rival ? How many votes did each receive ? ' 45. A housebreaker, having been brought before a judge, it was proved that he had stolen property to the value of £9 12s. 9d, 3 far. j he was sentenced to pay at the rate of £9 12s. 9d. 3 far. for every pound stolen. How much was the fine ? 46. A and B started together by railroad from Philadel- phia for Pittsburg, the distance being 356 miles ; A traveled by express, at the rate of 30 miles per hour ; B by mail train, at the rate of 25 miles per hour ; C left Pittsburg for Philadelphia, at the same time, by fast line, at the rate of 32 miles per hour. How far from Philadelphia were A and B respectively, when C passed them ? 47. What is the value of .6923828125 cwt. of coffee at 38| cents pound? ^ 1 ^S^^^/z^^ ? l/j 48. A wood-dealer delivered a quantitJ-TO^^ood at' a fac- tory ; it was in three piles, the first was 18 ft. 6 in. long, 7 ft. 6 in. high, and 4 ft. wide ; the second was 16 ft. 9 in. long, 6 ft. 9 in. high, and 4 ft. 6 in. wide ; the third was 20 ft. 3 in. long, 7 ft. 4 in. high, and 4 ft. 6 in. wide. How many cords were delivered ] 49. A farmer sold 19 bushels of rye and 23 bushels of bar- ley for 144.85; he received for the rye 15 cents more per bushel than for the barley. What was the price of each per bushel 1 50. Sold 4 village lots ; the first contained I of § of an 82 ARITHMETICAL EXAMPLES. acre ; the second 40^ rods ; the third ^ of an acre, and the fourth I of g of an acre. How much land in the four lots ? 51. A man bought a horse and two carriages ; for the first carriage he paid $250 j if this sum were added to what he paid for the horse, it would amount to f of the sum he paid for the second carriage ; if the sum he paid for the horse were added to the sum paid for the second carriage, it would amount to three times the sum paid for the first carriage. What did he pay for each ? 52. How far does a team walk in plowing an acre, allow- ing 10 inches for each furrow? 53. The aggregate receipts of the railroads in Pennsylvania for 1863 were $40523571 ; the expei^ses w^ere $20602804. How much were the net earnings ? I / ^ ^ ^""i f '5*'7V . 54. How much beef, at 7d. per pound, oi^tt I to receive for 27 lb. 12 oz. of butter at Is. 9d. per pound 1 55. A ship at the equator in 20° 30' W. longitude, sailed due West, until its longitude was 36° 18' W. How many statute miles did the ship sail ? 56. There were three candidates for the office of Mayor in the city of New York, Dec. 1863, and there were 71101 votes polled; the successful candidate received 6524 votes more than one competitor, and 9738 more than the other. How many votes did each receive ] 57. If a town, 10 miles square, be divided equally into 300 farms, what will be the size of each farm ? 58. How much must be paid for a pile of wood 12| ft. long, 3| ft. wide, and 34 ft. high, at $.64 per cord foot? 59. In the city of Springfield, Mass., for the year 1863 the number of scholars in the mixed schools was 272, which was -!§ of the number in the primary schools; || of the number in the primary schools were equal to the number in the inter- mediate schools, which was 2| times the number in the gram- mar schools ; the number in the high school was 1 less than ARITHMETICAL EXAMPLES. 83 rf^ the number in the grammar schools ; required the number ' in each grade of schools. 60. The annual expense of the schools in the above-men- tioned city was $23362.50. Now if the expense per scholar •was the same in the mixed schools as in the primary, and in the intermediate 1 1 times as much ; in the grammar schools 1 1 times as much as in the intermediate ; and in the high school 2 J times as much as in the grammar school. What was the expense of each grade of school for the year 1 61. A gentleman travelling west from Boston, which is 71° 3' W. longitude, finds, on his arrival at St. Louis, that his watch is 1 h. 17 m. 24 sec. faster than the time at the latter place ; if his watch has kept accurate time, what is the longi- tude of St. Louis ? 62. What will be the cost of 9 gal. 3 qt. 1 pt. 2 gi. of kero- sene oil at 6s. 8d. per gal.. New York currency 1 63. Express in acres and the decimal of an acre the area of 49 square lots, each measuring 5 rd. 8 ft. 3 in. on a side. 64. The number of cents coined at the U. S. mint in Phila- delphia during the month of January, 1864, was 220800; the silver coinage was | the value of the cents, and also | the value of the silver deposits ; the deposits of silver were 20 dollars more than j\ of the gold coinage, which was || of the gold deposits. Required the sum of the deposits and of the coinage. 65. Bought 48 bushels corn at 6s. 6d. per bushel, New York currency, and sold the same at 5s. per bushel, New England currency. How much did I gain on the whole ? 66. What is the value of a field 15 ch. 75 1. long, and 12 ch. 50 1. wide, at $64 per acre ? 67. The popular vote for president in 1860 was 4680193 ; Lincoln received 491295 more votes than Douglas, who re- ceived 527204 more than Breckinridge; and Breckinridge received 257322 more than Bell. How many did each receive ? 84 ARITHMETICAL EXAMPLES. 68. Reduce | of | of 45^ lb. to the decimal of a short ton. 69. Suppose the Erie canal to be 60 feet wide, and 6 feet deep, how many miles in length will it require to make one cubic mile of water ] 70. In the packing-yards of New York there were, Feb. 1, 1864, 88180 bbl. of pork, and 107643 bbl. of beef; the aver- age value of the pork per barrel was $20. 12^ ; of the beef, $14.75. What was the difference in their entire values? 71. There is a house 40 feet long, and each side of the roof is 20 feet wide ; allowing each shingle to be 4 inches wide, and 18 inches long, and to lie one-third to the weather, how many half-thousand bunches will be required to cover the roof? 72. How many bushels of grain will a bin contain that is 7.5 ft. long, 6.25 ft. wide, and 3.75 ft. deep ? 73. The difference in longitude between London and St. Louis is 90° 20' ; at a certain time each day it is as much past noon in London as it lacks of noon in St. Louis. What is the time in St. Louis ? 74. At what time between 8 and 9 o'clock is the minute- hand as far beyond the V mark as the hour-hand is beyond the VIII mark ? 75. A gentleman having $60, paid in Boston 14s. 8d. for a hat, 18s. 6d. for a vest, and $17,375 for a coat; going to New York, he paid $5.00 for his fare, and in the city bought 10 books at 7s. 6d. each ; gave 3s. 9d. to a blind man ; and paid 17s. 3d. hotel bill. How much money had he left ? 76. On an acre of ground there were erected 21 buildings, occupying on an average 3 sq. rd. 112 sq. ft. 8 sq. in. How much of the acre remained unoccupied ? 77. Colt's Armory, Hartford, Conn., which was destroyed by- fire, February 4, 1864, was insured in New Haven to the amount of $20000, which was | the insurance in Providence, and ^ the insurance in Springfield ; the amount insured in these three cities was | the insurance in Hartford ; and the ARITHMETICAL EXAMPLES. 85 lew York was 1^ much was the total insurance ? insurance in New York was li times all the others. How New Haven, Feb. 1, 1864. 78. T. M. CuRTiss, Bought of Bishop & Brothers, 450 lb. A. Sugar . ® $ .12^ 240 " B. " . . . 5701. What was the average debt and annual interest to each person ? 182. France, with a population estimated at 3G000000, had at the same time a debt of $2206000000, the annual interest of which was $110000000. What was the average debt and interest to each person ? 183. What will it cost to construct 8 mi. 6 fur. 16 rd. of plank road at $1325.65 p^r mile? 184. What part of a short ton is f of a long ton ? 185. How much copper and tin in the great bell of Mos- ARITHMETICAL EXAMPLES. 97 COW, which weighs 192 tons 17 cwt. 16 lb., bell metal con- sisting of 3 parts copper to 1 of tin 1 186. A gentleman buys 2 lots of land containing 110 acres each, for $1500. What is the value of an acre of land in each lot, if an acre in one lot be worth 1^ acres in the other 1 187. A farmer borrows 20 bushels of corn when it is 56 cents per bushel. How many bushels must he return when it is worth 75 cents a bushel, to pay the value of what he borrowed ? 188. The army of Gen. Banks in its retreat down the Shen- andoah Valley, May, 1862, marched 37| miles in 11 h. 24 min. 26 1 sec. How many steps of 2 ft. 8 in. each did his men take per minute ? 189. What number multiplied by 3| times itself will pro- duce 114? 190. Bought 425.75 lbs. wool at $.75 per lb., which was manufactured into cloth at an expense of $75.50, For how much must it be sold to gain $48.25 ? 191. How many feet of boards will be required to make 8 boxes, whose interior dimensions are 6 ft. 5 in., 5 ft. 7 in., and 3 ft. 6 in. respectively, the boards being 1^ in. in thickness? 192. How many feet less are required to make 8 boxes whose exterior dimensions are like the interior of those in the last example, the boards being of the same thickness? 193. What is the difference in the capacity of the two sets of boxes ? 194. There were sold in New York, in one week, 4678 beeves, 156 cows, 367 veals, 12281 sheep and lambs, and 6297 swine. The average price of the beeves was $80 per head; the cows, $44.25; the veals, $12.50; the sheep and lambs, $7.50, and swine, $18.25. What was the whole num- ber of animals sold, and for how much ? 195. A merchant bought 18 hogsheads of sugar, each con- taining .725 of a long ton, at the rate of $170 per ton, and 5 98 ARITHMETICAL EXAMPLES. sold the same at 10 cents per pound. How much was his^ gain 1 196. F. F. Smith has coffee at $.37^ per pound cash, but in trading with Seth Bishop, he charges $.42. What must Bishop charge him for potatoes that he sells at $.62^ cash ? 197. On I of my field I raise tobacco ; on I of the remain- der I sow oats; potatoes are planted on 4 of what still re- mains, and carrots on 4 of the residue ; I have left two small pieces, one of which is 4 rods square, and the other contains 4 square rods. How large is my field ? 198. There were 4419216 bales of cotton, each 400 lbs., exported from the United States in 1 860, at an average price of $.108 per pound, and 167248 hogsheads of tobacco at $95.12i per hogshead. What was the value of cotton and tobacco exported ] 199. If by selling cloth at 10s. 6d., J of the price is gain, what part of the cost would be gained by selling it at 13 shil- lings ? 200. From 10 years subtract 9 yr. 9 mo. 9 wk. 9 da. 9 h. 9 min. 9 sec. 201. A merchant bought 15 barrels of salt, of 4 bushels each, at $1| a barrel, and retailed it at § of a cent a pint. How much was his whole gain ? 202. The Pennsylvania Central Railroad is 356 miles long : 4 passenger trains and six freight trains pass over it both ways each day of the year, Sundays excepted. How many miles do the trains run each year ? and how many times the circumference of the earth, which is about 25000 miles? 203. A ship's chronometer, set at Greenwich, points to 5 h. 45 min. 24 sec. P. M., when the sun is on the meridian. What is the ship's longitude ? 204. Bought 7.88125 A. cf land at ^^^ of £2 lis. 6d., New England currency, per square rod. How many dollars did it cost ] ARITHMETICAL EXAMPLES. 99 205. The salary of the President of the United States is $25000 per annum. How much can he spend each week, and yet save $27200 in one term of office 1 206. Required the quotients of 1169 divided by its two prime factors next larger than 1. 207. A farmer bought some oxen, cows, and sheep for $1860, paying $45, $25, and $4 per head, respectively. There were 5 times as many cows as oxen, and 7 times as many sheep as cows. How many of each did he purchase ? 208. A owns ,-'3 of a field, and B the remainder ; | of the difference between their shares is 5 A. 3 R. 16^ P. What is B's share? 209. The average fall of rain at Worcester, Mass., is 48.92 in. ; of snow 53.5 in. ; allowing 5 in. of snow to make one of rain, how many hogsheads of w^ater fall annually upon a flat roof 40 ft. long by 30 wide? 210. A wine merchant wished twice as many quart bottles as pint ; twice as many pint as half pint, and twice as many half-pint as gill bottles filled from a cask of wine containing 58 gal. 1 qt. 1 pt. 2 gi. How many bottles of each kind could he fill ? 211. Peter Jones was born Sept. 7, 1830 ; he was 27 yr. 3 mo. 23 da. old when married ; and 3 yr. 21 da. after mar- riage his first child was born. What was the date of his mar- riage ? and what his child's birth-day ? 212. How much more is the cost of 39 A. 2 R. 15 P. of land at $87,375 per acre, than the expense of making 5 mi. 6 fur. 24 rd. of road at $587.75 per mile? 213. There were shipped over the Erie Canal in 1863 1603065 barrels of flour, 22336433 bushels of wheat, 19918- 464 bushels of corn, and 3816548 bushels of barley ; the toll for the flour was $.375 per barrel, and for the grain $.075 per bushel ; oats were shipped in such a quantity that the tolls from the oats, barley, and corn were equal to the tolls 100 ARITHMETICAL EXAMPLES. from the flour and wheat. How many bushels of oats were shipped ? 214. Two boys purchased a pair of skates in company; one paid $|, and the other $l/g ; they sold them so as to gain S/g. What did they sell them for ? and how much was each one's share of the gain ? 215. How long before the voting is ended in San Francis- co, Lon. 122° 13' W., can the voters of Eastport, Me., Lon. 67° W., telegraph to San Francisco the result of their election, the polls closing in both places at sunset ? 21C). At what time between 11 and 12 o'clock is the ifiin- nte-hand as far beyond the XI as the hour-hand lacks of being up to the XII mark ? 217. A man started from Portland, Maine, with $100; he paid ^3.25 for his fare to Boston ; in that city he bought a book for 5s. 6d., paid 8s. 3d. hotel bill and 3s. 3d. for amuse- ments ; he then took passage in a steamer for Charleston, S. C, paying $32; in that city he purchased 8 yards of cloth at 13s. Gd. per yard, and paid 18s. 9d. for having the cloth made lip ; he then went to Philadelphia, at an expense of $25, and there he purchased some pictures for 15s. lid., some presents ■ for 18s. 5d., and spent 17s. 8d. at a hotel ; the Camden and Amboy Railroad Company agreed to carry him to Now York for the rest of his money ; the regular fare being $3.00, how much did the company lose ? 218. At $1000 per acre, what is the value of a strip of land 44 yards long and 20 feet wide ? 219. The value of exports from the United States,- in 1801, w^as as follows: the products of the sea, $4451515; of the forest, $10260809; of agriculture, $1^1055833; tobacco, $13784710; cotton, $34051483; manufactures, $30418254; raw produce, $3543695 ; specie and bullion, $23799870. How much did the exports of the products of agriculture and manufacture exceed all others in value 1 220. The hour and minute hands of a clock being together ARITHMETICAL EXAMPLES. 101 at 12 o'clock, how long before they will be at right angles with each other ? 221. A cistern has three receiving and three discharging pipes ; the first three will fill it in 24, 36 and 48 minutes re- spectively, and the last three will empty it in 30, 40 and 60 minutes each. If the cistern is empty, and the pipes are opened in succession, each three minutes after the other, in the order given, how long after the last pipe is opened will the cistern be filled ? 222. By selling wheat at 12s. 6d..per bushel, I gain £30 on the quantity purchased; but if I sell it for 13s. 6d. a bushel, I shall gain £42 on the same quantity. How many bushels were bought 1 223. I had J of a yard of broadcloth, for which I paid at the rate of $8^ per yard ; I gave the broadcloth and 50 cents for 1| yards of cassimere. What did the cassimere cost me per yard 1 224. A liquor agent has 50 gallons of wine of a superior quality, worth $7.50 a gallon ; he wishes to reduce its quality by the addition of water, so that he may sell it at $5.25 a gallon. How much water must he add ? 225. The loans of all the banks in the city of New York, for two suGces3ive years, were: for the first, $165090329; for the second, $168302935. The deposits for the same pe- riods were $140464616 and $148014106 respectively. How much did the increase of deposits exceed that of loans ? 226. William Shakspeare was born April 23, 1564. How many years since 1 227. A man and a boy start from the same place at the same time, and travel in the same direction ; the man ad- vances as far in three steps as the boy in five, but the boy takes 4 steps while the man takes 3 ; after a certain time they are -\ mile apart. Allowing the man's steps to be 3 feet in length, how far has each traveled ? 228. If 1 cubic foot of water weigh .625 cwt., what will be 102 ARITHMETICAL EXAMPLES. the weight of water in a cistern containing 500 cu. ft. 864 cu. in. ? 229. What are the values of a bushel of peas, sold at 10 cents a quart, by wine, beer and dry measure, respectively 1 230. The total loss of the Federal army in the battle of Fair Oaks was 5739 ; the prisoners were 332 more than the killed, and the wounded were 459 more than 1^ times both the killed and prisoners. What were the various losses 1 231. What is the cost of a great gross of pens, at 6| cents for I of a dozen ] 232. A person desirous of giving Is. 6d. apiece to some needy boys, found that he had not money enough in his pocket by 5d. ; he therefore gave them each Is. 4d., and had 9d. left. Required the number of boys. 233. A housewife exchanged old silver for a feather bed worth $24; the feathers were valued at $.80 a pound, and the silver at 25 times the value of its own weight of feathers. What was the Troy weight of the silver 1 234. If a man can paint 4 sq. yd. in one hour, and is 31 h. 6 min. 40 sec. in painting two sides of a wall 7 feet high, how long is the wall ? 235. The earth moves through 59 .14'daily, how far did it move during the month of February, 18G4 ? 236. The average cost of the school houses in Ohio, in 1861, was $289.20. The total cost of the same was $4794- B57.60. Required the number. 237. The value of the common school libraries at the same Jime was $233499.76 ; the books were worth on an average t68 each, and were distributed in libraries averaging 47 >ols. each. Required the number of libraries. 238. In the same state 27106 teachers were examined dur- ing the year 1861 ; three times the number rejected were 934 tnore than the number considered qualified to teach. How inany passed examination, and how many were rejected ] ARITHMETICAL EXAMPLES. 103 239. A person bought a watch, chain and pencil, for £30 ; the chain cost twice as much as the pencil, and the watch twice as much as the chain and pencil. What did he give for each 1 240. If I exchange 4 bu. li pk. of potatoes for 2 bu. 2 pk, of apples ; how many bushels of apples ought I to receive in exchange for 33 bu. 1 pk. of pptatoes at the same rate ? 241. A man chopping wood at $.75 per cord, earned $35.25 during the working days of January, 1864, and was idle 2i days. How much wood did he cut, on an average, per day ? 242. A boy having been sent to the store with 5rJ- doz. of eggs, was directed to purchase with them equal quantities of sugar, coffee, butter and tea ; he disposed of his eggs at the rate of 2 for 5 cents, and paid for the articles purchased 17, 28, 37 i and 137i cents per pound respectively. What amount of each did he purchase 'I 243. A bowlder, containing § of § of 23 1 cu. ft., is what fraction of a perch ? 244. A grocer bought 10 bushels of beans at $3 per bushel, and ordered his shop boy to retail them at 15 cents a quart. By mistake the boy used a wine quart. How much more was the grocer's gain than he expected ? 245. What part of 12 yd. 1 ft. 6 in. is j,j\^ of a mile ? 246. Four men receive $27.27 for hauling coal ; the first hauled 2 T. 3 cwt. 3 qr. 18 lb. ; the second, 5 T. 16 cwt. 7 lb.; the third, 4 T., 18 cwt. 2 qr.; the fourth, 14 cwt. 20 lb. How must the money be divided ? 247. What is the difference in weight between 8 lb. of gold and 8 lb. of lead? 248. A speculator purchased 10,000 bushels of corn in Chicago, at 5s. 6d. per bushel, and sold one-half of it in New Jersey at 8s. 4d. per bushel, and the other half in New York at 9s. 6d. per bushel; the freight was $.10 a bushel, and other charges amounted to $230. The corn being bought and sold by weight, how much did he gain ] 104 ARITHMETICAL EXAMPLES. 249. My garden is 10| rods long, and 8'J rods wide, and surrounded by a fence 7| feet high ; I have laid out a walk around it, within the fence, 7^ feet wide on the two sides, and 5^ feet wide on the ends. How much remains for cultiva- tion] 250. What part of a cord of wood is a load 71 fl. long, 2 J ft. high, 3| ft. wide? 251. It is estimated that England uses annually, 1000000 pounds of ivory. The average product of ivory from each elephant is 120 lb. ; and for every 25 elephants captured 12 men are killed. Required the number of men killed annually in hunting the elephants that supply England with ivory ? 252. How many dollars, Canada currency, are equal to $150 United States currency 1 253. If ^3 of an acre produce 28 bushels of potatoes, how many bushels will 4 acres produce, at the same rate? 254. Bought 78 A. 3 R. 15 P. 7 sq. yd. 5 sq. ft. 9 sq. in., at ISO per acre ; I sold | of it to A, at $120 per acre ; | of the remainder to B, at $1.00 per square rod ; and the residue to C, at $.005 per square foot. How much did I gain ? 255. How thick is a cubic inch of gold, beaten so as to cover a space 83 ft. 4 in. long and and 23 ft. 5 in.^ wide ? 256. During 1861, the Dead Letter Post Office sent out for delivery 10580 money letters, and 10235 letters contain- ing other articles of value ; 8998 of the former and 9552 of the latter were delivered; 1214 money letters and 475 others were returned, unclaimed ; and nothing was heard from the rest. How many were unreported ? 