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Les diagrammes suivants iilustrent la mdthode. 1 2 3 1 2 3 4 5 6 MICROCOPY RESOLUTION TEST CHART (ANSI and ISO TEST CHART No. 2) 114.5 2.8 2.5 3.2 2.2 3.6 4.0 2.0 1.8 1.6 A APPLIED IfVMGE Inc 1653 East Main Street Rochester, New York 14609 USA (716) 482 - 0300 - Phone (716) 288- 5989 - Fax ,t PROBlwKMS IN d-} ■^X ARITHMKTIC M Suitable for Candidates preparing for the Entrance Examinations to the Prince of Wales College and Normal School. SELECTED FOR USE IN THE SCHOOLS OF PRINCE ED\^•ARI) ISLAND ¥i BY .^ D. J. JvIACLBOD >;H1EF superintendent ok gDUCATIUN ^ HASZARD & MOORE, VICTOIUA ROW 1892 \J./ / .c mml EDWAR3 ISUNO pUBLiC ABCK^VES ACCESSION No- 2feH^ ITEM ^lo.... *.Ji.^«»-*— -M).'- -•**• I^ROHL.l:!:i\lS IN ARITHMETIC Suitable for Candidates preparing for the Entrance Exaini nations to the Prince of Wales Collep". and Normal School, SKI.KCTEU FOR USK IN THE SCHOOLS OF I'RINCE EDWARD ISLAND OY IJ. J. rvlACLEOD CHIKK SUl'EklNTENDKNT OF KUUCATIOX CharlottetoUju^ HASZARD & MOORE, VICTOI ^ ROW 1892 PROBLEMS IN ARITHMETIC SUITABLE FOR CANDIDATES I'REl'ARING FOR THE ENTRANCE EXAMINATIONS TO THE PRINCE OF WALES COLLEGE AND NORMAL SCHOOL. 1. Show which is the least and which the greatest of .he folIow-.g fractions :~l of 9,1, U of 9, ^ of 8.2. 2. If telegraph posts are placed 80 yards apart, and a train passes one every 4 seconds ; how many miles an hour is it running ? 3. A regiment marching 3/^ miles an hour takes no steps in a mmute. What is the length of the step ? 4. llow many yards of carpet 15 inches wide will cover the floor 01 a room 22 j^ ft. by 19 ft.? 5. Simplify 83-1^ of 2j\ of i| + 2Kt^-7. 6. Find the sum of 6.27, 18.651, and 12.345, and the differ- ence between .34027 and .27. 7. If a room be 12 ft. square, what must its height be in order that the area of the walls may amount to 60 sq. yds.? 8. A stone house is 36 ft. by 24 ft. How many perches of mason work are there in the basement walls if they are 24 in '^, thick and 9 fi. hi|_: rROHLKMS IX acre 9- I'Mi'l the cost of a square mile of prairie land at $3.25 per \ 10. A field in tlie form cf a rectan^de is 15 chains long and 40 rods \vi^ per chain ? 19. Find the cost of carpeting a stairway of 24 steps, each 12 in. wide, and having a rise of 8 in., allowing 2 ft. extra for the projection of the steps ; the carpet costing $i.2q oer vard. 'i iNrniMF/nc ■ 20. From a lot 40 r.xls s(|uarc I sol. I 40 s(|iiarc 1. .Is. What is tlu' value (.f '.he remainder at $120 |)er ;u-re ? 21. How many Irct of lumber in n sidewalk 160 yds. loni;, S ft. wide, and f,'. in. thick? 22. What time vnouM 36 men, workitij; jo>^ hours a dav, reciuire to Imild a wall uhidi 24 men working; 9 hours 20 minutes a (!.iy, ran huild in 9 days ? 23. I low many revc.Intions will he made hy a wheel which revolves at the rate of 360 revolutions in 7 minutes, while another wheel, which revolves at the rate of 470 in 8 minutes, makes 658 revoj 11 lions .•' 24. If I borrow ^'500 for 13 months when money is worth 4>^ per cent., how much ouj.;hL I to lend in return for 15 months when money is worth 3^4 per cent } 25. If 7 men, working 16 days, can mow a field 1320 yards hmiT, and half a mile wide, what will l,e the length of a field 1320 yards wide, which 4 men can mow in 42 days ? 26. Fifteen horses, having four {t'Mi\<, a day, can be kept for two months for 16 guineas, what will be the cost of keeping 20 mules for 5 months, giving them three feeds a day, a infse's feed being % of a mule's ? 27. Sixty thousand bricks are required for a wall 50 yards long, 15 ft. high, and i ft. \o)A in. thick. Knowing each brick to be 9 inches long, and 43^ inches wide, find its thickness. 28. A man left ]ns eldest son one-third of his property ; his two other sons, each, one-seventh ; his three daughters, each, one-tenth; the remainder of hi> property, which amounted to ^680, he left in legacies. What was the whole amount he left ? 29. Divide ;^3,8oo among A, B, and C, so that A shall have twice as much as B, and C shall have one-sixth of B's share. Il . 