257. The money letters contained $53565.90, of which $46- 880.26 was delivered, and $4782.99 w^as returned; of the re- mainder, $297.30 belonged in the loyal States, and the rest in thq disloyal. What amount belonged in the rebel States ? " 258. At $3.87^ per square, what will be the expense of flooring a house in which there are 4 rooms, 14 ft. 6 in. by 15 ARITHMETICAL EXAMPLES. 105 ft. 3 in. ; G rooms 9 ft. 9 in. by 11 ft. 4 in., and 3 rooms 12 ft. 3 in. by 8 ft. 2 in. 1 259. What is the value of || Cong. ? 260. Bought 1500 bushels of oats in Iowa, at $.40 a bushel. For how much per bushel must I sell them in Connecticut, so that, after paying $75 expenses, I shall neither gain nor lose by the transaction, the buying and selling being by weight ? 261. Bought 140 yards of cloth at 14s. 8d. a yard. New York currency, and gave in payment 75 bushels of barley at 7s. 4d., New England currency, and 100 bushels of oats at 6s. 9d. per bushel, New Jersey currency, and the balance in money. How much money did I pay ? 262. A steamer, going from New York to Hamburg, trav- ersed 10.^ degrees of longitude daily. What length of time was it from one noon to the next ? 263. A certain number is divided by 9, and the quotient multiplied by 17 ; the product is then divided by 300, and 33 is added to the quotient ; the result is next divided by 3, and from this quotient 31 is subtracted, and the resulting dif- ference divided by 12.1. Now ^ of | of 4 of this last quotient is 23^. Required the original number. 264. What is the value in statute miles of -j^^ of a Great Circle of the earth ? 265. The military expenses of England, during the last war with the United States, were as follows: for 1811, £52859- 025; for 1812, £56615577; for 1813, £71316435 ; and for 1814, £71686706. A pound being valued at $4.84, what were the average daily expenses in U. S. currency ? 266. A clothier has 920 soldiers' coats to make, each coat containing 2| yd. of cloth Ij yd. wide, and lined with drilling I yd. wide. How many yards of lining will be required ? 267. Reduce |i of a long ton to the decimal of a short ton. 268. Two persons traveling in the same direction, the first at the rate of 9| miles per hour, the second 14^ miles, pass 106 ARITHMETICAL EXAMPLES. the same mile-stone at an interval of 5 hours. How long and how far must the second travel, after passing the mile-stone, to overtake the first ? 269. What is the length of the shortest piece of cloth from which a number of garments can be cut, without waste, con- taining a yard, an ell Flemish, an ell English, and an ell French, respectively ? 270. The shadow of a cloud was observed to move 600 ft. in 23| sec. What was the wind's velocity per hour ? 271. From 1838 to 1863, 3858 patients were admitted into the Central Lunatic Asylum, Ohio ; of these, 2000 wete dis- charged as fully recovered, 412 as improved, 724 as incurable, and 470 died. How many remained in the asylum, Jan. 1, 1863? 272. A gentleman bought 05 yards of cloth, | of a yard wide, for $100, and gave the same and $25 for cloth of the same quality, 1 yard wide. How many yards did he buy 1 273. If a vessel sail 80 leagues in a day, how many statute miles docs she sail ? 274. A farmer exchanged 1 1 loads of potatoes, each load containing 12 barrels of 2^ bushels each, at $.50 per bushel, for a number of pieces of cloth, each containing 12 yards, worth $2.75 per yard. How many pieces did he receive ? 275. How many feet of boards will it require to inclose a barn 40 ft. 6 in. long, 30 ft. 10 in. wide, 18 ft. 4 in. high, and each side of the roof 16 ft., allowing 385 ft. 3 in. for the gables ? 276. What is the value of .05751953125 Cong. 277. A degree of longitude, in the latitude of Boston, measures 44^ geographic miles. How many more statute miles in 10° of longitude at the equator than in the latitude of Boston ? 278. Rhode Island in 1862 expended $168365 in educating 27750 children. What was the average expense per child? 279. In the same year Ohio spent ^2834066 for tlie cduca- ARITHMETICAL EXAMPLES, 107 tion of 717726 children. How much more did Rhode Island expend per child than Ohio ? 280. Massachusetts, during the same period, paid out $1612824 for the instruction of 220010 children. How much did the average expense per child in Massachusetts lack of being twice the expense incurred by Ohio for each child 1 281. How many inches higher is a horse that measures 16^ hands than one that stands 14| hands high ? 282. A person, dying, left in cash $6250, and 4 houses. Valued at $3456.785 each; his indebtedness was $2261.60, and he left directions that $100 should be expended for a monument; the residue was to be divided among his 4 sons, so that each should receive | as much as his next older brother. Required the share of each. 283. If there are 31181 verses in the Bible, and a person reads 88 verses on Sunday, how many must he read each week-day to complete it in a common year 1 284. A tract of land measuring 4059 A. 2 R. 16 P. was divided among a regiment of men, consisting of one colonel, 1 major, 6 captains, 8 lieutenants, 24 sergeants, and 220 privates, so that a private had one share, a sergeant twice as much, a lieutenant 6 shares, a captain 8, the major 14, and the colonel 20 shares. Required the share of each ? 285. From the sum of | lb. 2/^ oz. 15| pwt, take the dif- ference between | oz. and § pwt. 286. The earnings of the Toledo and Wabash Railroad Com- pany in 1862 were $1374517, which was Jg of the earnings in 1863 ; the expenses each year were $47721 more than half the earnings in 1863. How much more were the net earnings of 1863 than of 1862 1 287. What is the least number, which, being divided by 3, 5, 7, 9, and 10, leaves a remainder of one? 288. What part of a hogshead of wine is 3 gal. 1 qt. 2 fg gills ? 108 ARITHMETICAL EXAMPLES. 289. A speculator in New York bought 1000 bushels of grain at $1.10 per bushel, and shipped the same to England, paying* $125 transportation; he sold the grain at $1.40 per Imperial bushel. What was his gain 1 290. If the diameter of the sun be 884000 miles, and that of the earth 8000 miles, how many bodies of the size of the earth, placed in a line, would reach across the sun's diameter ? 291. Reduce 6 leagues, 2 mi. 3 fur. 17 rd. 4 ft. 1] in. to statute miles. 292. The Austrian empire contains 7889925 Germans, I5027G46 Slavi, 5632689 Roumanians, 4947134 Magyars, and of other races a number making the entire population 34714326. How many belong to nationalities not mentioned 1 293. Paid in tondon £1951 for 12 bales of cloth. How many bales should be received for £536 j\ 1 294. A flirmer sold 8 loads of potatoes, averaging 27 bu. 3 pk. 5 qt. each, for $.45 a bushel. How much did he re- ceive ? 295. Divide $897.43 among A, B and C, so that B may have $93.40 less than A, and $69.18 more than C. 296. If the population of the world be as follows, viz. : Asia, 630700000; Europe, 265494300; Africa, 61700000; America, 57600000 ; Oceanica, 23400000 ; and the average length of life be 33^0 years, what is the average number of deaths each day 1 297. How many more bushels will a cubical box contain, whose sides measure 8 ft., than one that is 10 ft. long, 8 ft. wide, and 6 ft. deep ? 298. How many seconds in 40 tropical years, 340 da. 22 h. 37 min. 45 sec. ? 299. A surveyor, measuring a piece of land in the form of a rectangle, found one side to be 55 ch. 50 1., and the other, 63 ch. 24 1. How many acres did it contain 1 300. In Ohio there are 997 miles of canals, the aggregate ARITHMETICAL EXAMPLLS. 109 receipts from which for a period of 15 years, were $8521600.- 42. Required the average annual receipts per mile. 301. A block of granite containing 126 ft. 10' IV\ is 2 ft. 6' wide, and 3 ft. 7' thick, what is its length ? 302. If a young man, by early rising, can save 2i hours each day for study and improvement, how many years of study can be gained in 25 years, allowing 365 days in a year, and 12 hours in a day 1 303. Alexander Wilson estimated that a flock of pigeons which was 6 hours in passing, was one mile in breadth and flew at the rate of 40 miles per hour ; allowing ^ pigeons to a square yard, what was the estimated number of pigeons in the flock ? 304. How much cloth at $4.00 per yd., must be given for 9 tons, 8 cwt. 3 qr. 12^ lb. of sugar at $9.50 per cwt. 1 305. If 22 1 cords of wood last as long as 15j\ tons of coal, how many cords of wood will last as long as 11 ^/^^ tons of coal ? 306. A fruit grower put 178 bu. 1 pk. 6 qt. 1 pt. of cherries into casks, each containing 2 bu. 3 pk. 6 qt., and sold them for $315.90. How much did he receive per cask ? 307. The Post Office receipts in New York for the year ending June 30, 1861, were as follows : Letter postage, $191879.63; newspaper postage, $80153.42; registered let- ters, $2679.10 ; stamps sold, $1460955.89; the expenditures for the same period were $344757.04 for salaries of post- masters ; $328661.44, incidental expenses ; $444166.75, trans- portation of mails. What was the net income to the Post Office Department for that y eat from the State? 308. If a grocer use scales that weigh 15 oz. 4 dr. for a pound, how much does he cheat in selling $55.04 worth of sugar ? 309. Three men cjit 15^ cords of wood in 2| days, for which they received $11.62^. What were the average daily wages of each man ? 110 ARITHMETICAL EXAMPLES. 310. A merchant bought 150 gallons of molasses at $.60 a gallon, and intended to have it sold at $.75 a gallon, but his clerk, by mistake, sold half of it by beer measure at $.15 a quart ; discovering the blunder he directed him to sell the re- mainder at $.18 a quart, wine measure. How much more than the cost did he receive for the molasses ? 311. A meteorological observer, in Cayuga County, New York, registered the total fall of rain, in 1861, of 34.86 in.; of snow, 40.495 in., and 3.5 in. of snow made one inch of water. How many hogsheads of water fell, during the year, in the town of Genoa, which is 10 miles square? 312. The whole length of railroads in the United States Jan. 1, 1852, was 10900 miles; ten years after, the number of miles open for traffic was 23 less than 3^'^ times this num- ber of miles ; the total cost of the roads and equipments, at the last period mentioned, was $1192400424. What was the average cost per mile in 1862? 313. How many pipes of Port are equal to 23 of Sherry? 314. If there are 371.25 grains of pure silver in one dollar, how many silver dollars are equivalent in value to 5.6 lb. of English standard gold ? 315. What cost 4 bundles, 1 ream, 6 quires, 12 sheets of paper at $45.72 per bundle ? 316. The Austrian army, in 1863, was composed of 160316 active infantry ; 424000 reserve ; the active cavalry was | the active infantry, less 235; the reserve cavalry, 2490 less than I the reserve infantry ; all other active troops, 5674 more than the active cavalry ; and all other reserve troops were 169 less than all the. cavalry ; the population being 34714326, what proportion of the people were soldiers? 317. Gunpowder made according to the government re- ceipt, is a compound of | nitre, and equal parts of sulphur and charcoal. How much of each in 1 ton of powder ? 318. How many cubic quarter inches in a slab of marble 2 yd. long, 1 ft. 6 in. wide, 3 in. thick ? ARITHMETICAL EXAMPLES. Ill 819. A ship captain, sailing from London to New York, found, on taking an observation, that the sun at noon was 3 h. 25 min. 40 see. later than the London time, as shown by his chronometer. How many degrees west had he sailed ? 320. In 1855 the U. S. Government sold 15729524 acres of public lands, for $11246609.66. How much did John Smith pay for a quarter section, at the average price per acre ? 321. A farmer planted a field, 30 rods long and 20 rods wide, with corn ; the hills were in squares, 3 feet apart, and the outside rows 1 ft. 6 in. from the fence ; allowing each hill to produce 5 ears, and 8 ears to make a quart, how much was the corn raised on the field worth at |.80 a bushel 1 322. The five different races number as follows : American, 11000000; Malay, twice as many + 1500000; Ethiopian, 30000000 more than the Malays ; Caucassian, ^ the whole population of the earth — 19400000 ; and the Mongolians, 450800000. How many more Caucassians than Mongolians, and what is the total population of the earth ? 323. If the longitude of Boston is TO"* 4' West, what will be the time in that place when it is 3 h. 35 min. A. M. in London ? 324. Albert Tucker, owning 80 acres of land, cultivated li acres potatoes, 3| corn, 2^ rye, 1| oats, i carrots, | turnips, from which he harvested 160 bushels potatoes, 48 1 corn, 28 rye, 5G\ oats, 650 carrots, and 720 turnips per acre, respec- tively. He cut 1| tons hay on each of 12| acres, and upon the remainder he pastured 30 sheep, 5 cows, 2 horses and 8 steers, for 24 weeks. He sold his potatoes, corn, rye, oats, carrots and turnips at $.75, $1.12|, $1.25, $.40, $.25 and $.15 per bushel, respectively ; he sold his hay at $16 per ton, and received 3, 20, 45 and 15 cents each per week, respectively, for pasturing the sheep, cows, horses and steers. What were the net profits of the farm, supposing he paid $25 taxes, and $30, $28, $16, $16, $40, $32 and $5 per acre, respectively, for cultivating and harvesting the potatoes, corn, rye, oats, carrots, turnips and hay ? • CHAPTER V. 1. My salary is $800 a year. I pay S5% of it for board, Ufa for clothing, 12^ for books, and 7% for incidentals. How much are my yearly expenses 1 2. If 13^ bushels of wheat make 3 barrels of flour, how many bushels of wheat will be required to make 40 barrels of flour 1 3. A farmer raised 20^ more of wool this year than last ; the amount raised during the two years was 1320 lbs. What amount of wool was raised each year? 4. A horse which cost me $135 I sold for §150, on months' credit. How much did I gain, money being worth 6^ i 5. The debt created by the U. S. Government from March 7, 1861, to July 1, 18(32, was $451450806; $125090 more than j\ of this pertained to civil affairs ; the remainder was caused by the war. How much did the rebellion expenses average per day ? 6. I purchased 0000 bushels of wheat in Chicago at $1.37d, and shipped the same to my agent in Albany, who sold it at $1,621. How much did I make, after paying $543 for ex- penses and a commission of 2|^ ]. 7. A man sleeps 7i hours each day. What per cent, of liis time does he sleep? 8. The amount of money deposited in the savings banks of New York, in 1803, was $54557500; the amount with- drawn from the same during the year was $11347900. What per cent, of the amount deposited was withdrawn, and how much was the annual interest at 5^ on the money re- maining ? 9. If 24 men, in 9 days of 12 hours each, build a wall 200 ARITHMETICAL EXAMPLES 113 feet long, 6 feet high and 2 feet thick, how many men, in 72 days of 10 hours each, can build a wall 950 feet long, 8 feet high and 5 feet thick? 10. A man drew 30^ of his bank deposits, and expended 25% of the money thus drawn to purchase a horse, worth 1^97.50. How much money had he in bank ? 11. A grocer bought 2 T. 14^ cwt of cheese at $240 per ton, and retailed the same at 16 cents per pound. What per cent, was his profit ? 12. The capital of an insurance company is $250000; its receipts for one year are $58760 ; its losses and expenses are $40010. What rate of dividend can it declare ? 13. If 360 bushels of oats will last 12 horses 15 days, how long will 636 bushels last 18 horses ? 14. I own 25 shares of $50 each in the ^tna Insurance Co., which has declared a semiannual dividend of 3^^. How much do I receive ? 15. If 41 bushels of potatoes are sold for $1.50, how much r.ro 27.25 bushels worth? 16. A railroad jobber contracted to build 20 mi. 5 fur. 25 rd. of railroad for $25000 per mile ; after finishing the work, he found the actual cost was $75 per rod. How much did he clear by the job, and what was the rate of his profit ? 17. A man, wishing to sell a horse, asked 25^ more than it cost; he finally sold it for 15^ less than his asking price, and gained $7.50. How much did the horse cost him, and what was his asking price 1 18. Required the average maturity of the following ac- count : A. Z. Armour. Dr. Cr. 1859. 1859. Feb. 12 To Mdse 86 75 March 15 By bal. old acc't. 97 1 86 " 25 " " 36 V4 April 17 " cash 56 1 00 April 16 a u 174 96 May 25 25 00 May 20 04 V8 1 June 8 " Bundries . 94 1 75 114 ARITHMETICAL EXAMPLES. 19. The expenses of a school for one year were $2000 for salary of teachers, $105.50 for fuel, $56.25 for incidentals; the public money was $750.75, and the remainder was paid by a rate bill. If the aggregate attendance was 35275 days, how much must John Spencer pay, who sent 3 pupils 175 days each ? 20. Sold I of a hhd. of molasses for what the whole cost me. What was my gain per cent. ? 21. When does the amount of the following bill become due, per average ? George Barbour, 1864. To J. B. Hale & Co., Dr, Jan. 20 . To 100 yd. Broadcloth . (3^ $3.25 25 . " 2500 " Sheeting . . ® .12 March 20 . " 3000 " Merrimac Prints © .18 April 1 . " 300 " French Silk . © 1.75 22. If a man, by laboring 12 hours each day, can perform a piece of work in 3 weeks, by laboring 6 days in a week, how long would it take him to do the same, if he labor 10 hours each day ? 23. Bought 4 hhd. of sugar, each containing 1825 lbs., at 6^ cents per pound, and paid $31,975 for freight, storage and cartage. Allowing t>% for leakage and waste, for how much per pound must I sell the remainder to gain 25^ ] 24. Bought a house for $4500, and paid $500 cash ; the bal- ance is to be paid in 8 equal annual installments. What is the mean time for paying the balance ? 25. What is the difference between the interest and dis- count of $337.50 for 1 yr. 4 mo., at 6^? 26. Sold a horse at 33^^ gain, and w^ith the money bought another horse, which I sold for $120, and lost 25^. Did I gain or lose by my trading ? and how much ? 27. An insurance agent, whose commission was 10^ on all ARITHMETICAL EXAMPLES. 115 sums received for the company, cleared $1524.45 in one year. What were the company's net receipts from the agent ] 28. In 1862 the cavalry in the French army were 19^^^% of the infantry ; the artillery were 66^ of the cavalry ; the engineers were 22j^j^ of the artillery ; and the gens-d'armes .39 of the artillery. If the engineer corps numbered 15000 men, what was the strength of each of the other arms ? 29. The Financial Committee of a graded school invested $33901. in U. S. 7 ^\ Treasury Notes, which were at a prem- ium of 4|^, as a fund for the support of the school ; the sal- aries of teachers amounted to $1975, and $227.04 was paid for incidentals. What sum was annually left unexpended 1 30. If 12 boarders eat $25 worth of bread in 2 mo., when flour is $9.50 per barrel, in how many months will 15 board- ers eat $60 worth of bread, when flour is $12 per barrel ? 31. A shipment of wheat was insured at 2?^, to cover | of its value; the premium paid was 44.07; the wheat being worth $.80 per bushel, how many bushels were shipped 1 32. Which is the more profitable to buy 7's at 105^, or 5's at 80^ ? 33. The cash capital of the West Roxbury Horse Railroad Company is $40400 ; the net receipts for one year were $3312. If 2 07 of the net receipts be reserved in favor of the Company, how large a dividend may be declared ? 34. A, who is worth $6845, is taxed $55.14; what is B worth, who is taxed $256.18 1 35. J. Burns in account with Tyler & Co. Br. Cr. 1860. I 1860. Feb. 25 To Mdse. on 3 mo. 360 75 March 1 By Cash on acct. 250 00 March 20 *' »' ti 3 « 240 56 April 20 " Accept, at 30 da. 300 00 April 26 (« it " 3 " 875 24 June 12 " Sundries, 1 375 00 June 24 " " " 2 " 235 25 " 27 " Cash on acct. 1400 00 Required the cash value of the above account, July 1, 1860, interest at 6^. 116 ARITHMETICAL EXAMPLES. 36. The loans and discounts of all the banks of Philadel- phia amounted to $29705200, Oct. 19, 1861 ; the specie in vaults was $6375750; the deposits $21100085; and the capital stock paid in, $11811500. On thef first of Jan., 1863, the loans and discounts had increased 26| per cent. ; the specie had diminished 29 1 per cent. ; the deposits were /g more; and the capital stock paid in, | of one per cent, less than in Oct. 1861 : loans, discounts, and specie being re- sources ; deposits and capital stock being liabilities, how much were the resources in excess of the liabilities, Jan. 1, 1863? 37. A stack of hay will keep 24 cows or 18 horses one week. How many days will it keep 5 cows and 5 horses ? 38. A merchant pays $10050 for a stock of goods; he sells them at an advance of 33^^ ; the expenses connected with the business are $1750. How much does he gain? 39. The value of real estate and personal property in Ken- tucky in 1850 was $301628456; in 1860 it was $666043112. What was the increase per cent, in 10 years] 40. The value of real estate and personal property in Illi- nois in 1850 was $1562655006 ; in 1860, $871860282. What was the increase per cent, in 10 years? How many times as great was the increase of property in Illinois than in Ken- tucky ? 41. $1200j^. Boston, Feb. 1, 1863. Six months after date I promise to pay Knowles, Leland, & Co., or order, twelve hundred and ~^q% dollars, with interest, for value received. S. M. Smith. Indorsed as follows: April 16, 1863, $215.77; Aug. 1, 1863, $317.50; Dec. 16, 1863, $315.75. How much was due April 1, 1864? 42. A farmer bought 100 oxen, cows, and sheep for $1160; there were 6 times as many cows as oxen, and 3 times as many sheep as cows-, the oxen cost twice as much per head, ARITHMETICAL EXAMPLES. 117 and the sheep |- as much, as the cows. How many oxen, cows, and sheep were bought '? and at what price ? 43. What per cent, is gained by buying oil at 80 cents a gallon, and selling it at 12 cents a pint? 44. A man bought a farm of 160 acres at $32 per acre ; he paid $200 for fencing, $150 for repair of buildings, and S18 for improving the grounds; at what price per acre must it be sold to gain 25^ on the entire cost ? 45. The taxable property of a School District is $756000 ; a Union School-house is to be built, worth $24956.16; the number of taxable polls is 520, each of which is assessed $1.50. Allowing S% for collecting, what will be the tax upon $1.00? and how much will be the tax of S. P. Norton, who pays for 2 polls, and is worth $15420 ? 46. If 6 men in 8 days, working 10 hours each day, can cut 40 acres of grass, how many men in 12 days, by working 8 hours a day, can cut 96 acres 1 47. If the use of $250 for 1 yr. 8 mo. is worth $30, how much is the use of $425.50 for 3 yr. 7 mo. 25 da. worth ? 48. What must be the face of a note at 60 days, the pro- ceeds of which, when discounted at Bank at 6^, are $100? 49. A western grain-dealer bought wheat as follows, viz. : 400 bushels of red wheat at $1.40; 800 bushels of white wheat at $1.62] ; and 300 bushels of spring wheat at $1.20: he shipped the whole to his correspondent in Albany, who sold the first kind at an advance of 15^, the second at an ad- vance of 20^, and the third at $1.15 per bushel : deducting from the gross proceeds, his commission at 3^, $108.23 for expenses, he remitted to the consignor the net proceeds. What was the rate of the grain-dealer's gain? 50. If $400 gain $16 in 8 months, what is the rate of in- terest ? 51. A town levies a tax for building a bridge, which costs 118 ARITHMETICAL EXAMPLES. $2520; allowing A% for collecting, for what sum must the tax be levied ? 52. A merchant tailor bought 4 pieces of cloth, each con- taining 30 yd. 3.75 qr., at $2.00 per yd. ; he sold I of it at 12.20 per yard, and made up the remainder into suits, each containing 7 yd. 2 qr., which he sold for $18.50 each. How much did he gain 1 53. What sum must I invest in United States 6's, selling at 2^^ premium, to secure an annual income of $840 ? 54. What is the rate of income upon money invested in 6 per cent, bonds, purchased at a discount of 10 per cent. 1 55. If it require 192 reams of paper to print 2400 copies of an 8vo book, containing 440 pages, how many reams will be required to print 6000 copies of a 16mo book, containing 220 pages ? 56. Goodman and Barbour bought bills of goods of Mellen, Claflin, and Co., New York, as follows, viz. : Jan. 1, 1863, $750; June 1, 1863, $1250; Sept. 16, $2525; Dec. 31, 1863, $895.65 : they bought on time, paying legal interest. What was their whole indebtedness. May 1, 1864? 57. What must I pay for U. S. 6 per cents, that the invest- ment may yield 8 per cent. ? 58. A man, dying, left $3565 to be placed at interest for his son, who was 16 yr. 5 mo. 15 da. old ; how much will he receive when he is 21 years old, allowing 7^ interest ? 59. The population of New York city, in 1860, was 805650 ; it was estimated to have increased 20 per cent. Jan. 1, 1864. Suppose at this last date the whole population were drawn up in single file, each person occupying a space of 2i ft., and the whole line should begin to march at the rate of 2A miles per hour, what would be the length of the line, and how long would the procession be in passing any given point 1 60. A house being rented for $12 a month pays 7^ per cent, interest, what is the, value of the house ? ARITHMETICAL EXAMPLES 119 61. Bought 5000 bushels of wheat on 6 months' credit, at $1.37^ ; I immediately sold it at $1.35 cash, and put out the money at 6^ ; at the end of 6 months I paid for the wheat. Did I gain or lose by the transaction, and how much? 62. Thomas Baker bought a farm for $20000 cash, or 110000 payable in 6 months, and $12000 in 1 yr. 6 vao. ; he chose the latter mode of payment. Money being worth 7^ did he gain or lose, and how much ? 63. The earnings of the Chicago and Northwestern R. R. for the week ending Jan. 14, 1864, were $6926.12 more than for the same period in 1863 ; the earnings for the week men- tioned, in 1864, being an increase of 48^ over the earnings of the corresponding week of the previous year, what were the earnings for the week in 1864? 64. A's money is 50^ more than B's. How many per cent, less is B's than A's? 65. Bought 450 barrels of flour at $8.50, which I paid for ill iron at 3 cts. per pound ; the purchaser of the iron after- wards sold I of it to a scythe manufacturer. What quantity did he sell ] (j6. What is the difference between the simple and com- pound interest of $700 in 3 years at 5 per cent, per an- num ] 67. Reduce 9 sq. rd. 9 sq. yd. 7 sq. ft. 120 sq. m. to the decimal of i of f of f of 35 A. 2R. * 68. A man dying left 33]^ of his property to his wife; 50^ of the remainder to his son ; 75^ cent of the residue to daughter, and the balance, $120, to a faithful servant. How much did each receive 1 69. A house that cost $3125, was rented for $328,121. What per cent, did it pay on the investment 1 70. A grocer bought 60 gallons of milk by beer measure at 4 cents a quart, and sold it by wine measure at 5 cents a quart. How much was his gain ? 120 ARITHMETICAL EXAMPLES. 71. If I borrow $1000 in Mass. and lend it in New York, how much do I gain in 1 yr. 3 mo. 20 da. ? 72. The total population of America is 70415000, 39^ of which are Protestants; the total population of Europe is 282823000, 23;^ of which are Protestants. How many more Protestants in Europe than in America 1 73. If 300 sheep require 150 A. 3 R. 36 P. of pasture, how many acres will 450 sheep require? 74. I sent $12300 to my agent in New York, with which to purchase flour at $10 per barrel, after deducting his com- mission of 24^. How many barrels of flour did I receive ? 75. A manufacturer eflfected an insurance upon his factory and machinery, valued at $20000, paying an annual premium of 2^ ; in the second year the establishment was damaged by fire to the amount of $1560. How much did he save by the insurance ? 76. Average the following account : John Lyman. Dr. Cr. 1860. 1 1 1860. 1 00 1 June 24 ! 1 1 — ■ June 12 1 To Mdse. 530 By draft at 30 da. 1 480 00 Sept. 12 1 '' '* 428 00 1 Aug. 20 1 00 1 Oct. 8 1 " cash, 1 280 00 Oct. 28 " " 440 140 00 77. Three persons purchased a block of tenements for $350000, of which A paid $150000 ; B, $80000 ; C, $120000 ; the net proceeds of the rent were $21000. How much should each receive 1 78. How much gold, silver and copper in an eagle, its weight being 10 pwts. 18 gr. ? 79. A capitalist invested | of his money in Tl. B. stock, which depreciated 6|^; the remainder he invested in real estate, which advanced xl 5^, and thereby he gained $1500. How much did he gain in both investments ? 80. Boise, Smith & Co. failed in business ; their indebted- ness was $75000 ; their assets were. Cash, $3000; Mdse., $15- 500 ; Store, $28000 ; Bills Receivable, $5500 ; the expenses of ARITHMETICAL EXAMPLES. 121 settling were A% of the amount distributed to the creditors. What per cent, of their indebtedness can they pay 1 81. If 3 yd. 3 qr. 1 na. cost $12.20, how much will 18 yd. 2 qr. 1 na. of the same cloth cost ? 82. Bought a hogshead of molasses for a certain sum, but 16 gallons having leaked out, the remainder was sold for $1.87^ per gallon, at a loss of (S% on the cost. How much was the cost ? 83. A merchant bo't 400 yds. broadcloth @ $3.00 ; he sold A 60 yds. @ $3.50 ; B, 125 yds. % $3.40 ; C, 75 yds. @ $3.20; and the balance to D @ $2.95. What per cent, profit did he make on the whole ? 84. Jan. 1, 1863, Rhode Island had sent 14626 men to the war; Connecticut 1033 less than twice as many; Maine, 4886 more than Connecticut ; New Hampshire and Vermont together, 3639 more than Maine; and Massachusetts, 1189 more than Maine, New Hampshire and Vermont. How many men had the New England States sent to the army ? 85. An agent for a Hartford nurseryman sells 5000 apple trees at $24 per hundred ; 3000 pear trees at $40 per hun- dred; 2000 peach trees at $18 per hundred; 1500 cherry trees at $45 per hundred ; 500 plum trees at $45 per hun- dred, and 1000 ornamental trees at $50 per hundred. What is his commission, at 25^, and how much should he return to his employer, as the net proceeds after deducting $300 for expenses ? 86. How much is gained by investing $5250 in government bonds at 105^, brokerage 1|^, and selling the same at 116^, brokerage If^'? 87. A man traveled 19| miles the first day, 22? j miles the second day, and 19 mi. 1 fur. 20 rds. 15| feet the third day. How far did he travel in the three days 1 88. A broker charges melj^ for purchasing some uncur- rent bank bills at 25;^ discount; of these bills, three of $10 122 ARITHMETICAL EXAMPLES. each, and one of $50 became worthless ; I dispose of the re- mainder at par, and thus make $520. What was the amount of bills purchased ? 89. I bought 2345 bushels of wheat at $1.20, and imme- diately sold it at $1.30, on a note of 6 months, which I got discounted at bank at 7 per cent. How much did I gain 1 90. I sent $9020 to my agent in Chicago, who purchased grain at an average price of $1.10 per bushel, and charged 2\^ commission. How many bushels did he buy? 91. On the first of Jan., 1862, there were 10869 miles of railroad in operation in Great Britain, and the total receipts for the year were £28565355 ; the expenses were £878681 less than the net receipts. How many dollars U. S. currency were the net receipts per mile, sterling bills being quoted at 189^? 92. The number of men sent into the army, up to Jan. 1, 1863, from Illinois, Ohio, Pennsylvania, and New York, was proportional respectively to the numbers 27 y^^, 34, 40 and 44^ ; Ohio sent 34743 more men than Illinois. What num- ber of men did each State furnish? 93. A farmer exchanged 25 bu. 3 pk. 3 qt. of corn at $.80 per bushel, for 32 yds. sheeting and 8| yds. broadcloth. Al- lowing 1 yd. of broadcloth to equal in value 24 yds, of sheet- ing, what was the amount paid for each ? 94. If I make a profit of 15y\^ by selling Worcester's Dictionaries for $.85 above the cost, how much must I ad- vance on the price to realize a profit of 32^^^ ? 95. A farmer sold 4 loads of oats, averaging 35 bu. 3 pk. 7 qt. each, for $120.85^. How much are 100 bu. 3 pk. worth at the same rate? 96. Three men engaged in the manufacture of pails ; A put in $2550 for 8 months ; B, a sum not specified for 12 months ; C, $1080 for a time not specified. A received for his stock and profit $3400 ; B, $4200 for his ; C, $1485 for his. Re- quired B's stock and C's time. ARITHMETICAL EXAMPLES. 123 97. A man has two sons, one living in New York, the other in Massachusetts ; he wishes to place at interest $1000 for each, so that the amounts shall be the same in 5 yr. 7 mo. ; he supposes he has accomplished his object by loaning the given principals, one in New York at simple interest ; the olher in Massachusetts at compound interest, payable semi- annually. What is the difference between their respective amounts ? 98. Bought 42 lb. of coffee at the rate of 3^ lb. for $1.00, and 75 lb. more at the rate of 7 lb. for $2.33^ ; sold the whole at the rate of 9 lb. for $3.25. How much did I gain or lose ? 99. If 7 cwt. 2 qr. 18 lb. of sugar cost $90.24, how much sugar can be purchased for $300.80 ? 100. For what sum must a store and contents, valued at $25640, be insured, so as, in case of its destruction, to recover the entire value of the building and contents and the premium of 2 per cent. ? 101. A person traveled from New York to Harrisburg in 12 days, walking 4 miles the first day, 6 miles the second, 8 miles the third, and so on. How far is Harrisburg from New York? 102. The total length of mail routes in the U. S., June 1, 1861, was 140349 miles ; the total annual transportation was 54455412 miles. Allowing that no mails were carried on Sunday, how many times per day, on an average, were the mails carried over each route ? 103. A commission merchant receives 125 bbls. of flour from A, 150 bbls. from B, 225 bbls. from C; he finds on in- spection that A's is 10^ better than B's, and C's is ^fj% bet- ter than A's ; he sells the whole lot at $7.00 per barrel, and charges 4^ commission. How much must he remit to each? 104. A man sold a farm of 105 A. 2 R. 32 P. at $33.50 124 ARITHMETICAL EXAMPLES. per acre, and took a note payable in 5 mo. 15 da., at l^o in- terest; wishing the money for immediate use, he got the note discounted at a bank. How much did he receive ? 105. I wish to line the carpet of a room, 6i yd. long and 5\ yd. wide, with duck, | yd. wide. How many yds. of lining must I purchase, if it will shrink 4^ in length and 5^^ in width ? 106. Bought cloth at $4.00 per yard. What must be my asking price, that I may fall on it 12^, and still make 21^ on my purchase % 107. A, B and C engaged in partnership with a joint capi- tal of $']000 ; A putting in stock for 8 months, B for 9 months, G for 12 months ; A's part of the profits was 164, B's $81, and C's $84. Required the capital of each. 108. What is the net value in Chicago of a sum due in Paris of GoOO francs, which is sent to Liverpool, at \% com- mission ; exchange, 25.20 francs to £1 ; a draft for the net amount in Liverpool is drawn on Boston at 7^ premium, after deducting \% commission ; the proceeds of this bill being re- mitted to Chicago in a check at \^% discount? 109. What is the cash balance of the following account on Dee. 31, at 7 per cent.? James Hanson. Dr. Cr. "1859." 7 _ . 1 1 1859. L. Sept. 3 Oct. 2 To Sundries 4T8 ' 36 1 Sept. 17 By Sundries 96 1 54 '' Mdse. on 3 mo. 25G 1 37 1 " iO *' Cash on acct. 200 00 '» 21 1 Cl ., ii 3 u .375 ' 26 Oct. 3 H U 44 325 00 Nov. 12 j " " " 3 " 80 i 00 Nov. 17 " U 44 50 00 Dec. 15 1 " Sundries 148 i 76 Dec. 27 (4 44 44 84 00 110. In the battle of Shiloh, April, 1863, 4% of the Federal army engaged were slain upon the field ; 1^1% were wounded ; and the prisoners were 77 more than 50^ of the wounded, also 2355 more than the killed. How many men were in the engagement ? 11,1. A merchant bought 64 yd. broadcloth, which was 1| yd. wide, for $5 per yard ; but the cloth being wet, shrunk ARITHMETICAL EXAMPLES. 125 4.1 per cent, in width, and the same in length. For what must the cloth be sold per square yard to gain 20 per cent ? 112. The population of the United States in 1860 was 31446400, and the number of deaths reported was 1 for every 91 80 citizens ; —- of the deaths were of females. How many of each sex died during the year ? 113. I can sell a certain piece of property for $9000 cash, or for $4750 payable in 9 months, and $5200 payable in 1 year ; how much shall I gain by accepting the second offer, if money is worth 9% 1 114. A gentleman deposited $100 in a savings bank for the benefit of his son, at compound interest, at a semi-annual rate of 2^% ; he was to receive the amount as soon as it be- came $268.50 ; allowing that the deposit' was made when the son was one year old, what was his age when he received the money? 115. One-fifth is what per cent, of three-fourths 1 116. The receipts of the Post Office department in Ken- tucky for the year ending June 30, 1861, were as follows: letter postage, $8029.59; newspaper postage, $13981.36; registered letters, $388.00 ; stamps sold, $136453.98. The expenses were $59612.19 for compensation of postmasters, $16423.14 incidentals, $270273.23 for transportation of mails. What was the net expense to the Government of carrying the mails in Kentucky during the year 1 117. 1 exchanged 60 Ohio State bonds of $1000 each, at 81% premium, for Indiana bonds of $200 each, at 5% pi'c- mium. How many of the latter did I receive ? 118. If 12 oz. of wool make 2| yd. of cloth, 1| wido, how many pounds of wool are required to make 115 yds. of cloth 1 yd. wide] 119. A and B contracted with Gwinn and Co. to erect a cotton-mill for $50000. Not wishing to be burdened with 126 ARITHMETICAL EXAMPLES. the salary of a book-keeper, it was arranged that each partner should keep a strict account of all his expenditures and re- ceipts, and report at the completion of the job, at which time they would have a general settlement. At the time of set- lement they found their affairs standing as follows, viz. ; A had paid out for building material and wages $16750.50, and had received from Gwinn & Co. $12790 ; B had paid out for building material and wages $20186.75, and had received of Gwinn and Co. $15842. There was due the hands and for material; $4729.38. What was their entire profit? How much was due from Gwinn & Co] How much should be paid to A and B respectively 1 120. Bought a bill of goods for $1500, I payable in 3 months, -3 in 6 months, and the remainder in 9 months. How much ready cash ought I to pay for the goods, money being worth 6 per cent.? 121. If a ship sail 5 mi. 3 fur. 9| rd. per hour, how long will it be in going 1618 mi. 2 fur. 18.254 rd. ? 122. A house that cost $15725, rents for $1478.15; the insurance is | ^, and the repairs j%% each year. What rate of interest does it pay ? 123. A merchant, having soM a number of yards from a piece of cloth, found there were 8.75 yards left, which was 65 per cent, less than the quantity cut off. Required the number of yards in the piece at first. 124. The capital stock of the Boston and Worcester Rail- road Company is $4500000, and its debt $126000. Its gross earnings in 1861 were $928932, and its expenses $520338. If the company paid expenses, interest on its debt of 6%, and reserved $18534, what dividend would a stockholder receive who owned 25 shares of $100 ? 125. If $990.73 gain $55.67 in 9 mo. 19 da., what princi- pal is required to gain $31.12 in 2 yr. 5 mo. 26 da. ? 126. !Find a number between 893 and 931, which shall ARITHMETICAL EXAMrLES. . 127 have with each the same greatest common divisor that they have with each other. 127. A merchant has |216 due him, to be paid in 7 months ; but the debtor agrees to pay one-half ready money, and | of the remainder in 6 months. What time should he be allowed for paying the balance ? 128. Imported from Havre 120 baskets of champagne, 12 bottles eaoh, b% breakage, duty 40^, freight and other charges $134.10; and the whole cost 11166.42. How much did it cost per bottle in Havre? how much in store? and what must I charge per bottle to clear 20^ 1 129. How much butter at $.37^ a pound, must be given for 12 gal. 3 qt. of molasses, at. $.75 a gallon? 130. The paid-in capital of the United States Insurance Company in 1863, was $879720; its receipts for the year were $314470 ; and its losses and expenses $138526. What rate of dividend could it declare ? 131. How many feet of boards will it take to inclose a garden 40 ft. 6 in. long, and 30 ft. 3 in. wide, with a close fence 7 ft. 6 in. high ? 132. A pork merchant charged 12^ commission, and cleared $2251.30, after paying out $1565.24 for all expenses of packing ; if the pork cost him $.06^ a pound, how many pounds did he pack ? 133. How much more can a bank make in 528 days, with $10000, by discounting notes on 45 days' time, than by dis- counting them on 30 days, the rate of discount being 6^, and the profits in both cases retained in bank till the expiration of the time ? 134. Sold Hiram Jones goods to the amount of $2084, on credit for 6 mo. from Sept. 20, 1862; Oct. 8 he paid me $520; Nov. 20, $340; Dec. 25, $800; Jan. 12, 1863, $100. When, in equity, ought I to receive the balance ? 135. When a bill on Paris for 28965 francs costs $7183.32, what per cent, is the rate of exchange above par ? 128 ARITHMETICAL EXAMPLES. 130, Tlio average dividends of all the savings banks in Mass. in 1801, Avere 4^^, and $1943532 was distributed among the depositors. What were the aggregate deposits in the savings banks ? 137. A sells goods which had cost $800, to B at an ad- vance of 12^^; B sells them to C, and gains 11^^ of what ho had paid. What per cent, would A have gained had he sold the goods to C for the same which B received ? 1S8. There was paid in New Orleans $7840 for £1600 drafl on Liverpool. At what per cent, premium was it purchased ? 139. If it require $900 to support a family of 12 persons, 41 weeks and 1 day, how much at the same rate will be re- quired to support a family of 24 persons 23 weeks 6^ days ? 140. Subtract 2 fur. 10 rd. 5 yd. 2 fl. from 2 fur. 11 rd. 1 ft. 5 in. 141. The Cleveland, Columbus and Cincinnati Railroad re- ported its earnings for 1863 to be $2145080 ; and its expenses, $961785; the company invested in new depots, engines, cars and railroad stock, $551739; Aug. 1, 1863, it declared a 6% dividend of its paid-in capital of $5000000, and Jan. 1, 1864, another 5^ dividend. What surplus revenue still remained ? 142. The stock of three partners. A, B and C, was $2400, $2000, and $1800, and their gain $768, $960, and $1152 re- spectively ; C's stock continued in trade 4 months longer than B's. How long >yas the money of each in trade ? 143. If 12^ of what is received for goods is gain, what is the gain % 1 144. I sold I of my goods at an advance of 25^ ; j\ of them at a loss of 8^ ; r^^ of them at a profit of 30^, and 4 of them at a discount of 20^. For what % of the cost must the remainder be sold in order to lose b% on the whole ? 145. The charter of a new railroad company limits the stock to $1500000, of which 3 installments of 10^, 20^, and 40^, respectively, have been paid in ; the cost of construction has ARITHMETICAL EXAMrLES. 129 reached $850000, and the estimated cost of completion Is $850000. If the company call in the final installment of its stock, and assess the stockholders for the remaining outlay, what will be the rate % '? 146. At the surrender of Island No. 10, the privates taken were 60^ of the number of arms taken ; the line officers were 34^ of the privates, and the field officers and generals, 30 in number, were -| % of the privates. How many privates, and what number of arms were captured ? 