6 PROBLEMS JN 30. A cistern has three pipes, A, B, C, which together can fill It in 15 minutes. The pipe A l.y itself could fill it in an hour ; B could fill it in 45 minutes ; in what time could C fill it ? 31. A can mow a field in six days of 9 hours ; B can mow it in 8 days, and C in 12 days. Supposing that A after mowing for a day is joined l,y B, and that after another day they are joined by C, when would the work be finished ? 32. Divide 1.56 by 156.25; and subtract 4.156 from 13.^5. 2,Z' Find the value of 3.751875 of ^3 6j. ^d. 34. Find the simple interest upon £2> 375 for 2% years at 6 per cent, per annum. 35. A room is 20 ft. 9 inches long, 15 ft 3 in. wide, and 12 ft high ; find the cost of papering it with per ^ feet wide at ^Yzd. a yard. 36. Simplify .031339 X 3. i■3-^/^2^. Z1' If a tradesman with a capital of ^500 gain ^60 in seven months, how much will he gain in a year with a capital of ^^420? Z^. Two men or 5 women can do a piece of work in 12 hours, how long will 5 men and 2 women take to do it ? 39- If 3^nien or 5 women can do a piece of work in 20 days in what time will it be done by 8 men and 20 women working together ? 40. Reduce 3. 1136 miles to yards. 41. Find the circumference of a wheel which makes 1048 revolutions in 3j^ miles. 42. Reduce 100,196,196 square inches to acres, etc. 43- In 1,749,134 seconds, how many weeks, days, etc.? 44- Keduce 1,186,126, inches to miles, etc. ARITHMETIC 45- Keduce % of a pound Troy to the fraction of a pound Avoirdupois. 46. Find the vahie of .009943 ^^f a mile. 47- Divide loi by i. 01, and .101 by 10. i. 48. Reduce 14 hours 15 minutes to the fraction of y/^ days. 49- Divide .05625 by .0275. 50. Divide .5 by 25; 87.5 by 2.5, and .055757592 by .009207. ^ 51. Resolve 18, 16, 36, 44, 45, 48, 63, 121 into their simplest factors, and find their least common multiple. 52. A dishonest milkman mixes a pint of water with every two quarts of milk. How many gallons will he make in this way out of 20 gallons of pure milk. 53- A well is 18 yards 2 inches deep, and the wheel is 4 ft. 2 inches round. H. many turns of the wheel will raise the bucket ? 54. Find the value of .2625 of a mile. 55. Add .60457 ; 46.70056 ; 5.80007 ; and 4.7896. 56. Reduce 2.025 miles to yards. 57- If a bankrupt has assets to the amount of $1,020 and debts to the amount of $3,225, how many cents on the dollar will his creditors receive ? 58. A person sold % of his estate, bequeaths % of the remainder to his son, and leaves the rest to be distributed equally among three charities. If each of these charities receives $136.25 what is the value of the estate ? 59. A hat IS the circumference of a wheel which makes 514 revolutions in passing over i mile, 467 yards, i foot ? 8 PROBLEMS IN 60. A j)iece of cloth when measured with a yard measure that IS 2./ of an inch short ai)pears to be lo/X yards long. What is its true length ? 61. Reduce 42 rods, r yard, 8 inches to the fraction of a mile. 62. Divide the product of 6.225 an hours. They start to walk a match of 55 miles. Which will win and by how much time ? 79- If a room is 27 ft. 5 inches long, 14 ft. 7 inches wide, 12 feet 10 inches high,, how much paper y^ of a yard wide is recjuired to cover the walls? 80. If I buy sugar at $7 per cwt., at what rate per lb. must I retail it to gain 7f per cent ? 81. 8implify-i^-4^-°-^'^^'^-^-°66 will 0.002 82. Find the cost of papering a room 21 feel long, i6>i feet wide, 10,14: feet high, at fifteen cents per square yard^ 83. A can run 10 yards to B's 9. How many yards' start must A give B in a mile to make an even race ? ^ 84. If $850 amounts to $913.75 at 2]/. per cent, find the time. 85. A^ room is 10 ft. high, ^y^ yards long, and 3 yards wide. It contains a door 8 ft. by 4 ft., two windows each 5 ft. by 4 ft., and a fireplace 6 ft. by 4 ft. 6 inches. IIoW many square yards on its walls require to be painted ? 86. If 120 men build a house 60 ft. high in 15 days, how many men will build a house 55 feet in 10 days ? 