147. The greatest common divisor of three numbers is 18, each of the numbers exceeds 18, and their least common multiple is 540. What are the numbers ? 148. If 97 sheep are bought for $100||, how much should be paid for 25 sheep at the same rate 1 149. I sold goods at an advance of 20^, and invested the money received in goods which I sold at a loss of 10^, and with the sum received purchased goods which were sold at a discount of 1G|^. What was the gain or loss per cent. ? 150. Borrowed of my neighbor $500, for 1 yr. 3 mo., at Q% ; not being able to pay at the end of the time, my neigh- bor agreed to let it run till the end of the second year at simple interest, but he was obliged to borrow $535.88^ for 9 mo. at the same ratOo How much more did my neighbor owe at the end of the year than I ? 151. The earth moves 19 miles per second in her orbit. How far does she travel from 7 h. 30 min. A. M. till 5 h. 15 min. P. M. ? 152. $1000. COLLINSVILLE, Conn., Mar. 1, 1863. Six months after date 1 promise to pay James Gray, or order, one thousand dollars, for value received. T. M. CURTISS. On this note were the following indorsements: Sept. 1, 1863, $300; Jan. 16, 1864, $200; March 1, 1864, $200; Mr.y 1, 1864, $200. How much was due July 4, 1864 ? G* 130 ARITHMETICAL EXAMPLES. 153. The Milwaukee and Prairie xiu Chiea Railroad report- ed, for the year 1863, gross earnings, $1184840 ; total ex- penses, 1793747 ; the interest on sinking fund was 1^204480, and $31613 was expended for various items of construction; the balance was a 5^ dividend on the capital stock. Required the capital stock. 154. Having used my carriage three years, I sold it for $(j6, which was 40^ less than the cost. What was the cost ? 155. What is the value of 25 hhd. sugar, each weighing 12 cwt. 3 qr. 16 lb.; draft, 3 lb. per cwt, and tare 10 lb. per cwt., at $11,625 per cwt. net? 156. A man having $28 1, gave | of it for 5| bushels of clover seed. What was the price per pound? 157. A merchant imported from Bremen 40 pieces of linen of 35 yards each, on which he paid for duties, at 26^, $218.40, and other charges to the amount of $131.60. What was the invoiced value per yard ? and the cost per yard after duties and charges were paid ? 158. At the battle of Fredericksburg, Dec. 13, 1862, the losses of the Federal army in killed, wounded and prisoners, were in the proportion of 12, 22 and 97 respectively, and there were ^< 9^0 more prisoners than killed. Required the total loss. 159. How many sacks of coffee, each containing 108 lb., at Is. 6d. per pound. New York currency, will pay for 135 yards of broadcloth, at $3| per yard? 160. A buyer expended equal sums of money in the pur- chase of wheat, rye and oats ; in the sales he cleared 7^ on the wheat, 5% on the rye. but lost 15^ on the oats ; the whole amount received was $1782. What sum did he expend for each kind of grain ? 161. I received an S% dividend on New York city railroad stock, and invested the money in the same stock at 80^. My stock having incroaced to $13750, what was the amount of my dividend ARITHMETICAL EXAMPLES. 131 162. Great Britain and Ireland have an area of 112190 square miles, and a population of 29169400. Supposing the families to average 5 persons, and the whole area to be equally divided among them, how much land could each family pos- sess? 163. If molasses cost 20^ less than $.75 a gallon, and it be sold at a profit of 25^, at what price is it sold ? 164. The quick step in marching being 2 paces of 28 inches each, per second, what is the rate per hour ? 165. How much time nmst a general allow for a detach- ment of soldiers, marching quick step, to reach a place 50 miles distant, giving the men a halt of 1^ hours? 166. A capitalist holding bonds of the Columbus and Indianapolis Railroad, to the amount of $27000, exchanged them at the market price of 96^, for capital stock of the same company, worth 81^; the bonds drew S% annually, while the stockholders received two dividends during the year ; the first of 3^ ^, and the second of 4^. How much did the capitalist gain annually by the exchange 1 167. The population of Mass. in 1850 was 994500; in 1860, 1131191; of Penn. in 1850, 2311800, and in 1860, 2901309. How much more was the increase per cent, in Penn. than in Mass. for the ten years ] 168. If the interest of $6786.24 for 1 yr. 10 mo. 16 da. is $1273.89, what will be the amount of $5772 from Oct. 26, 1859, to Apr. 12, 1864? 169. Find the day of maturity, the time to run, and the proceeds of the following note : ^575JL3_ Chicago, March 2, 1864. Six months after date, I promise to pay to the order of Marks dc Willis, five hundred seventy-five j%\ dollars, value received. Hiram Bennet. Discounted at a bank, Apr. 10^ at 6.^. 132 ARITHMETICAL EXAMPLES. 170. If 8 men can perform a piece of work in 32 days, how many men must be added to the number to perform the work in 8 days ? 171. The total value of all the property, real and personal, of the Free States in 1860, was $10852081600; and of the Slave States, $5225307000. The products of the Free States for the same year were valued at 14178051416 ; of the Slave States, $1149567540. How much greater per .cent, of the capital invested, were the products of the Free States, than of Slave States? 172. In what time will any sum of money amount to 10 times itself at 7 per cent. ? 173. A merchant sold a quantity of goods for $480, and loses at the rate of 9 per cent. What ought he to have sold them for to realize a profit of 7 per cent. ? 174. If a man dig a cellar 8 feet square and 6 feet deep in 2 days, how long will it take him to dig a similar one 12 feet square and 7 feet deep ? 175. The cost in store of 40 puncheons of Jamaica rum, 84 gal. each, was $1262.86; duty 15^; leakage 2^, and charges $106.68. What was the cost per gallon in Jamaica ? 176. In the examination of a class, 160 questions were sub- mitted to each of the five members ; A answered 130 ; B, 125; C, 115; D, 122; and E, 158. What was the standing of the class ? 177. If an army of 5000 men have provisions for 15 days, at the rate of 20 oz. a day to each man, and they be reinforced with 3000 men, upon what daily allowance must each man be put that the same provision may last 20 days ? 178. The British Industrial Exhibition remained open 141 days, and the average number of daily visitors was 42831 ; the whole amount received for admission was £6039171. What was the price of admission? 179. What per cent, of 24^ is I of 54^ ? ARITHMETICAL EXAMPLES. 133 180. A liquor dealer receives an invoice of 300 dozen bot- tles of porter, rated at $1.50 per dozen; allowing 2% for breakage, what will be the duty at 2A% 1 181. If the transportation of 8 hhd. sugar, each weighing 12i cwt. 25 leagues, cost $65, what must be paid for the transportation of 80 tierces of 2^ cwt. each, 75 leagues'? 182. I wish to obtain at a bank $840.25 ; for what sum must I give my note payable in 5 months and 21 days ? 183. A portion of a cargo of tea being damaged, was sold at $1.20 per pound, and at a Ipss of 16|^. At what rate must the remainder be sold to gain 25^ ? 184. A merchant bought 2 pieces of goods containing 60 yds. each, at $.75 a yard ; he also paid | of a cent per yard for freight. For what must he sell the goods per yard to make a profit of 25^, if the pieces fall short in measuring 2^% 1 185. A person paid a tax of 5 per cent, on his income. What must his income have been if, after he had paid the tax, there was $5671.50 remaining? 186. If 11 lb. of cheese are equivalent in value to 7 lb. of meat, and 21 lb. of meat to 4 bu. of corn, and 20 bu. of corn to 22 bu. of rye, and 9 bu. of rye to 2 cords of wood, how many pounds of cheese must be given in exchange for 12 cords of wood ? 187. What is the compound interest of $512.50 for 3 yr. 6 mo. 21 da., at 8^? 188. A store and its goods are worth $12740. What sum must be insured at 2% to cover both property and premium 1 189. The value of flour and meal produced in the United States, in 1860, was $225000000 ; of cotton during the same year, $115500000. The value of cotton was what % of the value of the flour 1 190. How many square feet in the four walls of a room 36 ft. long, 30 ft. wide, and lOi high? 191. A merchant sold flour at $6.50 per barrel, and gained 134 ARITHMETICAL EXAMPLES. 10^; he afterwards sold the same kind of flour at '^8.25 per barrel. What per cent, did he gain at the latter price ? 192. How shall a merchant tailor mark coats that cost $8.00 so as to fall 20^ from the marked price, and yet make 25^ on the coats ? 193. What must 2| lb. of tea be sold for, if 22i lb. cost $14, and the retail profit is 20^ ? 194. The area of Rhode Island is 519G98 acres, the cash value of which in 1860 was $19488675 ; the area of Delaware is 1004295 acres, of which the cash value was $31426357 ; at the same time there were 2290 slaves in Delaware. Now, if by freeing the slaves in the latter State the cash value of the farms would become the same per acre as in Rhode Island, how much would the State gain, reckoning the slaves at an average value of $250 ? 195. I of 28 is y\ of how many % of 55 ? 196. A man owed $420, due Oct. 1, 1863; he payed part of it, Aug. 15, 1863, and the rest Jan. 1, 1864. What were the payments 1 197. If 372 men in 7^ days, of 11 hours each, dig a canal of 7 degrees of hardness, 310 yards long, 5^ yards wide, and 21 yards deep, in how many days, of 8 hours each, will 27 men dig a canal of 4 degrees of hardness, 270 yards long, 7 yards wide and 3^ yards deep? 198. The net proceeds of the sale of 1000 tons of hay, at $20 per ton, after deducting $875 for charges, were $18325. What rate of commission was charged ? 199. What principal will gain $213, at 7 J per cent., in 2 yr. 4 mo. 12 da.? 200. The area drained by the ponds and lakes which sup- ply the city of Brooklyn with water is 621 square miles, upon which the average annual fall of rain is 38A inches ; the average daily supply to the city is 20000000 gallons. How much water falls for every gallon cc^nveyed to the city ? ARITHMETICAL EXAMPLES. 135 201. What is the least common multiple of G^, 9|, 10| and 7j\ 1 202. An army which has been three times decimated in battle now numbers only 14580 men. What was the origi- nal number in the army ? 203. Sold 2978 bushels of wheat at $2.00 per bushel ; in- vested the proceeds in sugar, as per order, reserving my com- mission of 5^ for selling and 1^^% ^^^ ^^yi^^g? ^^^ the expense of shipping, $53.37. How much did I invest in sugar ? 204. A and B had the same amount of money ; A spent 7G^ of his money for land, and B lost by gambling a sum equal to 28^^ of what both had at first, when both together had $50.25. What sum had each at first, and how much had each left 1 205. There are 20 colleges in New York, having an aggre- gate of 118060 volumes in all their libraries. What is the average value of these libraries, at $| per volume ? 206. What per cent, of a number is 40^ of | of it ? 207. How far does a man walk in planting a field of corn 207 ft. square, the rows being 3 feet apart and 3 feet from the fence 1 208. A merchant owes $440, payable in 20 months, and $896, payable in 24 months ; the first he pays in 5 months, and the second in one month after that. How much should he pay, allowing 8 per cent, per annum ? 209. Willis, Markham, & Co. of New Orleans import from Liverpool 8 pieces of Turkey Carpeting, 35 yd. each, at 6-. per yd., duty 33|^; 300 yd. woolen goods at 4s. per yd., duty 18^, and 25 pieces of silk, 18 yds. each, at 2s. 6d. per yard, duty 24^. Required the whole amount of duty, allow- ing the value of the pound sterling to be $4.84 ? 210. Paid $63.90 duties at the rate of 9 per cent, on 50 casks of raisins, tare 15 lb. per cask ; allowing the gross weight of each cask to have been 115 lb., what was the in- voice value per pound ? 136 ARITHMETICAL EXAMPLES. 211. The total value of real estate and personal property in California in 1850 was $22161872 ; in 1860, $20787401^ What was the total increase, and increase per cent. ? 212. Divide $435 among A, B, and C, so that A of A's money shall be equal to | of B's, or | of C's. 213. James Haynes buys a bill of merchandise in New York, at cash price, to the amount of $2973.80, and gives in payment his note at 3 months at 7^^. What must be the face of the note ? 214. If 6 men do as much work as 14 women, and 10 women as much as 27 boys, and 14 boys as much as 25 girls, and 18 girls bind 250 sheaves in an hour, how many sheaves can 24 men bind in the same time ? 215. If A owes $500 due in 6 months, $400 clue in 4 months, and $300 due in 7 months, and pays | of the whole in 3 months, when ought the remainder to be paid ? 216. The population of Cha'rleston, S. C, in 1850 w^as 42982, and in 1860, 40575; the population of New Haven, Conn., at the same dates was 20345, and 39266, respectively. What w^as the increase per cent, in New Haven, and w^hat the loss per cent, in Charleston, during this time ] 217. The interest of $4000 for 1 month and 6 days is $36, what is the rate per cent. 218. William Hatch, born Feb. 29, 1844, received from his father a present of $50 on each birthday till he became of age. What was the amount received ? 219. If I of a hogshead of oil is worth $48, what is the value of I of the remainder ? 220. Bought a quantity of wine for 675.32^, at $.85 pei* gallon ; but a part having leaked out, the remainder was sold at 40^ advance, and the original cost was realized. What quantity leaked out 1 221. In 1860 there were 7766 manufacturing establish ments in Massachusetts, with an aggregate capital of $133 ARITHMETICAL EXAMPLES. 137 000000; these establishments employed 210000 hands, and consumed during the year $140000000 worth of raw ma- terial, which, when manufactured, increased in value to $266000000. How much did each dollar of capital produce ? each dollar of raw material ? and what was the average value produced by each hand 1 222. Bought of M. J. & Co. as follows : April 1, 1863, on 60 days' credit, a bill of $250 " 20, " " 90 " " " 600 July 5, " " 80 " " " 400 Also, sold to M. J. & Co. : April 5, 1863, on 2 months' credit, a bill of $450 May 20, " " 3 " " " 600 From what date ought the balance of the debt to draw inter- est ? 223. Gave my note at a bank for $]2")r).38, payable in 4 mo. 12 da. ; if discounted at 6^, what sum did I receive ? 224. A merchant sold goods for $600, and gained 25^ ; he invested the proceeds in flour, on which he lost 20^ ; did he gain or lose by the transaction ? and how much % 225. Eour per cent, of 325 bushels is what per cent, of 3^ per cent, of 200 bushels ? 226. A owes B $600 due in 4 months, and $840 due in 6 months ; B owes A $1600 due in 7 months. If A should make present payment of his debts, when ought B in justice to pay A ? 227. The manufacturing establishments in all the Southern States in 1860 numbered 1806, in which $100655000 capital was invested; these establishments employed 110110 hands, and consumed $82609000 worth of raw material ; the pro- ducts for the year wxre valued at $145360260. How much did each dollar of capital produce ? each dollar of raw ma- terial? and what was the average value produced by each hand? 138 ARITHMETICAL EXAMPLES. 228. Bought a number of bales of velvet, each containing 126 yards, at the rate of $10 for 7 yards, and immediately sold the whole at the rate of $13 for 9 yards, thereby making $26. Required the number of bales ? 229. If eggs are bought at the rate of 10 for $.25, and sold at the rate of 6 for $.16, how many dozen must be sold to gain $20 1 j 230. In what time at 12^ will $240 amount to $720 ] 231. I have $58650 to invest, and can buy New York Cen- tral 6's at 102^, or New York Central 7's at 115^. How much more profitable will the latter investment be than the former per year ] 232. In 1862 there were 38 instructors in Harvard Univer- sity, and the ratio of teachers to students was 1 to 22 ; of teachers to alumni, 1 to 189 ; of alumni to the volumes in the library, 9 to 190. Required the number of students, alumni, and volumes in library. 233. One thousand dollars was to be divided among A, B and C, in the ratio of ^, | and 4, but C relinquished his share ; how much did A and B each receive 1 234. A wholesale merchant sent a quantity of goods into the country to be sold at auction, on a commission of 4^^. What amount of goods must be sold, that his agent may buy produce with the avails to the amount of $1910, after retain- ing a commission of 2% 1 235. How many yards of cloth, 1| yards wide, are required for a garment containing 23 square yards, if the cloth m being sponged shrinks 10^ in length and S% in width? 236. The products of Rhode Island in 1860, were valued at $52440000, or $300 per capita; of Delaware, $16159000, or $143 per head. What was the difference in population in the two States? 237. If I of A's money equals ^ of B's, what part of B's money equals | of A's? ARITHMETICAL EXAMPLES. 139 238. What are the proceeds of a note of $5600, payable in 6 months, discounted at 7|^ ? 239. If the annual rent of 23 A. 1 R. 27 P. of land be 1187.35, how much will be the rent of 71 A. 20 P. ? 240. The Julian Calendar assumed the year, 365 da. 6 h., instead of 365 da. 5 h. 48 min. 49.7 sec, its true length. In how many years was 1 day gained ? 241 . I got a note of $800, payable in 4 months, discounted iQt a bank at 6^, and put the money received, upon interest at the rate of 74^^. When the note matured, I paid it with the pro- ceeds of a bank-note, at 5 mo., discounted, also at 6^, and, as before, paid this with the proceeds of a third, which matured in one year from the date of the original note, at which time I collected the sum due, and paid the bank note.. What did 1 gain by the transaction ? 242. If the interest of £179 12s. lid. for 1 yr. 7 mos., is £14 4s. 5|d., what is the rate per cent. 1 243. Three persons found $120, which they agreed to share in the proportions of 5, 7 and 8. How much did each re- ceive? 244. A commission merchant sold goods to the amount of $59376.50, for which he charged a commission of | of one per cent. What was his commission ? 245. The public debt of the United States, March 1, 1864, was as follows: Immediate Liabilities, $48725728.68; Old Public Debt, $67447412.55; 7-30 Bonds, $.38772300; U. S. Notes, $449119548.10; Fractional Currency, $18745720.- 15; Twenty Years Loans and Bonds, $51227000; Treasury Notes, $101362031.22; Oregon War Debt, $1016000; Cer- tificates of Indebtedness, $136121650 ; and 5-20 Bonds $510- 165446.92; the amount in the Treasury being $9411795.27, what was the debt ? 246. A has $12000 loaned in Connnecticut, and $10600 loaned in New York. On which sum is the legal interest the greater, and how much per year 1 140 AlUTHMETICAL EXAMPLES. 247. A man took out a life policy for $3000, at the rate of $21.50 per $1000. What sum must he deposit in a savings bank, the compound interest of which at 5^, payable semi- annually, shall discharge his annual premium ? 248. A merchant bought 500 barrels of flour at $6.50 a barrel, and sold it immediately at $7.25 a barrel, receiving in payment a note due three months hence, which he had dis- counted at a bank at 6^. What did he gain on the flour ? 249. If a staff* 2 ft. 9 in. long, cast a shadow 1 ft. 1 J in., what is the hight of a pole which casts a shadow 63 ft. ? 250. The gross earnings of the Michigan Southern Railroad, for the year ending March 1, 1864, were $3308011 ; the ex- penditures, $1669006. It paid interest to the amount of $690000, and a 10^ dividend upon its preferred stock of $2893600. How much remained for a sinking fund ? 251. If I of a ton of coal be sold for what | of it cost, what is the gain per cent. ? 252. A's money is to B's as 3 to 4; ^ of A's money placed at interest for 3 yr. 8 mo. 15 da., at 6 per cent, will amount to $418,095. How much money has each ? 253. Sold wheat at $1.64 }§ per bushel, and gained 12^. For what should it have been sold to have lost 15^ ? 254. What is the cost of a 90 days' bill on Philadelphia, to the amount of $1000, at ^% premium, and interest off* at 6^? 255. The interest of a certain sum for 1 mo. 19 da. at 13^ per cent, is $.866. What is the principal ? 256. The Illinois Central Railroad sold in one month 26780 acres of land at an average price of $10.95 per acre, and an average credit of 3 yr. 6 mo. What \vas the cash value of the sales, money being worth 6^? 257. A and B are partners ; A's stock i3 to B's as 5 to 8 ; after 4 months A withdraws | of his, and B | of his. How shall the year's gain, $920, be divided I ARITHMETICAL EXAMPLES. 141 258. If a garden of a certain length and 4 rd. 8 ft. 3 in. wide contain g of an acre, how much would it contain if it were 9 rods wide ? 259. When is the balance of the following account due, per average ? Charles Derby. Dr. Cr. 1859. 1 ia59. — ' Jan. 21 To Mdse. 32 00 1 Jan. 1 By Cash, 84 00 Mar. 5 145 00 1 Feb. 4 00 1 Mar 30 40 00 " 22 U t« 194 12 00 260. A owed $2520, due July 18, 18G3; he paid 8720 be- fore, and the rest after it became due. When were the pay- ments made if they were 49 days apart ? 261. If $500 dollars is deposited for a child at birth, at 1% compound interest, payable semi-annually, what will it amount to when the child is 21 years of age ? 262. Bought fish at $6.37^ per quintal, and sold the same at $7,391. What was the gain per cent. ? 263. The amount of specie in Sub-Treasury, New York, Feb. 1, 1864, was $39963000; during the month two steam- ers from California brought in $1250069; $88150 was im- ported from foreign ports, and $4825748 was gathered in from hoarded specie ; the amount of gold exported for the same time was $3015367. How much remained in the Sub- Treasury, March 1, 1864? 264. J. S. Sanborn purchased 80 acres of land of the Illi- nois Central Railroad Company, on the following terms : Cash payment, $48 ; payment at the end of the first, second and third years, $48 each ; payment at the end of the fourth year, $236 ; at the end of the fifth year, $224 ; at the end of the sixth year, $212 ; and at the end of the seventh year, $200. What was the cash price per acre 1 265. Bought a watch for $60, and sold it for $100. What per cent of the cost was the gain ? 266. If 3 pounds of tobacco cost $.84, and 5 pounds to- 142 ARITHMETICAL EXAMPLES. bacco are worth 10^ pounds of sugar, what will 90 pounds of sugar cost ? 2G7. What must be paid in Boston for a draft on New York at 30 days, for $4500, exchange being at 1% premium ] 2G8. The cost of producing fine salt at the Onondaga Salt Works, is 1 1 :\ cents per bushel, and coarse salt 5 cents ; in 18G2, 1884697 bushels of coarse, and 5315C94 bushels of fine salt were produced, and sold at an average price of 19 cents per bushel. What was the per cent, of profit 1 2G9. At what rate must a note, payable in one year, with- out grace, be discounted to produce 6^ interest ? 270. The factors of a certain number are 16|, 30|, and 19 1 ; what is | of | of ^ of the number 1 271. A bank has $20000 loaned on call at b%\ how much is the daily interest, reckoning 365 days in a year 1 272. Bought a horse for $110; for how much must he be sold to gain 37^^? 273. The total value of real estate and personal property in the United States in 1850 was $7135780228; in 18G2, $16159616068. What was the actual increase m property 1 and the increase per cent, in 12 years 1 274. A man, engaged in business with a capital of $25000 is making 10^ per cent, per annum on his capital*; but on account of failing health, he is obliged to quit business, and loan his money at 7 per cent. How much does he lose in 2 yr. 7 mo. 20 da. ? 275. If one cubic foot of anthracite coal weighs 56 lb., what must be the length of a bin 8 ft. wide and 6 ft. deep, to hold 14 long tons of coal ] 276. A and B invested equal sums in trade ; A lost 20^ of his money, and B gained $50.05 ; A's money was then 75^ of B's ; what sum did each invest ? 277. In what time will $4500 gain $181.25 at 5 per cent. 1 ARITHMETICAL EXAMPLES. 143 278. A merchant bought goods in Chicago to the amount of $850, and gave his note, July 1, 1860, on interest after 2 months ; 4 months after the note was given, he paid $400, and 6 months after the first payment, he paid $360. What was there due Sept. 19, 1862 ? 279. Jowa produced in one year 18350000 bushels of wheat, valued at $7200000; 60000000 bushels of corn, worth $.12 per bushel ; 10000000 bushels of oats, valued at $1500- 000 ; 3000000 bushels of potatoes, worth $.25 per bushel. Required the whole number of bushels and their total value. 280. If the price of a farm of 160 A. 2 Jl. 20 P. be $7850.- 25, what will be the price of another farm, containing 120 A, 30 P., if 3 acres of the latter be worth 4 of the former 1 281. A man bought 840 bushels of oats in New York at $.35 per bushel, and sold them in Connecticut for $349.44. The transactions being made by weight, how much advance upon the cost was the selling price per bushel ? 282. A gentleman, traveling east from Lawrence, Kansas, in 95° 10' W. Long, found, on arriving at Boston, that his watch, an exoeilent time-keeper, was 1 h. 86 min. 28 sec. slower than the time at Boston. What is the longitude of Boston 1 283. The revenue of the English Government for the year 1861 was $332142625, and the expenditures for the same year exceeded the revenue by 3i^. How much was the national debt increased during the year ? 284. A and B can do a work in 10{^ days ; B and C in 13^ days'; and A and C in 12 days. In what time would each do the work alone 1 and how long would it take them, working all together, to do it ? 285. The net proceeds of a shipment of hay, sold at $14 per ton, after deducting a commission of 3^, and $500 for other charges, were $6290. How many tons of hay were shipped 1 144 ARITHMETICAL EXAMPLES. 286. In how many years is a day gained by the Gregorian Calendar, which allows for the fraction of a day by adding 97 days in 400 years ? 287. How many shares of |50 each must be bought at 25% discount, brokerage 1|^, and sold at 16% discount, brokerage life, to gain $134? 288. Bor>ds at 25% premium, brokerage ^% cost $527.93 more than the face ; what is the face 1 289. In the United Kingdom of Great Britain 593284200 letters were delivered in the year 1861, of which 486679200 belonged- to England and Wales, or 24 to each inhabitant ; 50049000 belonged to Ireland, or 9 to 6ach inhabitant ; and 56556000 to Scotland, or 18 to each inhabitant. What was the population of the United Kingdom'? 290. A factor receives $30056, and is directed to purchase cotton at $289 per bale ; he is to receive 4% commission. How many bales does he buy ? 291. B. F. Sears bought a house and lot, Apr. 1, 1863, for which he agreed to pay $2500 on the 16th of the following Nov., and $1800, Apr. 1, 1864. If he could iiave got a dis- count of 9^ for present payment, how much would he have gained by borrowing the sum at 7^, and how much would he have borrowed 1 292. Three men engaged in the lumber trade ; A furnished $4000, and B $6000 ; they gained $1680, of which Cs share was $840. Required C's stock and A's and B's gain. 293. If a cistern 19A ft. long, 101 ft. wide, and 12 ft. deep, hold 546 barrels, how many barrels will a cistern contain that is 18 ft. long, 9 ft. wide and 15 ft. deep 1 294. A speculator gained 25^ on | of his investment, and lost 5% on the remainder ; his net profits were $1140. Had he gained 25^ on |, and lost 5^ on the remainder, what would have been his net profits? 295. A lady bought 23 yards of sheeting and 57^ yards of ARITHMETICAL EXAMPLES. 145 calico ; she paid 2^ cents more per yard for the sheeting than for the calico, and the entire cost of the calico was twice as much as the sheeting. What was the price of each per yard 1 296. I is how many per cent, of | ? 297. The national debt of England, Mar. 1, 1862, was £805000000. If this debt were paid in silver, of which there are 3 oz. 7 pwt. 12 gr. to a £, how long a train of cars, allowing each car to occupy a space 30 ft. in length, and to carry 10 short tons, would be required to carry it ? 298. One pound of gold is equal in value to 14.29 pounds of silver. If the above debl were paid in gold, how long a train would be required to carry it? 299. A merchant bought a quantity of butter at $24 per cwt., cash. For how much per pound must he sell it to gain 15^, and allow S% discount for cash? 300. If a stone 20 inches long, 15 inches broad, and 8 inches thick, weigh 217 pounds, what will be the length, breadth and thickness of a similar stone that weighs 13888 pounds ? 301. Twenty-five workmen have agreed to labor 12 hours a day for 24 days, to pay an advance made to them of $900, but having lost each an hour per day, five of them engage to fulfill the agreement by working 12 days. How many hours per day must these labor ] 302. Says B to C : " | of my money is equal to | of yours, and the difference between your money and mine is $10." What sum had each ? 303. What is the amount of $872.50 for 3 yr. 6 mo. 18 da., at 7^% ^ 304. Four men hire a pasture of 125 A. 48 P. at $1.75 per acre ; A puts in 125, B 150, C 200 and D 225 sheep. How much rent ought each to pay 1 305. Sept. 15, 1862, 11460 men, forming 12 regiments of infantry and 6 batteries, surrendered at Harper's Ferry ; the 7 14G ARITHMETICAL EXAMPLES. average number of men attached to each battery was J J of the average number in each regiment; there were 123 pris- oners unclassified. Required the number of infantry and ar- tillery and the total surrender. 306. Gave $533.33| of notes at 4fo discount for $500 gold. What rate of premium was the gold ? 307. A and B made a joint stock of $1666, and gained §204, of which B had $60 more than A. How much did each contribute to the stock 1 308. A grocer bought 11 bushels of chestnuts at $3.00 a bushel, and retailed them at 3 cents a half pint. What ^ profit was his gain ] 309. July 1, 1859, four balloonists left St. Louis at 4 h. 80 mhi. P. M., and landed in Jefferson Co., N. Y., 1150 miles from St. Louis, at 20 minutes past noon of July 2nd. What was the average velocity per minute ? 310. If the use of $6919.32 for 7 yr. 6 mo. is worth $3113.694, what sum is that whose use for 10 yr. 10 mo. 20 d. is worth $3266.663^ 1 311. Forty per cent, of brandy is alcohol. How much alcohol does a man drink in 52 years, if he take | of a gill of brandy 3 times a day ? 312. A house that rents for $848.25 cost $8700. What fo does it pay on the investment ? 313. When shall a note be made payable to balance the following account ? James Tyler. Dr. Cr. 1860. 1 1860." June 12 To Mdse. on 3 mo. 530 |84 Sept. 14 By Cash, 4*^6 00 " 20 U U tt It 236 48 " 25 n u 320 no 30 " U (C n 739 56 Oct. 3 (( (( 560 00 July 5 l( (( (( n 27B 44 IT U (( 370 00 - 16 U (( it u 194 iT8 ! Nov. 16 tl (( 840 00 29 " " " " 536 42 24 " " 560 00 814. M, N, and S, are partners. On closing business, they have the following resources and liabilities; cash on ARITHMETICAL EXAMPLES. 147 hand, $5430 ; shop and fixtures valued at $2560 ; bills receivable, $956 ; Barns &; Co. owe them $865 ; ten shares .in Canal R. R. stock, $1000. They owe on notes unre- deemed, $1865. M invested $2400 ; N, $3000, and S, $2700. What is the net gain ? 315. What per cent, of an acre is 2 R. 20 P. 1 316. In the battle of Perryville, Ky., Oct. 8, 1862, the Rebel loss in killed and prisoners together was 50^ of the loss in wounded, and the prisoners were /^ of the killed* What per cent, of the loss were prisoners 1 The prisoners numbered 200. What was 'the whole Rebel loss ? 317. The Federal loss in the same battle was 350 more than I the rebel loss ; the prisoners were 16^ of the entire loss ; and the killed 50 more than 20^ of the entire Federal loss; the remainder being wounded, what was their number ] 318. At $11.75 per cwt., how much sugar can be bought for $90.25 ] 319. If it require 2250 bricks, 8 in. long by 4 in. wide, to pave a court 25 ft. by 20 ft., how many tiles, 10 in. long by 5 in. wide, will be required to pave a walk 300 ft. by 8 ft. ? 320. My salary is $800 a year. If I pay 25^ for board, 10^ of the remainder for rent, 20^ of the residue for clothes, $32 for books, and loan ^ the remainder, what ^ of my salary is unexpended ? 321. Invested $3432 in Government bonds at 106^, paying 11^ brokerage, and afterward sold the stock at 12;^ pre- mium, brokerage 1^^. What was my gain ? 322. A merchant bought a quantity of flour at $8.00 per barrel on a credit of 3 months, and kept it 6 months ; then sold it on 3 months' credit, and gained 5^. Money being worth 6^, for how much did he sell the flour per barrel ? 323. 1 qt. 1| pt. is what per cent, of 2 gal. 3| qt. ? 324. I own $12500 in a Mutual Insurance Company. How 148 ARITHMETICAL EXAMPLES. many shares shall I possess after a dividend of 8^ has been declared, payable in stock ? 325. Twelve million gallons of petroleum were sent to Europe from the United States in 1862 for $3600000 ; the cost of production being $.20 a gallon, what was the rate of profit 1 326. What is the value of 40 casks of sugar, each weigh- ing 12 cwt. 3 qr. 5 lb., draft 5,^, tare 10;^, at $8.75 per cwt. net? 327. At what rate of discount must the Illinois State Q^ bonds be purchased that the person investing may receive 6~^ upon his money ] 328. Jones, Brown, Hall &; Smith are partners; Jones takes I of the gains or losses ; Brown |, Hall i, and Smith the remainder. At the close of the year the resources of the fu-m are : Cash $6875, Merchandise $8965, Bonds and Mort- gages $7650, Bank Stock $3000 ; Jones has drawn from the business $600, Brown $350, and Hall $190; the liabilities are: Notes outstanding $3640; Balance in favor of Reed &; Co., $750; Balance in favor of Suffolk, $2645; Jones invested $6365, Brown $5270, Hall $4180, and Smith $2320. What is each partner's interest in the business at the close of the year ? 329. What will be the duty at A^fo on a case of jewelry and watches amounting to $2780 ? 330. A merchant bought 16 barrels of salt at $1| per barrel, and put it into sacks of 10 and 25 lb., each an equal Qumber, selling them for $.08 and $.20 each. What fo was \iis profit ? 331. In the series of battles from Aug. 27 to Sept. 1, 1862, Tought before Washington, the killed of the Union army were 50^ of the prisoners, and the prisoners 33^^ of the wounded. What per cent, of the v^ounded, and what per cent, of the whole loss were the killed 1 ARITHMETICAL EXAMPLES. 149 332. The total Union loss in the above-mentioned battles being 9000 ; how many were killed, wounded, and taken pris- oners, respectively ? 333. Where $37.70 fg will purchase 7 yd. 3| qr. of cloth, what is the price per yard ? 334. If a horse trot 2 miles in 5 min. 55 sec, how far would he trot in an hour at the same rate ? 335. A ship has a leak that will fill and sink her in 24 hours ; all her pumps are capable of emptying her in 25 hours. If the pumps are worked after the vessel has been leaking 3 hours, how long before the ship will sink ? 336. How much wine can be bought for $1.82, when a hogshead is worth $70.56 ? 337. Three shafts together make 465 revolutions in a minute ; the first makes a certain number, the second 3 times as many, and 10 more, and the third 15 less than twice as many as the second. How many revolutions does each make? 338. A farmer sold at one time 35 bushels of corn and 60 bushels of wheat for $157.50 ; at- another time 56 bushels of corn and 42 bushels of wheat for the same sum of money. What was the price of each per bushel 1 339. A hired a house for one year for $500 ; at the end of three months he takes in H ; and after 3 months more, M ; and at the end of 9 months, K. At the end of the year how much rent must each pay ] 340. The longitude of Paris is 2° 20' 22" E., and of Con, stantinople, 8° 59' E. When it is 1 A. M. at the latter place, what time is it at the former ? 341. How much gold at 68g^ premium can be bought for $5396 currency 1 342. If 12 pipes, each delivering 12 gal. a minute, fill a cistern in 3 h. 24 min., how many pipes, each delivering 16 150 ARITHMETICAL EXAMPLES. gal. a minute, will fill a cistern 6 times as large in G hours 48 minutes 1 343. The earnings of the Hudson River R. R. for Feb. 1864 were $472240, which was an increase of llg^ over the earnings for the same month in 18(33. How much was the increase ? 344. A town, 6 miles square, is divided into 325 equal farms. What must A. G. Dickey pay for one of these farms at $21.25 per acre ? 345. If $1500 in 7 mo. 20 da. produce $95,833, what prin. cipal must be loaned to gain $58 in 10 mo. 20 da. ? 346. M and N enter into a partnershij? for 2 years ; M puts in $8000, and N $2500 ; N is to do the business, and his services are regarded as worth the use of $5500 ; after 6 months M increases his stock to $12000 ; at the end of 2 years the partnership is closed, and there is a net gain of $4750. Required each partner's share of the gain. 347. A merchant bought 500 barrels of flour at $5.00 a barrel, payable in 3 months ; after keeping it 30 days, he sold it for $5.50 a barrel, receiving a note payable in 3 months ; the purchase money becoming due, he got the note discounted at a bank to meet it. How much did he gain by the transaction ? 348. What was the cost of 12 Ohio State Bonds of $500 each at 12^ premium, |^ brokerage? 349. At the battle of Pea Ridge, March 7, 1862, j% of the whole loss of the Rebel army were prisoners ; the killed were 500 less than the prisoners, and the wounded were 300 more than twice the killed. What was the total Rebel loss ? 350. If a man, by traveling 9 hours each day, can go 234 miles in 15 days how far can he travel in 30 days of 8 hours «ach ? 351. How many shares of mining stock at 80^ must be ARITHMETICAL EXAMPLES. 151 sold in order that the proceeds invested in California 8's at 108^ may yield a profit of $960 ? 352. The duty on 1000 drums of figs, each containing 14 lb., invoiced at 6| cents per pound, was $74.37^. What was the rate of duty 1 353. How much was the New England currency depre- ciated at the adoption of United States money, when £1 was worth $4| ? 354. How much had New York currency depreciated at the same time ? 355. How much had New York currency depreciated below New England ? 356. Sold goods to a certain amount on a commission of 5^, and having remitted the net proceeds to the owner, re- ceived for prompt payment l^ which amounted to $16,15. What was the amount of commission 1 357. What is the difference in cost between a draft on Boston of $17302.80, at 1|^ premium, and one on Chicago, for the same amount, at ^^ discount 1 358. A man, engaging in trade with $9600, found at the end of 3 years that he had gained $138,75 more than | of his 'Capital. What was his average annual gain ? 359. In 1837, the silver dollar contained 412^- grains of standard silver, but in 1853 the weight was changed to 384 grains. The fineness remaining the same, one dollar of the old coinage was worth how much of the new 1 360. A man has a piece of land 95 J rods long and 58 J rods wide, which he wishes to lay out in the largest possibl square lots of equal size. How many lots will there be ? 361. A owes $1500, of which $400 is to be paid in 4 months, $500 in 5 months, and $600 in 6 months. If he pays the whole at once, at what time must he make the payment ? 362. What is the duty at 25^ on 27 tons 8 cwt. 3 qr. 20 lb. of iron, invoiced at $48 per ton ? e 152 ARITHMETICAL EXAMPLES. SC)3. S. F. Root has cloth at 13.50 per yard, and S. Smith has hay at $14.70 per ton. If in trading Root puts his cloth at $4.50, what should Smith charge for his hay 1 364. The Erie Railroad earned from all sources, during the year 18G3, 110469480, and the expenses of operating the road were 61^ of the earnings. It paid for interest, rent of other roads, taxes and sinking fund, 11986315. July 1, 1863, it paid a 4i^ dividend upon its paid-in capital of $14000000, and a 5^ dividend upon the same, Jan. 1, 1864. There was a surplus of $26621.28, Jan. 1, 1863. What was the balance to the credit of the road, Jan. 1, 1864 ? 365. The cargo of a ship is worth $96000, and | of l of /^ of the cargo is worth | of | of | of the value of the ship. What is the value of the ship ? 366. A Boston merchant, having received an importation of wine from Lisbon, invoiced at 3008 milrees, 470 reis, al- lows his correspondent in Lisbon to draw on him for the necessary sum, exchange on the United States being in Lis- bon 940 reis=$l. How much would the merchant have saved by remitting a draft on Lisbon purchased at $1,055 per milree ? 367. How many eagles, each containing 9 pwt. 16.2 gr. of pure gold can I get for 2278.269 oz. pure gold at the mint, allowing 1^% for coining expenses'? 368. A owes B $500, payable in 4 months ; at the close of 2 months he wishes to make such a payment as will extend the time of the balance to one year. What must be the pay- ment? 369. Massachusetts paid $2750 internal revenue tax, in 1863, on gold plate, at the rate of $.50 per ounce Troy. What was the value of the gold plate, allowing it to average 18 carats fine, an ounce of pure gold being worth $20,672 ? 370. A, M and S form a partnership, with capitals of $5000, $10000 and $15000, respectively ; A draws out $500 ARITHMETICAL EXAMPLES. 153 at the end of each year, M, $800, and S, $900 ; at the end of 5 years their joint capital is $28600. How niuch of it does each own 1 371. An agent received $65 for collecting a debt of $1300. What was the rate of his commission ] 372. If 6 A. 3 R. 3 rd. of land are worth £65 4s. 9d., what is the value of 47 A. 1 R. 21 rd., U. States money, sterling money being 10|^ above the par value? 373. If the net earnings of a bank with $250000 capital are enough to pay an annual dividend of 10^, and reserve a surplus of $2500, also to pay 8^^ of its net earnings to the State instead of taxes, what is the rate of taxation on its cap- ital? _ 374. The Lackawanna and Bloomsburg Railroad paid $254384 expenses for one year, and $141985 interest, leaving a surplus equal to S^q% of the capital stock of $1342500. What were the gross earnings for the year] 375. A's gain was $840, B's $1125, C's $1820; A's capi- tal was in trade 7 months, B's 9 months, and C's 1 yr. 2 months. How much of the capital, $13875, did each own ? 376. A merchant marked a piece of goods 25^ above the cost, but its season passing, he determined to sell it 20^ be- low the marked price, supposing he should make 5^. Did he make or lose ? 377. Exchanged 156 bu. 3pk.7 qt. 1 pt. of wheat, at $.93| per bushel, for 87i yd. of silk at $ 87^ per yard, and the balance in cash. How much money was received ] 378. James Fitch owes three notes to George Holmes ; one of $200, due in 8 months ; another of $200, due in 1 6 months ; and the third of $400, due in 2 years. Should the three notes be converted into two notes of equal amount, one to run one-half as long as the other, when ought they to be made payable ? 379. The cost of constructing all the canils in New York, 154 ARITHMETICAL EXAMPLES. up to 1802, was $62292500 ; the amount of tolls collected from these, in 1861, was $3908785. How much less were the tolls than the legal interest upon the sum invested in building the canals 1 380. 1 of a quarter is what per cent, of | of a cwt. 1 381. The sales of a clothing house amount to $100000 a year ; | of the sales are made at a profit of 25^, ^^ at a profit of 20^, and the remainder at a loss of 4'^. Required the cost of the goods. 382. A company of 50 men drank wine at 2s. 6d. per bot- tle, to the amount of £10. How many men at the same rate will £18 worth of wine supply, when wine is worth 2s. 3d. per bottle ? 383. What must be paid in Philadelphia for a draft on St. Louis, drawn at 90 days, for $5000, at a premium of If^? 384. A merchant in Cincinnati wishes to remit $14331.60 to New York. Exchange on New York is |^ premium, but on St. Louis ^^ premium, from St. Louis to New Orleans l^ discount, and from New Orleans to New York 1^ dis- count. What will be the value in New York by each method, and how much better is the circular 1 385. The gross earnings of the Erie Railroad for 1861 were $5590916, and the expenses were $4067391.39; the gross earnings of the same road for 1863 were $10469480, and the expenses $6386382.80. How much greater fo were the net earnings of the gross earnings in 1863 than in 1861 ? 386. What is 20^ of 30^ of 50^ of $66.66| ? 387. A man can sell his farm for $4000 cash, or for $5000, payable in 2 years. If he accept the last offer, and receive instead its present worth, at 10^ discount, how much more would he receive than by the former 1 388. If he accept the first offor, and loan the $4000 at 10^ interest, how much less would he receive at the end of 2 years than by the second offer ? ARITHMETICAL EXAMPLES. 155 389. What is the interest of $193.G8 from Nov. 27, 1859, to July 3, 1862, at DJcl 890. When $2.60 are paid for 8 gal. 1 pt. of milk, what is the price per quart ? 391. The manufacturers of Massachusetts paid in one year $3251325 internal revenue, which was 23j^q per cent, of the sum paid by all the manufacturers in the United States. Re- quired the entire revenue from this source. 392. If I gain $46.27 on $578,371 worth of sugar, how many dollars' worth must I sell to gain $134.64? 393. A man obtained an insurance for life at the age of 37, and died when 51 years old. The policy required annual payments during life, at $2.8674 per $100, and secured to the heirs $1709.69 more than the amount of all the premiums paid. What was the face of the policy ? 394. $3250. Hartford, March 6, 1859. On demand we promise to pay Brown & Gross^ or order, three thousand two hundred and fifty dollars, for vahie re- ceived. Church & Brothers. Indorsed as follows: July 1,1859, $406.87^; Nov. 7, 1859, $50; Jan 1, 1860, $285 ; Aug. 10, 1860, $400.62; July 1, 1861, $125; Nov. 4, 1862, $544.60; Apr. 22, 1863, $473.76 ; July 1, 1863, $600. What was due Apr. 1, 1864 1 395. A grocer bought 760 lb. of Java coffee, at 26 cents per pound. Allowing 16^ for shrinkage in roasting and grinding, at what price per pound must he sell it to gain 25;^ ? 396. If it require 50,000 bricks to build a house whose walls are 1 ft. 6 in. thick, 20 ft. high, and 108 ft. long, how many will build one whose walls are 2 ft. thick, 30 ft. high, and 324 ft. long ? 397. A man 33 years old, takes out a policy for $2000, the payments to cease at 50, the annual premium being $3.50 per 156 ARITHMETICAL EXAMPLES. $100. If he survive that age, how much more money will he receive from the company than he pays them 1 398. In the year 1860, 66^% of all the printing in the New England States was done in Massachusetts ; 14|^ in Connecti- cut; 6 g^ in Maine; 2f^% in Vermont; Rhode Island per- formed i^ as much as New Hampshire ; the cost of the print- ing done in Rhode Island was $107360 more than the cost of wliat was done in Vermont. Required the value of all the printing done in the New England States for the year 1860. 399. Paid $5392.35 in New York for a 30 days' draft on Boston, exchange being at ^^ premium. Required the face of the draft. 400. Smith & Boise traded in company with a joint stock of $8400. Smith's money was invested 14 months, and Boise 10 months. The profits being equally divided, how much of the capital did each furnish ? 401. A man with the proceeds of a note for $4164.22 on 60 days, discounted at 6^, purchased flour at $10.25 per bar- rel, allowing ^^ commission to a factor for buying it. At the end of 1 month he sold the flour on 90 days' credit for $11.50 per barrel ; when his note at the bank matured, he had the note received for the flour discounted, and paid his own note. How much did he gain by the transaction ? 402. If 4 gal. 1 qt. 1 pt. of oil is bought for $1,225, what is the price per gallon ? 403. The total sales of Wheeler & Wilson's sewing ma- chines for seven years ending Jan. 1, 1860, were 38991 ; of Grover & Baker's, 24818 ; of Singer's, 23353, and of all others such a number that the aggregate sales of all kinds were 103372. What was the value of the miscellaneous class at an average price of $30 a machine? 404. A farmer had a dairy of 48 cows, each furnishing 18 qt. of milk a day, from which he made 40 cheeses of 60 lb. each in 30 days. He made a contract to deliver ICO cheeses of 96 pounds each in 80 days. How many cows must ha ARITHMETICAL EXAMPLES. 157 add to his dairy provided each additional cow furnish 4 gallons of milk daily ? 405. In what time will $3045.20 gain $190.32 if the gain of $2404.75 for 1 yr. 13 d., is $258.48, and what is the rate per annum ? 406. Marks, Willis & Sterrett were partners in the flour- ing business; Marks had invested |, Willis i, and Sterrett j'V of the capital. They were to share equally the gains or losses. The business not being successful, the partnership was dis- solved at the close of the year, when the resources of the firm were found to be : Cash, $1785 ; wheat on hand, $2500 ; corn, $1752; rye, $350; flour, $1650; mill and fixtures, $5000. The liabilities were: Notes outstanding, $1562; they owed Milo Chidsey, $1200, and S. Combs, $1875. The net losses were $750. What was the net capital of the firm at com- mencing, and what was each partner's net capital ? 407. What is the distance around a rectangular field, whose length is twice its breadth, if one end measures 35 rd. 5 yd. 2 ft. 6 in.? 408. The average number of horse cars running daily on the railroads of Boston and vicinity, is 132 ; and each car carries an average of 2000 passengers per week ; the average fare being 4d. N. E. currency, what is the net income of all the roads per year, the expense of working the roads being $624936, supposing 1000 passengers do not pay fare] 409. When exchange at New York on Paf-is is 5 francs 25 centimes per $1, and at Paris on Hamburg 2| francs per mark banco, what will be the arbitrated price in New York of 6580 mark bancos ] 410. The value of real estate and personal property in the United States in 1860 was $16159616068; the debt of the United States Jan. 1, 1864, was $1373567365.78 ; if a direct tax were levied to cancel the debt, what would be the rate of taxation, and how much would John Smith pay who is worth $5000 ? 158 ' ARITHMETICAL EXAMPLES. 411. How many bushels of corn in Illinois are equal to 8000 bushels in New York ? 412. What is the value of a house and lot that pays a profit of 9 per cent, by renting it at |50 per month ? 413. A draft was purchased in New York on Chicago for $3000, drawn at 60 days, for $2850. What was the course of exchange ? 414. How many bushels of oats in Connecticut are equal to 5000 bushels in Iowa 1 415. A farmer sold three hogs, one weighing 275 pounds, at 5 cents per pound ; a second, weighing 310 pounds, at 5] cents per pound ; and the third, w^eighing 345 pounds, for $25. What was the average price per pound for the whole ? 416. At what rate of premium is Prussian coin, when $352.92 in United States silver coinage of 1837, is paid for 500 thalers] 417. A father left his four sons, whose ages are 15, 11, 7 and 6 years, $57770, to be so divided that the respective parts placed at simple interest in Connecticut shall amount to equal sums when they become 21 years of age. What are these parts 1 418. It is estimated that a sewing machine does the work of six persons, and that its use in making boots and shoes in Massachusetts annually saves $7500000 ; allowing 300 work- ing days in a year, and $1.25 as the average daily wages of shoemakers, how many persons engaged in this trade does the use of sewing machines leave free to follow other pursuits ? 419. A grocer sold 12 hams, each weighing 15 lb., at cents per pound, and took in payment 1 load of apples, con- sisting of 18 bags, each containing 2^ bushels. Required the price of the apples per bushel. 420. A merchant in New York wishes to pay £3000 in London. Exchange on London is 9-1^ premium ; on Paris, 5 francs 25 centimes per $1, and on Amsterdam 40 cents to T2! ARITHMETICAL EXAMPLES. 159 a guilder. The excLange between France and England at the same time is 25 francs to £1, and that of A'msterdanj on England 121 guilders to £1. Which is the most advanta- geous, the direct exchange, or through Paris, or through Amsterdam 1 421. Received from Charleston 500 bales of cotton, each weighing 560 lb., invoiced at 9d. per lb. Georgia currency ; sold it at an advance of 20^, commission 1^^, and remitted the net proceeds by draft. What was the face of the draft, exchange being l-^^ discount? 422. There were 153366425 bushels of bituminous coal, and 9416333 tons of anthracite coal mined in the U. S. in 1860, and 25 bushels of the bituminous made one ton ; the average cost of the coal at the mines being $1.30 per ton, what w^as the total value of all the coal mined ? The value in 1850 being $7173750, what was the rate of increase in ten years? 423. A merchant in Syracuse, N. Y., purchased a draft on Chicago for $2660, draw^n at 60 days, paying $2570.89. What was the course of exchange 1 424. A horse which was bought for 20^ less than his real Value, became injured, and w^as sold for 40^ less than his cost, at a price $130 below his original value. For how much was he sold ? 425. A gentleman sent a silver cake basket, weighing 3 pounds 9 ounces, to a jeweler, and ordered him to take 31^ of it for his work, and manufacture the remainder into small dessert spoons, each weighing 1 oz. 9 pwt. How many dozen spoons ought he to receive ? 426. Two men in Hartford, Conn., hire a carriage for $20 to go to Waterbury, 40 miles distant, and back again, with the privilege of taking in 3 more persons. Having gone 10 miles, they take in A; at Waterbury they take in B; and, on their return, w^hen 20 miles from Hartford, they take in C. How much, respectively, shall A, B, and C pay? CIIAPTEE VI. 1. The Winchester bushel is of cylindrical form, 18.5 in. in diameter, and 8 in. deep. What must be the dimensions of a cubical box which shall contain 27 bushels 1 2. A gentleman deposited in a savings bank for his son, 15 years of age, a sum of money, which, at 5^ compound inter- est, payable semi-annually, amounted to $10000 at his major- ity. What was the sum deposited ? 3. A grocer mixed 5 lbs. of sugar, at 8| cts. per pound, with 80 lbs., at 7| cts. per pound, and 60 lbs. at such a price that the mixture was worth 9| cts. per pound. Required the price per pound of the last kind of sugar. 4. How much less will it cost to fence 32 A. 64 P. in the form of a circle, than in the form of a square 1 and how much less in a square form than in the form of a rectangle, whose length is 4 times its width, the price in each case being $1.50 per rod ? 5. One-third of a quantity of goods was sold to gain a certain ^, one-fourth to gain 1^ times as much ^, and the remainder to gain 2^ times as much ^. What is the gain % on each part, the gain upon the whole being 21^ ? 6. If a cask, 45 inches long and 36 inches bung diameter, contain 167 gallons of wine, what must be the length an J bung diameter of a cask of the same shape, containing 314 gallons ? 7. If $600 gain $72 in 1 yr. 6 mo., in what time wiil $850 gain $189.83^ ? ARITHMETICAL EXAMPLES. 161 8. Two rcechanics work together; for 10 days' work of the first and 8 days' work of the second they receive $50 ; and for 15 days' work of the first and 14 days' work of the second they received $81. What is each man's daily wages ? 9. It is 80 rods between the opposite corners of a square field. How many acres in the field ? 10. Four towers— A 125 feet high, B 25 yards high, C 160 feet high, and D 70 feet high — stand upon the siirae plane ; B directly south, and 40 rods from A ; C east from B ; and D south from C. The distance from A to C plus the distance from C to B is i a mile, and the distance from D to B is 82^ yards farther than the distance from C to D. Required the length of a line to connect the tops of A and D. 11. A farmer took some butter to the store and received therefor $12.25, the price per pound being as many cents as there were pounds. How many pounds were there ? 12. A miller is required to grind 160 bushels of provender, worth $1.00 a bushel, from oats worth $.40, corn worth $.80, barley worth $.90, and rye worth $1.10, and wheat worth $1.30 per bushel. How many bushels of each kind may he take] 13. There is a park containing 15 A. 3 R. 30 P., and the breadth is | the length. If two men start from the same corner and travel at the rate of 4 miles per hour, one going around the park, and the other taking the diagonal, how much sooner will the latter reach the opposite corner than the for- mer 1 14. If I own I of a farm, and sell | of my share for $3460, what part remains to mel and what is the whole farm worth ? 15. G and H trade in company ; G's capital is | of H's : at the end of 5 months H draws out | of his capital ; and at the end of 9 months G draws out ^ of his. What part of the gain, which is $4222.50, should each have at the end of the year 1 162 ARITHMETICAL EXAMPLES. IG. I owe a man the following notes: one of $500, due April 1 ; one of $750, due July 15 ; and one of $1750, due Sept. 10. The holder wishes to exchange them for two notes of $1500 each, and wants one to fall due May 10 ; when should the other be made payable ? 17. A and B traded together ; A put in $400 for 512 days, and received ^ of the gain ; the number of dollars which B put in was equal to the number of days it was employed in trade. What was B's capital ? 18. The longitude of Springfield, Mass., is 72° 35' 45'' W., and of Constantinople, 28° 49' E. When it is 9 o'clock A. M. at the latter place, what time is it at the former ? 19. A note was given for $500, with interest payable an- nually, at 7^. Nothing having been paid for 10 years, how much did the total amount of interest due exceed the simple interest of the principal ? 20. A rectangular piece of land, containing 8 A. 1 R. 32 sq. rd. is i as wide as it is long. What is the distance around it? 21. Bought a quantity of goods for $2500 cash, and sold them for $3125 on 3 months' credit. What did I gain, money being worth 9fo ? 22. What is the diflference between the interest and dis- count of $730, for 5 yr. 9 mo., at 8 per cent. ? 23. Wishing to ascertain the height of a tower, I erected near it a stick 2|- feet high ; by measurement I found the shadow of the tower to be 36| ft., and of the stick 9 in. at the same time. Required the height of the tower. 24. A man agreed to work for a blacksmith for $1.50 per day and his board ; for each day lost he was to allow $.40. At the end of 11 weeks he received $77.15. How many days did he lose ? 25. What is the daily interest on $63300 in U. S. demand notes, bearing 7/q5^ interest 1 AKITHMETICAL EXAMPLES. 163 28. A ship sailed due south and due east on alternate days, at the same rate each day ; at the end of six days it was found to be 203.646 miles south-east from the place of starting. What was the daily rate of sailing ? 27. If a body put in motion move | of an mch the first second, ^ an inch the second, 1 inch the third, and so continue to increase its velocity in geometrical ratio, how far would it move in | of a minute ? 28. An importer sold cloth to a wholesale dealer at 10^ advance; the wholesale dealer sold it to a clothier at 12 \% advance ; the clothier sold it at a farther advance of 25^, and received $1452. How much did it cost the importer ? 29. The Federal debt, Feb. 16, 1864, was officially stated to be $1482600000. What per cent, is that of the whole taxable property of the loyal States, the latter being esti- mated at $14000000000? 30. What is the balance of the following account, and when is it due ? Thomas Lardner. Dr. Cr. 1860. 1 March 1 To Sundries, April 12 " Mdse. July 16 " " Sept. 14 1 " " 1 1860. 436 00 1 March 25 548 00 1 April 6 312 00 June 20 536 00 1 Aug. 3 By Draft at 60 da. 1' Cash, 400 00 650 00 200 00 84 00 31. When shall a draft for the settlement of the following account be made payable ? David Sanford. Dr. Cr. 1859. Jan. 1 Feb. 12 March 16 June 25 To Mdse. on B mo " Sundries " Mdse. 54 36 28 1 45 95 , 75 26 32 1859. April 1 May 16 June 12 " 20 By Cash, " Draft at 30 da. " Cash, 50 00 30 1 00 r-5 00 150 1 00 32. Three contractors engaged to build a piece of road for $8775; A employed 20 hands 24 days, 10 hours a day ; B, 25 hands 20 days, 12 hours a day ; and C, 30 hands 25 days, 9 hours a day. How much should each contractor receive ? 164 ARITHMETICAL EXAMPLES. 33. A quantity of wheat was heaped up in a corner of a square room forming a portion of a cone, of which the per- pendicular height was 4 ft. 3 in. and the slant height 7 ft. 1 in. What was its value at $1.66^ a bushel? 34. Oliver Wainwright. Dr. Cr. 1853. 1 1858. 1 Jan. 1 To Mdse. 36 72 Jan. 10 By Cash, 98 72 Feb. 1 n n 48 25 21 " " 25 84 March IT n n 72 36 March 23 " Sundries, 15 17 April 1 98 48 April 6 tt n 8 96 If the above account were settled April 6, 1858, by draft on time, how many days' credit should be given ? 35. $1200. CmcAGO, Jan. 1, 1858. For value received, I promise to pay Stephen Hopkins, or order, twelve hundred dollars, on demand, with interest at 7^. Thomas Bobbins. Indorsed as follows : Jan. 1, 1859, $300 ; March 16, 1860, $350; Jan. 1, 1862, $250. What was due February 20, 1864? 36. A church is 80 ft. long and 50 ft. wide, and the eleva- tion of the roof is 14 ft.; the rafters extend 2 ft. bey ond the plates, and the boarding projects 2 ft. at each end. How many feet of boards will be required to cover the roof, allow- ing I for waste ? 37. Divide || of a piece of cloth, which contains 45 1 yd., into equal parts, each of which shall contain -f^ of the whole piece. How many yards in each part ? 38. If it cost $85,60 to inclose a circular field containing 2 A. 28 P., how much will it cost to inclose another con- taining 26 A. 23 P.I 39. A merchant in New York gave $1000 for a bill on London of £200. What was the rate of exchange ? 40. A grocer desires to mix teas worth $1.50 and $1.20, with 140 pounds worth $.75, that the mixture may be worth $1.00. What quantities of each must he take 1 ARITHMETICAL EXAMPLES. 165 41. A, B and C traded in company; A put in $1400; B, 12500, and C, 300 barrels of flour ; they gained $2300, of which C took $1000. What were the shares of A and B, and what was the price of C's flour per barrel ? 42. An orchard containing 6 A. 12 sq. rd. is 3 times as long as it is wide. Required the length and breadth. 43. If from 68 and 82 respectively, a certain number be subtracted, ^ of the first remainder will be equal to ^ of the last. What is the number subtracted 1 44. A man left $10000 to be divided between his three sons, whose ages were 10 yr., 13' yr. 4 mo., 17 yr. 6 mo., re- spectively, in such proportions that the share of each at sim- ple interest at 6^, should amount to the same sum when they should arrive at the age of 21 years. What was each one's share ? 45. A grocer sells a farmer 150 lb. of sugar at 14 cents a pound and makes 5^ ; the farmer sells him 1 50 lb. of meat at 12 cents a pound, and makes a profit of 8^. Which gains the more by the trade and how much ? 46. A mechanic received $3 a day for his labor, and paid $5 a week for his board; at the end of 8 weeks he had saved $74. How many days did he work ? 47. The great pyramid built by Cheops has a square base 746 ft. on each side, and its perpendicular hight is 450 feet. What is the area of the base, of each side, and how many cubic feet of masonry does it contain ? 48. A trader bought merchandise as follows : Apr. 8, $150.22; May 23, $55.64, on 30 da.; June 2, $82.60 on 2 mo., and July 14, $90. What was due on the account Sept. 26, money being worth 7^ 1 49. A plot of ground is 80 rods square. What is the breadth of a graveled walk around it, covering an area equal to ^ the area of the field ? 50. A gentleman bought an annuity of £500 in English 166 • ARITHMETICAL EXAMPLES. consols, bearing 3;^ interest for 20 years. What was tlic present worth ? 51. An importer sold a quantity of goods to a wholesale merchant at an advance of 10 fo\ the latter sold them to a re- tailer, gaining 12^^, and the retail merchant sold them for $3093.75, gaining, thereby 25^. How much did the goods cost the importer ? 52. There are three houses so situated that the lines con- necting them form an equilateral triangle, the sides of which are 70 rods in length. Plow many acres are included in the triangle ? 53. A merchant failing in business can pay 76 cents on a dollar. He offers to pay his whole indebtedness without interest in five years if his creditors will allow him to go on with his business ; his offer being accepted, how much will his creditors lose in the five years, money being worth 1% ? 54. In how many different positions may a family of 7 persons seat themselves at a table ? 55. A triangular orchard has 1 tree in the first row, 3* in the second, 5 in the third, and so on in arithmetical progres- sion. How many trees in the orchard, there being 50 rows ? 56. What are the interior dimensions of a cubical box that contains 40 bushels of grain '? 57. How many strokes of a common clock are struck in 24 hours 1 58. A man wishes to enclose a circular field which shall contain .^'^ as many acres as it will require rails to build a fence around it. The rails being 15 feet long, and the fence 6 rails high, how many acres must there be in the field ? 59. J. Bagg & Co., becoming insolvent, their indebtedness was $1 1666| their assets were 19012.50. What % of their indebtedness can they pay, allowing to the assignees 3;^ on the amount distributed to the creditors ? GO. The Treasurer of the State of Pennsylvania, Nov. SO, ARITHMETICAL EXAMPLES. 167 18G3, made the following report of the finances of t ■ e State : Balance in teeasury, Nov. 30, IS^Gl, $1592037.72; receipts from ordinary sources, to Nov. 30, 1862, $4047822.39; from extraordinary sources, $1163925.24; payments to the same date, $4590509.25. Required the balance in treasury, Nov. 30, 1862. 61. Receipts for the year ending Nov. 30, 1863, $4289- 451.65; payments to the same date, $4314964.05. How much less in the treasury, Nov. 30, 1863, than Nov. 30, 1862? 62. I wish to pay a bill in Naples of 1500 ducats ; the direct exchange is $1.40=1 ducat; the exchange on London is 171^; of London on Paris is £1=26 francs; of Paris on Naples is 4| francs=l ducat. What is the difference between the direct and circuitous exchange ? 63. A square pyramid of cannon-balls has 12 on each side at the base. How many balls in the pyramid ? 64. How many pounds of sugar at 8, 13, and 14 cts. per pound, may be mixed with 3 pounds at 9^ cts., 2 pounds at 8;^ cts., and 4 pounds at 14 cts. a pound, so as to gain 16^ by selling the mixture at 14^ cts. per pound ? 65. What is the difference between the true and bank dis- count of $3000, payable in 120 days at 8^^? 66. Two churches stand on opposite sides of a street 120 feet wide; the height of the towers is 70 and 95 feet, re- spectively. What is the distance from the top of one tower to the top of the other 1 and what is the distance from the top of each to the base of the opposite church 1 67. What is the hour when | of the time past noon is | of the time till midnight 1 68. E, F, and G start from the same point and in the same direction to walk around a trotting course 1 mile in circum- ference ; E takes 60 steps, of 26 inches each, a minute ; F, 90 steps, each 28 inches in length; and G, 120 steps, each 32 inches in length. What distance must each travel, and how 1G8 ARITHMETICAL EXAMPLES. long, before they will be together again at the point of start- ing] CO. A man wishes to tether his horse to a stake, so that it may graze on i of an acre. What must be the length of rope 1 70. A bought a house of B, and gave him his bond for 86000, dated April 1, 1860, payable in 5 equal annual install- ments of $1200, the first to be paid April 1, 1861 ; A took up his bond April 1, 1863, semi-annual discount at the rate of 7% per annum on the payments due after April 1, 1863, being deducted. What sum canceled the bond ? 71. What is the compound interest of $1 for 143 years, allowing it to double once in 11 yr. 11 mo 1 72. A servant being ordered to purchase 40 animals for $40, brought home calves at |4, lambs at $1.00, and kids at $.50 each. How many of each kind did he purchase 1 73. If I borrow $1000, and agree to pay 6^ at the end of each year for the use of it, and at the end of 18 months it is called for, how much do I strictly owe ? 74. If a cannon-ball, 8 in. in diameter, weigh 128 pounds, what is the diameter of a ball weighing 250 pounds ? 75. I have sugars worth 12, 14, 16, and 18 cents a pound. How many pounds of each kind may I mix to make a barrel of 260 pounds, which I can sell at $.16^ per pound, and gain 10;^] 76. A and B gain in business $5040, of which A is to have 10^ more than B. Required the share of each ? 77. What length of fence will inclose a circular field con- taining 10 acres? 78. An ox, whose girth is 8 ft., weighs 1500 lb; what is the girth of another ox that weighs 632 lb. 13 oz. ? 79. X and Y entering into partnership, X at first put in $1600, and after 1 year added $400 to his capital ; Y put in $2000, and after 6 months withdrew $800; at the end of 2 ARITHMETICAL EXAMPLES. 169 years they have gained $6960. Required each one's share of the gain ? 80. How many miles of furrow, 1 ft. 3 in. wide, must be turned in plowing a rectangular field, whose width is 30 rods, and whose length is 10 rods less than its diagonal ? 81. The wholesale price of coffee in New York in 1863 was 33i cents per pound, and the price in 1847 was | of a cent more than i the price in 1863o Tho price of 1 pound in the latter year would have bought how many pounds in the for- mer year ? 82. The pressure of air being 15 pounds to a square inch, what is the pressure upon a pair of Magdeburg hemispheres, 8 inches in diameter 1 83. In the city of New York in 1862, 3198 marriages were reported to the city Inspector, and he estimated the numbei reported to be 26^ of the actual number. What was his estimate of the whole number 1 84. A park, 8 rods square, has a gravel walk around it of the same width on all sides, the area of which is ^^^^j the area of the park. Required the width of the walk. 85. A merchant in New York purchased 350 bales of cot- ton, each containing 450 pounds, at $.80 a pound, and shipped it to Liverpool at a cost of 16^ for freight and duties. How much in U. S. currency did he gain by selling it at 2s. lOd. a pound, rate of exchange 111% 1 86. What is the cash balance of the following account, Jan. 1, 1864, interest at 6^? Richard Rathburn. Dr. Cr. 1863. 1863. Jan. 20 To Mdse. $400 March 1 By Cash $?00 Feb. 25 250 April 3 " Sundries 500 April 1 60;) June 5 " " 200 June 10 850 Sept. 1 " Cash 350 Sept. 12 575 Dec. 2 ti u 500 Nov. 30 980 170 ARITHMETICAL EXAMPLES. 87. A merchant mixes 13 pounds of tea with 7 pounds of an inferior quality, and gains 20^ by selling the mixture at $1.05? per pound. Allowing one kind of tea to be worth 20 cents a pound more than the other, what is the cost of each per pound 1 88. How much less will the fencing of 20 acres cost in the square form than in the form of a rectangle, whose breadth is I the length, the price being $2.25 per rod ? 89. A. Smith, 34 years old, insures his life for $5000, at the rate of $2.5232 per $100 ; he dies at the age of 53. Al- lowing 6^ compound interest on all premiums paid, how much has his policy actually cost ? 90. How much bank stock, at 3^^ premium, can be pur- chased for $6240, brokerage J^ 1 91. A merchant bought 200 bbl. of flour for $1665, paying $9 per barrel for first quality, $8 for second, and $7.50 for third. How many barrels of each quality did he buy. 92. A cistern 15 feet deep will hold 5640.192 gallons. What is its diameter ? 93. A young man inherited an estate of $40000 ; after spending I of it, he invested the remainder in an unsuccessful business, losing 33]^ of the investment; with his remaining money he purchased 5-20 United States bonds at par, bearing G^ interest, payable in gold. How much was his yearly in- come in currency, gold being 175^ ? 94. A Chicago merchant shipped 1000 barrels of flour to his agent in New Orleans, directing him to sell it, and invest the proceeds in cotton ; his agent sold the flour at $14 per bbl., paid $275 charges, and bought cotton at $.65 per pound, charging S% commission for selling the flour and b% for buy* ing the cotton. How many pounds of cotton did he buy ? 95. M and N are joint tenants of a house, paying $62.50 and $87.50, respectively, each quarter for rent. The land- ARITHMETICAL EXAMPLES. 171 lord having raised the annual rent $100, what rent must each now pay quarterly 1 96. Having placed a bill of $775 in the hands of a col- lector, who succeeded in obtaining 75^ of it, and charged 8^ commission, how much did I receive ? 97. How much larger is a square circumscribing a circle 40 rods in diameter, than a square inscribed in the same circle ? 98. A grocer sold 2000 gallons of molasses for $1880, and gained on each gallon sold the cost of 1 1| pints, beer meas- ure. What did the molasses cost per gallon ? 99. By the fortification bill of 1863, Congress appropriated for forts as follows : Maryland, $200000 ; Mississippi River, IJ times as much ; Pacific coast, f § of the two preceding ap- propriations; Florida, l^^^ times the three preceding appro- priations ; New York, 1 1 of the four appropriations already mentioned ; and New England || of all the others. How much was the amount of the bill ? 100. A's money was to B's as 2 to 3 ; when A had spent $40, and B had spent 40^ more than A, A's money, minus $20, was to B's money, plus $2, as 4 to 9. How much had each at first ? 101. A merchant bought a certain quantity of corn, for which he paid a certain sum of money ; but on measuring, he found only |g of the quantity he expected. He sold it, gain- ing I the cost, and received $2160, which was at the rate of 12j^3 cents per bushel more than he would have paid had he received the quantity he expected. How many bushels did he suppose he had bought, and at what price '? 102. How many thousand shingles, averaging 4 in. wide, and lying 6 inches to the weather, are required to cover both sides of a roof 36 ft. long, whose rafters are 20 feet in length ? 103. Andrew Combs purchased of H. Alexander wheat on 3 months credit, as follows : Apr. 5, 500 bu., © $.87 A ; Apr. 172 ARITHMETICAL EXAMPLES. 25, 300 bu., @ $.95 ; June 20, 350 bu., @ $1.10 • July 10, 250 bu., @ §1.05. When was the acc(3unt due by average? 104. A, B and C entered into partnership. A put in $12000, B $8000, and C $7000. At the end of the first year A drew out $2000, B $1000, and C put in $3000. At the close of the second year A and B each drew out $1000, and C put in $2000 more. At the end of the third year they dis- rolved partnership, and found that their joint property was $28500. What was each partner's share ? 105. If a pipe 3 inches in diameter discharge 12 hogsheads of water in a certain time, what must be the diameter of a pipe which wnll discharge 48 hogsheads in the same time 1 lOG. If I buy 50 shares Hudson River R. R. stock at 141^, and 50 shares Michigan Central R. R. stock at 139^, the for- mer paying a semi-annual dividend of 4^^^, the latter of 5^; what rate of interest shall 1 realize on my investment 1 107. The horizontal distance between "the eaves of a certain building is 40 ft. ; the elevation of the ridge above the eaves is 15 ft. AVhat is the length of the rafters ? 108. If a man by laboring 15 hours a day do a work in 8 days, how many hours a day must he labor to do the same in 10 days? 109. A speculator purchased 255| acres of land at $45| per acre, but w^as obliged to sell it at $23 1 per acre. For how much more than his loss did he sell it ? 110. What number, increased by I, J and ^ of itself, equals 317? 111. A wdne dealer desires to mix 20 gallons of wine, worth $3.50 per. gal., with wines w^orth $3.25 and $1.80 per gal., so as to form a mixture of 96 gallons, w^orth $3.00 a gallon. How much of each kind may he take ? 112. J. Smith bought of Ivison, Phinney, Blakemnn ^ Co., the following bills of goods ; Nov. 1, 1863, a bill of $750, on 6 mo. credit; Dec. 15, 1863, a bill of $300, on 5 mo.; Jan, 1, ARITHMETICAL EXAMPLES. 173 1864, a bill of $425, on 4 mo. ; Feb. 5, 1864, a bill of $275, on 2 mo. What sum would settle the account. May 29, 1864, interest at 7^? 113. A gentleman wishes to set out a rectangular orchard of 1260 trees, so placed that the number of rows shall be to the number of trees in a row as 5. to 7. If the trees are 8 yards apart, how much ground will the orchard occupy 1 114. A merchant insures a ship and cargo for $79325, at 4|^, the policy covering both property and prerfiium. What is the value of the ship and cargo ? 115. A, B and C formed a partnership for 2 years ; A put in $10000, B $5000, and C $2500 ; it was agreed that C should receive $1500 a year for superintending the business. A drew out $1000 at the end of each quarter for one year, and at the end of 13 months put in $15000 more; B with- drew $600 at the end of each quarter. At the time of settle- ment the net gain was $22500. Required each one's share. 116. If 496 men, in 5 days of 11 hours each, can dig a trench 620 yd. long, 3 yd. wide and 2 yd. deep, in how many days of 12 hours each will 48 men dig a trench 210 yd. long, 6 yd. wide and 3 yd. deep 1 117. When exchange on England is at 10^ premium, and freight at Is. 3d. per United States bushel, how much can be paid in Philadelphia for wheat per bushel, in answering an order from London limited to £3 10s. per Imperial quarter ? 118. In a pair of scales a body weighed 32 pounds in one scale, and only 24^ pounds in the other. What was its true weight ? 119. Suppose a number of stones were laid a rod apart for 30 miles, the first stone by the side of a basket. What dis- tance will a man travel who gathers them up one by one, re- turning with each one to the basket 1 120. A merchant shipped a cargo of flour, worth $23940, from Racine to Liverpool. . To insure it from Racine to Buf- 174 ARITHMETICAL EXAMPLES. falo he paid l^^'ji] from Buffalo to New York, |^; and from New York to Liverpool, 8|^. For what sum must it be in- sured to cover the value of the flour and premium for the voyage ? 121. A man in Cleveland purchased a draft on St. Louis, Missouri, for $10640, drawn at 60 days, paying $10283.56. What was the course of exchange ? 122. A merchant sold 350 barrels of pork for $8662.50, and gained 10^. What did the pork cost him per barrel ? 123. A gentleman insures his house, worth $9000, and his furniture, worth $3500, for | of their value at ^%. What premium did he pay ? 124. I have a circular field 600 rods in circumference. What must be the side of a square field that shall contain the same area ] 125. A's age is double that of B, and B is three times as old as C, and the sum of their ages is 70. What is the age of each one ? 126. A and B having the same income, A spends | of his. and B, by spending $200 a year more than A, finds himself at the end of 5 years $450 in debt. How much was their income ? 127. Insert 7 geometrical means between 5 and 1280. 128. What sum of money must be invested in 5-20's, bearing 6^ interest in gold, and purchased at 105^, to produce a semi- annual income of $600 U. S. currency, gold being 172|^? 129. A merchant bought, on 10 mo. credit, 25 pieces of cloth, each containing 30 yards, at $4,66 f per yard; after keeping the goods 3 mo. he sold them at $5 per yard on a credit of 9 mo. ; money being worth 6^, what was his net cash gain at the time of the sale ? 130. An irregular piece of land containing 305 A. 41 P., was exchanged for a square piece containing the same area. What was the length of one of. its sides? If divided into ARITHMETICAL EXAMPLES. 17J 169 square building lots, what will be the length of a side of each? 131. Bought wheat at $1.75, $1.80 and $2.00 per bushel. In what proportion may they be mixed so as to sell the mix- ture at $2.15| per bushel, on 3 mo. credit, when money is worth 10^, and make a present gain of 12^ ? 132. A man purchased a farm for $3000, and agreed to pay principal and interest in 4 equal annual installments. What was the annual payment, interest being 6fo ? 133. At a certain time between one and two o'clock, the minute hand is between 2 and 3, and within an hour the hands will exactly change places. AVhat is the first mentioned time? 134. What sum of money, with its semi-annual dividends of 4^ invested with it, will amount to $25000 in 3 years ? 135. When gold is quoted at 162^, what is the value in gold of a U. S. note of the denomination of $10? 136. Account sales of 100 pipes of gin, received per ship Ilispaniola, from Havana, on % of Tyler, Jones, & Co. I860. April 15 May 5 June 28 April 1 1 1 June 28 Sold 32 Pipes, 4160 gal. at $1.05, on 30 days,. " 40 " 5240 '* at 1.02, cash, " 28 " 3650 " at LOO, " CHARGES. To Freight and Primage $136.T6 " Wharfage and Cartage 48.54 " Duty Bonds, at GO days 3207.07 " Storage from April 1, viz. : On 32 Pipes, 2wks.. 64 wks. " 40 " 5 " ..200 " *' 28 " 13 " ..364 " 100 " equal to 628 *' at 6c 37.68 " Commission on $13362.80, at 2^ per cent 334 07 " Guaranty on $4368, at 2| per cent 109.20 4368 5344 00 80 00 13362 80 8873 32 What are the net proceeds of the above account, and when due ? Note. — The time for which storage is charged on each part of the shipment is the interval, reduced to weeks, between Apr. 1, when the pipes were received into store, and the date of sale. Every fraction of a week is reckoned a full week. 176 ARITHMETICAL EXAMPLES. 137. A walk 9 ft. wide surrounds a square garden ; the area of the walk being | of an acre, what is a side of the in- closed square ? 138. A man in Worcester, Mass., has $2400 due him in Chicago. How much more will he realize by making a draft for this sum on Chicago, and selling it at |^ discount, than by having a draft on Worcester remitted to him, purchased in Chicago for this sum at |^ premium ? 139. A father divides an estate Avorth $5555.66 between his two sons, giving the elder i more than the younger. How much is each son's share 1 140. M began business with $1000; four months after, S entered into partnership with him, and put in 6 houses, each of the same value ; at the close of the year their profits were $3000, of which S's share was $2000. What were his houses each valued at ? 141. A grocer mixed 4 pounds of tea at $1.20 with 3 pounds at $1.40, 1 pound at $2.20, and 2 pounds at $2.40. What per cent, profit will he make by selling the mixture at 12.00 per pound 1 142. A farmer has sheep worth $4, $6 and $8 a head re- spectively. How many of each kind must he sell to realize an average price of $6.25 a head 1 143. What is the distance from one corner of a cubical block to the opposite diagonal corner, the side of the cube being 5 feet ? 144. A and B traded in company. A put in $845 for 300 days, and received | of the gain. The number of dollars which B put in was equal to the number of days it was em- ployed in trade. What was B's capital 1 145. Insert 5 arithmetical means between 2 and 4. 146. If a stack of hay 8 ft. in hight weigh 8 cwt., what is the weight of a similar stack that is 24 ft. in hight 1 147. Allowing 5^ of the hay in the stack last mentioned to ARITHMETICAL EXAMPLES. 177 be worthless, what is the value of the remainder at $14 per ton ? 148. There is a circular field 100 rods in circumference. How far will a person have traveled, in setting the border with trees 1 rod apart, when the last tree is set, provided he returns to the point of starting for each tree, and always travels around in the same direction ? 149. A man engaged a boy at the rate of $.25 for the first day, $.30 for the second, $.35 for the third, and so on, in- creasing his wages 5 cents per day. How many days must the boy work that his average wages may be $.60 per day 1 150. The triangular gable of a certain building has a base of 44 ft. and an altitude of 18 ft. How many square feet of boards will cover the two gables ? 151. If I rent a house which cost $9000, for $900 a year, and lay out $150 in repairs, what ^ interest do I receive ? 152. A man bought | of a vessel, and sold | of his share for $11700, which was 30^ above the cost. What was the cost of the vessel ? 153. A merchant sold 238 hhd. of sugar, each containing 963 pounds net weight, at 13 cents a pound, on 4 months' time, and immediately got the paper discounted at a bank at 7^. How much money did he receive ? 154. If 6| oz. of bread can be bought for 4|d. when corn is 5s. 6d. per bushel, what weight of bread can be bought for Is. 3d, when the price per bushel is 6s. 3d. 1 155. A captain, commanding a company of 100 men who had performed a daring exploit, being asked what reward could satisfy him, replied, ''a cent for every different Jile of ten men that can be made with my company." What did his demand amount to ? 156. H. Jones & Co. failed in business. They owed A $4000, B $5000, and C $7000; their assets amounted to $11200, and the charges of the assignees were S^- on the 178 ARITHMETICAL EXAMPLES. amount distributed. What % did they pay % and how much did each creditor receive % 157. A lot of land, containing 15 acres, is 30 rods wide, and is a plane inclining in the direction of its length *, one end being 120 feet higher than the other. How many acres of surface does the inclined plane contain ? 158. By selling sugar at $15 per cwt. I gain 20^; what ^ should I gain by selling it at $13.50 per cwt. % 159. A man paid annually $10 for tobacco from the age of 14 until he was 50, when he died, and left $1000 for his heirs. What sum might he have left them had he dispensed with tobacco, and loaned the money thus saved at the end of each year at 6^ compound interest ? 160. Two ships start from New York at the same time; one sails due south at the rate of 12 miles an hour, and the other due east at the rate of 9-^ miles an hour. How far apart are they in 48 hours ? 161. A. Banks received a legacy of $3000, $800 of which was payable in 9 months, $800 in one year, and the balance in two years ; but the executor being willing to make present payment, discounting at 7^, what ought he to receive % 162. A merchant receives 10000 barrels of flour to sell on commission, and is directed to invest the proceeds in United States demand notes bearing 7 j^^^ interest; he pays $759 charges, and sells the flour at $9 per barrel ; his commission is 3^ on the sales. What amount of Treasury Notes can he buy at 36^ premium, brokerage \% % 163. The fore wheels of a carriage are 3 ft. 6 in. in diame- ter, and the hind wheels 4 ft. 9 in. How many times must each revolve in running from Springfield to Chicago, a dis- tance of 204 miles? 164. The exterior diameter of a spherical shell is 12 in., and the shell is 1 in. thick. What is the difference between the exterior and interior surfaces % ARITHMETICAL EXAMPLES. 179 165. What was the balance of the following account, Jan. 1, 1864, money being worth 7^? B. Newton in account current with J. Dailey. Dr. Cr. 1S63; 1 1863. Jan. 1 To Mdse $225 00 Feb. 10 By Cash, $150 00 Mar. 10 n u 370 50 i Mar. 25 (1 i( 300 00 June 15 (( it 550 00 July 1 *' Mdse. 430 50 Sept. 1 n t» T20 25 Sept. 1 " Cash, 500 Nov. 5 4t t< 160 25 1 166. What is the present worth of an annuity of perpetuity at 6^ ? 167. If 9| acres of land are bought for $301 /g, what will be the cost of 196| acres of land, worth | as much per acre? 168. A ball falling from a height of 12 ft. bounds 6 ft. by its elasticity, and again falling, bounds 3 ft., and so on, bound- ing each time ^ as high as it falls. How far will the ball fall before coming to a state of rest ? and what will be the dis- tance of all the successive bounds ? 169. For what sum must a note be drawn at 3 mo. that the proceeds, when discounted at a bank at 7^, shall be $981.91|? 170. A Cincinnati merchant bought a quantity of pork for $6000, and forwarded it to New York, paying 9^ of the cost for freight and charges ; it was then sold by an agent at an advance of 30^ on the original cost, commission 5^. How much was the net gain 1 171. A broker bought 90 shares of $100 each of New York Central E. R. stock at 127^, and sold the same at 136^^. How much was the net gain 1 172. A circular cistern 7 ft. in diameter has a capacity of •2400.06 gallons. What is its depth ? 173. How many pupils in a school when I attend the gram- mar department, | the intermediate, and the remainder, which is 34 less than ^ the whole number of scholars, attend the primary ? 174. A man insured his house, valued at $18000, and fur- 180 ARITHMETICAL EXAMPLES. niture, worth $7000, for /g of their value,, at '^%, What premium did he pay ? 175. H and J traded in company ; H put in $8000, and J $20000 ; they were to share the gains or losses equally ; at the end of two years they dissolved partnership, and found their net capital to be $22500. What was each one's share ? 176. A person exchanged 180 shares of 6 per cent, stocks, at 80^, for 10 per cent, stocks, at 125^. How much was his yearly income increased 1 177. If a man dig a square cellar that measures 5 ft. each way in one day, how long will it take him to^dig one meas- uring 10 ft. each way*? 178. Sold coffee at 13 1 cents a pound, and thereby lost 20^ on the cost ; afterward sold a quantity of the same for $455, and gained 30fo. What quantity was sold] and at what price ? 179. The diameter of the sun is 110 times as large as that of the earth. The volume of the sun is how many times as large as the volume of the earth ? 180. Received an invoice of crockery, 5 per cent, of which was broken ; paid a duty of 20 per cent, upon the remainder. For what per cent, above the invoiced value must it be sold to gain 25 per cent, on the whole cost ? 181. The length of a rectangular field containing 13 A. 3 R. 5 P. is to its breadth as 9 to 5. What are its dimensions 1 182. A merchant in New York in 1863 gave $5044.72| for a bill of exchange on London for £650. What was the rate of exchange ? 183. A gentleman laid out a garden in the form of an ellipse, its longer diameter being 8 rods, and its shorter 5 rods. What was the area of the garden 1 184. If stock, bought at 20^ premium, pay 6}^ on the investment, what % will it pay if bought at 5^ discount ? 185. How many yards of plastering in a room 21 ft. 9 in. ARITHMETICAL EXAMPLES. 181 long, IG ft. G in. wide, and 10 ft. 8 in. high, there being 3 doors, each 8 ft. 3 in. by 4 ft. 3 in. ; 2 windows, each 7 ft. 6 in. by 4 ft. 6 in. ; 1 fire-place 5 ft. 2 in. by 3 ft. G in., and a base-board 8 in. wide S 18G. A produce dealer bought 80000 bushels of corn at $1.55 per bushel, paying $450 charges, and $225 storage; he immediately sold it at 25^ advance on the entire cost on 90 days' time. At what price per bushel did he sell the corn ? and what ^ did he gain at the time of the sale, money being worth 7fo ? 187. If 70 pounds of sugar cost £4 3s. lid., how many pounds of sugar worth | as much per pound can be purchased with £2 17s. 5d. 1 188. The present worth of an annuity to be continued 10 years at G per cent., compound interest, compounded annu- ally, is $7360.08. What is the annuity ? 180. A pipe 1| inches in diameter will fill a cistern in 40 minutes. In what time will G pipes, each | of an inch in diameter, fill a cistein of three times the capacity 1 190. What will the gilding of a ball 1 fc. 9 in. in diameter cost, at 2s. Gd. per square inch 1 191. A cubic inch of lead weighs | of a pound. How many feet of lead pipe can be made from 100 pounds of lead, the caliber of the pipe being | of an inch, and its thickness | of an inch ? 192. Divide $1048.80 among 3 persons, in such a manner that the share of the second may be ^ greater than that of the first, and the share of the third ^ greater than that of the second. 193. A, L and W bought a vessel, A taking i interest, L ^, and W the remainder ; during the year following A paid for expenses $1850, and received $3325 cash returns; L paid out $1320, and received $4500 ; W paid $2G00, and received $1570. At the close of the year, L sold the vessel for 182 ARITHMETICAL EXAMPLES. $24500. Interest not being reckoned on receipts and ex- penditures, how much must L pay to A and W ? 194. The contents of a cubical block of granite are 4913 solid feet. What are the superficial contents? 195. A offers to loan to B $1000 for 6 mo., at 10^^; the legal rate is 7^. For what sum must the note be drawn that the amount of it at 7^ will equal the amount of $1000 at 10^ for ths given time? 196. The duty at 30^ on a quantity of coffee in bags, each weighing 175 pounds gross, and invoiced at $.14 a pound, was $8491.25. Tare being 5^, how many bags were im- ported? 197. A father divided his property among his four sons, directing that A should have $6 as often as B $5, C $3 as often as A $4, and D $8 as often as B $9. What was the amount of property, D's share being $6000 ? 198. J. Ellis & Co. sold Thomas Strong goods to the amount of $2500, on 6 months' credit ; Strong paid $350 in 2 months, $600 in 4 months, $500 in 7 months, and the bal- ance in 12 months. What amount was due at the time of settlement, interest Ifo ? 199. What % in advance of the cost must a merchant mark his goods so that, allowing 4^ of his sales for bad debts, an average credit of 3 months, and 8^ of the cost of the goods for expenses, his net gain may be 15^ of the first cost of the goods, money being worth l^/o ? 200. A^Hiat is the present worth of an annuity of $1200 in reversion 7 years, and continuing 13 years, at Q% ? 201. The perpendicular height of a conical glass is 8 in., and its diameter at the top is 5 in. How much water w^ill it hold? 202. What costs a bill on London for £800 17s. 6d., when the rate of exchange is 9^^ premium ? 203. A miller grinds 500 bushels of provender, worth 75 ARITHMETICAL EXAMPLES. 183 cents a bushel, from 40 bushels of rye, worth 90 cents a bushel, and from oats worth 60 cents, corn worth 85 cents, and barley worth 80 cents a bushel. How many bushels of oats, corn, and barley may he take ? 204. A gentleman purchased an annuity of $1000, to con- tinue 20 years, at 6^, compound interest. What did it cost him ? 205. A and B engage in trade ; A puts in $10000, and at the end of 5 months takes out a certain sum ; B puts in $6000, and after 3 months puts in $4000 more ; at the end of the year, A's gain is $1800, and B's $2250. What sum did A withdraw at the end of 5 months? 206. A merchant sold 48 yards of gingham at 33| cents per yard, 12 pieces of sheeting, each containing 33 yards, at 25 cents per yard, and received in payment 40 bushels of oats at 62i cents per bushel, and the balance in money. How much money did he receive ? 207. If the interest of $691.04 for 1 mo. 3 da. is $3,167, what will be the interest of $640.50 for 10 mo. 26 da., at twice the rate ? 208. S. F. Boot bought 50 shares of bank stock at an ad- vance of 5^ on the par value of $100. From the time of purchase until the end of 3 yr. 9 mo. he received a semi-an- nual dividend of 31^, when he sold the stock at a premium of 10^. Money being 6^ compound interest, how much did he gain 1 209. My garden is 11 rods 7| feet long, and 9 rods 15j\j feet wide. What is the length of the longest rails that can be used in fencing it, allowing the end of each rail to lap by the other 5 in., and all the panels to be of equal length? How many rails will fence the garden, if 6 rails are allowed to each panel ? 210. If 4096 men are formed into an oblong, with 4 times as many men in rank as in file, how many will there be in rahk and file 1 184 ARITHMETICAL EXAMPLES. 211. A gentleman purchases a farm for $10000, wliicli he sells after a certain number of years for $14071, making on the investment 5^ compound interest. He now invests his money in a perpetuity, which is in reversion 11 years from the date of purchasing the farm. Allowing 6% compound interest for the use of monev, find the annuity and the length of time he owns the farm. 212. Three numbers are to each other as 3, 5 and 7, and their continued product is 2835. Required the numbers. 213. What sum must be invested in 8 per cent, stocks, at 130^, to produce an annual income of $2000 ? 214. The shadow of a steeple measured 8 rd. 3 yd. 1 ft. and 6 in. in length, at the same time when the shadow of a man 6 ft. high measured 4 ft. 9 in. Required the height of the steeple. 215. J. Smith owes C. Brown $2000, to be paid in equal annual payments of $400 each ; Smith, not being able to meet these payments at their maturities, and having an estate 12 years in reversion, arranges with Brown to wait till he enters upon his estate, when he is to pay him the whole sum with compound interest at 7^. What sum will Brown then re- ceive ? 216. J. Clarke bought ofClaflin & Mellen the following bill of goods: June 1, a bill of $650, on 4 months; Sept. 15, a bill of $800, on 3 months; Oct. 10, a bill of $1200, on 1 month. What was the equated time of payment? 217. If a cable 3 inches in diameter will sustain a weight of 18000 pounds, what weight c-oi? be sustained by a cable 15.708 inches in circumference? 218. Divide $2000 between A and B, so that A's money shall be | of B's. 219. An estate of $60000 was to be divided among a wife, son and two daughters, as follows : The wife was to have $5000 more than the son, the son $10000 more than the elder ARITHMETICAL EXAMPLES. 185 daughter, and the elder daughter $5000 more than the younger. How much should each receive *? 220. How many acres in a triangular field whose sides are respectively 40, 48 and 54 rods in length ] 'l^ 221. A son, having asked his father of his age, was answered, " g of my age is twice your age, and the difference of our ages is 22 years." Required their respective ages. 222. A boy in flying his kite got it entangled in the vane of a steeple; the string broke close to the kite ; by measuring he found that he stood 450 feet from a point directly under the vane, and had out 485 feet of string. What was the height of the steeple ? 223. In digging a circular pond, 70 yards in diameter, 294- 407.19 cubic feet of earth were excavated. To what depth was the pond dug % 224. A grocer mixed 300 pounds of sugar at 14 cents a pound, with 200 pounds worth 15 cents a pound, and 250 pounds at 12 cents a pound. What must be his price per pound to gain 25^ on the cost % 225. If the sum produced by adding 4, | and | of a num- ber to itself be multiplied by 3, the product will be 6834. What is the number ? 220. A merchant in New York imports from Havana 200 hhd. of W. I. molasses, each containing 63 gallons, invoiced at $.30 per gallon ; 150 hhd. of B. coffee sugar, each contain- ing 500 pounds, invoiced at $.05 per pound ; 80 boxes of lemons, invoiced at $2.50 per box ; and 75 boxes of sweet oranges, invoiced at $3,00 per box. What was the whole amount of duty, estimated at 24^ on molasses and sugar, and at 8^ on lemons and oranges ? 227. Sight exchange on New Orleans for $5000 cost $5075. What was the course of exchange ? 228. A man paid $165 to 55 laborers, consisting of men, women and boys ; to the men he paid $5 a week, to the wo- 186 ARITHMETICAL EXAMPLES. men |1 a week, and to the boys $i a week. IIow many- were there of each ? 229. A and B traded together; A put in |540 for 480 days, and received ^ of the gain ; and the number of dollars which B put in was equal to the number of days it was em- ployed in trade. What was B's capital ? 230. What is the present value of a reversionary lease of $100, commencing 14 years hence, and to continue 20 years, compound interest at 5 per cent. ? 231. If a cistern 6 feet in diameter hold 80 barrels of wa- ter, what must be the diameter of a cistern of the same depth to hold 1280 barrels ? 232. A gentleman in Boston drew on Wurtemberg for 6000 gilders at $.415 per gilder. How much more would he have received if he had ordered remittance to London, and thence to New York, exchange at Wurtemberg on London being 11| gilders per £1, and at London on New York 9|^ in favor of sterling* brokerage at 1|^ in London for re- mitting ? 233. Two boys, each 12 years old, have certain sums of money left to them ; the sum left to one is put out at 1% simple interest, the sum lefc the other at 6^ compound inter- est, compounded semi-annually, and the amount of each boy's money will be $2000 when he is 21 years old. V/hat is the sum left to each boy ? 234. Find the sum of 21 terms of the series, 5, 4|, 4i, etc. 235. A man traveled 13 days; his last day's journey was 80 miles, and each day he traveled 5 miles more than on the preceding day. How far did he travel, and what was his first day's journey ? 236. Find the 12th term of the series, 30, 15, 7^, etc. 237. Bought 12 yards of cloth for $15. How many yards must I buy at $1| and $| a yard, that the average price of the whole may be $11 ? ARITHMETICAL EXAMPLES. 187 238. A man bequeathed his property, amonning to $30000, to his wife and three children as follows : The wife was to have I, and the remainder was to be divided so that the shares of the children at simple interest at 6^ should all amount to the same sum when they were 18 years 8ld ; the ages of the children were respectively 4 yr., 5 yr. 6 mo., and 7 yr. 3 mo. What was the share of each child ? 239. What sum must be invested in United States 10-40's, bearing 5^ interest, payable in gold, purchased at par, to pro- duce a semi-annual income of $400 U. S. currency, when gold is quoted at 175^ ? 240. Imported 12 casks of wine, each containing 42 gallons invoiced at $3.25 per gallon ; paid $96 for freight, and a duty of 40^. How much shall I gain ^ in selling the whole for $2747.58? 241. H. Derby contracted to dig a trench 1000 yd. long, in 24 days. Having employed 54 men for 15 days, he found that only 450 yd. had been dug. How many more men must he employ to finish the trench according to the contract? 242. The duty of a garrison, consisting of 5 companies, containing respectively 40, 50, 60, 70 and 80 men, requires 90 men each day. What number must each company fur- nish 1 243. $750. MiDDLEFiELD, Sept. 1, 1858. Six months after date I promise to pay H. Harger or order, seven hundred fifty dollars, for value received, with interest. John Joslyn. Indorsed as follows: March 1, 1859, $200 ; June 16, 1859, $100; Jan. 1, 1860, $225. What was due Oct. 19, 1862? 244. The duty on an invoice of 300 dozen London porter, at 30^, was $190.512 ; breakage, 2^. Required the invoiced price per dozen. 245. In how many different ways may the letters of the alphabet be arranged, taking 15 each time? 188 ARITHMETICAL EXAMPLES. 246. What is the equated time for paying the balance of the following account ? J. Jones, in account with B. Day. Dr. Cr. 1862. • 186J. Jan. 1 To Mdse. on 6 mo. $350 00 April 1 By Cash, $250 00 March 1 " n " " '240 00 May 6 1.1. ik 200 00 April 15 " ♦' 4 " 1T5 00 June 30 " '« 300 00 June 20 " " 3 " 280 00 Aug. 1 " " 2 " 400 1 '4 247. How much sugar, at 4, 5 and 9 cents a pound, must be mixed with 72 pounds at 12 cents a pound, so that the mixture may be worth 8 cents a pound ? 248. Insert four arithmetical means between 2 and 79. 249. A person wishes to discharge a debt of $1125 in 18 annual payments, which shall increase in arithmetical pro- gression. How much must his first payment be in order that the last may be 120 ? 250. Three merchants have an interest in a steam vessel ; A puts in $960 for six months ; B, a sum unknown, for 12 months ; C, $640 for a time not known when the accounts were settled ; A. received $1200 for his share, stock and profit; B, $2400 for his, and C, $1040 for his. What was B's stock, and C's time ? 251. In the foregoing question A's gain was $240 during 6 months ; B's, $800 during 12 months, and C's, $400 during 15 months, and the sum of the products of their stocks and times was 34560. What were their stocks ? 252. In the same question the sum of the stocks is $3200 ; A's stock was in trade 6 months; B's, 12 months, and C's, 15 months ; at the settling of accounts, A is paid $240 of the gain ; B, $800, and C, $400. What was each person's stock ? 253. A man bought a piece of property for $10500, and agreed to pay principal and interest in 8 equal annual install- ments. How much was the annual payment, interest being ROBINSON'S Full Course of Mathematics. No Series of Mathematics ever offered to the public have attained so wide a circulation or received the approval and indorsement of so many comx)etent and reliable edu- cators, in all parts of the United States, in the same time, as this. l^rogressive TableSooU. This is a beautifully ILLUSTRATED little book, OD tile plan of Object Teaching. Progressive Primary Arithmetie^ Illustrated, Designed as an introduction to the ' Inieliectual Arithmetic." Progressive Intellectual Arithmetic^ on the INDUCTIVE PLAN, and one of the most complete, comprehoisive, aud disciplinary/ works of the kind ever given to the public. Hudiments of Written Arithmetic^ for graded Schools, containing copious Slate and Blackboard Exercises for beginners, and is designed for Graded Schools. Progressive Practical Arithmetic ^ containing the Theory of Numbers, in connection with concise Analytic and Synthetic Methods of Solution, and designed as a complete text-book on this science, for Common Schools and Academies. The different kinds of United States Securities, Bonds, and Trea- sury Notes are described, and their comparative value in commercial transactions illustrated hy practical examples. A full and practical presentation of the Metric System of Weights and Measures has been added. Progressive Higher AfHtJimetic : combining the Analytic and Synthetic Methods, and forming a complete Treat- ise on Arithmetical Science, in all its Commercial and Business Applications, for Schools, Academies and Oommer(jial Colleges. 2 ROBINSON'S SERIES OF MATHEMATICS. Particular attention has been given to the preparation of those subjects, which are absohitely esseniial to make good accountants and commercial business men. The different kinds of United States Securities are described, the differen<'.e between gold and currency, and the corresponding difference in prices exhibited in trade, are taught and illustrated ; also, a full Treatise of the Metric System of Weights and Measures has been added. Arithmetical Examples. This book contains nearly 1,500 Practical Examples, promiscuously arranged, and without the answers given, involving nearly all the principles and ordinary processes of common arithmetic, designed tho- roughly to test the pupil's judgment ; to cultivate habits of patient investigation and self reliance ; to test the truth and accuracy of his own processes by proof; in a word, to make him independent of a text-book J written rules and analysis. This work is not designed for beginners, but for those who have acquired at least a partial knowledge of the theory and applications of numbers from some other work, and it may be used in connection with any other book, or series of books on this subject, for Review or Drill Exercises. Aw edition is printed exclusively for teachers^ containing the answers at the close of the book. IS^eiv Ulementary Algebra: a clear and practical Treatise adapted to the comprehension of beginners in the Science. The introductory chapter is designed to give the pupil a correct comprehension of the utility of symbols, and of the identity and chain of connection between Ai'ithmetic and Algebi a, leading him by easy and .successive steps, from the study of written arithmetic to the study of mental and written algebra. Jff'ew University Algebra^ containing many new and original Methods and Applications both of Theory and Practice, and is designed for High Schools and Colleges. 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' The design throughout has been, not to conceal, but fully to reveal the difficulties of the science, and to encourage the learner, not to avoid, but to grapple with, and to overcome them; since, to the student of Mathematics labor rightly directed, is discipline, and discipline, after all, is the true end of education. "New Geometry and Trigonometry^ embracing Plane and Soiid Geometry, and Plane and Spherical Trigono- metry, with numerous practical Problems, the whole newly illustrated. New and original demonstrations of some of tlie more important principles have been given, and the practical problems and applications, both in the Geometry and the Trigo- nometry, have been g'^eatly increased. New Surveying and Navigation. With use of Instruments, essential Elements of Trigonometry, Mensuration, and the necessary Tables, for Schools, Colleges, and Practical ►Surveyors. 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