87. A garrison of 1000 men have provisions for 30 days. At the end of 10 days a reinforc last only 5 days. What is tl ement arrives, and th_^ nrovisionq le number of the reinforcement 1 lO PROBLEMS IN 88. A sum of money was Ixjrrowecl at 5 per cent, simple interest. In seven years it amounted to $810. What was the sum borrowed ? 89. If icxD men in 6 days of 10 hours can dig a trench 200 yards long, 3 yards wide, and 2 yards deep, in how many days of 8 hours can 180 men dig a trench 360 yards long, 4 yards wide, and 3 yards deep ? 90. By selling 12 pounds of tea for $7.56, I can gain 5 per cent. What do 1 gain or lose per cent, by selling 50 pounds of the same tea for $31 ? 91. If 20 men build a wall 800 feet long, 10 feet high, and 18 inches thick in 14 days of 8 hours, how thick a wall will 15 men build 900 ft. long and 15 feet high in 21 days of 9 hours? 92. If 2 horses can plough 7 acres of ground in a day, how many horses will plough 161 acres in ii)4 days? 93. -^If 14 men can now 168 acres in 12 days of 8}( hours, how many acres can be mowed by 20 men in 11 days of 7-*- hours ? (0.075 ^ <^-075) - (0.005 X 0.005) 0.75-0.C5 95. Simplify 3i±4±5i X ^t±4^^±4f q6. Smip ify -^ ^- '' -^^ OllT 7x5+0^-57^ 97. Fmd the cost of papering the walls of a room 10 feet 8 inches wide, 19 feet 4 inches long, and g}4 feet high, with paper 2 feet wide at 5 cents a yard, allowing 10 yards of the paper for waste. ^Q c- i-r S^ -0.042- 2.4 + 7f 98. Snnplify — -— ' -—^ — — 99. Find the circulating decimal equivalent to toVt' 94. Simplify now irs, 7* ARITHMETIC ,j l(X). If oranges are bought at the rate of 20 for 25 cents, how many should be sold for $12 to gain 40 per cent, on the cost ? loi. Divide 24.109932 by 3CI.28. 102. x\ bought 63 sheep, and sold % of them at a profit of 15 per cent., f at a profit of 50 per cent., and the rest at a loss of 25 per cent. What did he pay for the sheep, if his gain was $19.25 on the whole? 103. If -1- of a sheep is worth %%, and f of a sheep is worth tV of an ox, what is the value of ICXD oxen ? 104. How many bricks, each 9 inches by 4^ inches by 3 incher., are there in a pile 36 feet long, 9 feet wide, and 12 feel high ? 105. After paying ^ of my money to one person, ^ to another, and -^^ to a third, I had 7 cents remaining. How much had I at first ? 106. A person walks at the rate of 3^ miles an hour. Three hours after he has set out on a journey, he is followed by another person, walking at the rate of 5 miles an hour. In what time will he be overtaken ? 107. A grocer mixes 72 pounds of tea at 69 cents a pound, with 90 pounds of tea at 60 cents a pound. At what price per pound must he sell the mixture .so as to gain 10 cents a pound ? 108. Find the interest of $1,721.84 from April ist to November 12th, at 4^ per cent. 109. If two men can reap 2^ acres in 2^ days, how long will it take 11 men to reap 15 acres ? no. An army lost 18 per cent, of its strength by sickness and desertion, and then lost 14 per cent, of the remainder in battle. The number left was 84,624. Of how many did the arniy originally consist ? 42 PJWBt.EMS IN III. If 6 iron bars 4 feet long, 3 inches broad, and thick weigh 288 pounds, how much will 15 1 2 inches . ^«irs weigh, each 6^ feet long, 4 inches broad, and 3 inches thick ? 112. A rectangular cistern 9 feet long, 5 feet 4 inches wide, 2 feet 3 inches deep is filled with a liquid that weighs 2.520 pounds. Mow deep n ust a cistern be that w.:ll hold 3,850 pounds of the same liquid, if its length is 8 feet, and its width 5 feet 6 inches ? 113. In wiiat time will $2,275 amount to $2,673. 12^ at 5 per cent ? 114^ If 12 men can build a wall 6 feet high, 3 feet thick, in 9 days, how many men would build a wall of the same length, 5 feet high, 4 feet thick, in 24 days ? 115.^ If 5 per cent be lost by selling an article at $2.50, find the gain or loss per cent by selling it at $3. I2>^. 116. Reduce 167,948,604 square inches to acres, etc. 117. A man contracts to perform a piece of work in 30 days, upon which he employs 15 men. In 24 days it is half finished.' How many additional men must he employ to finish the work in time? 118. Reduce to its lowest terms the product of i +i + ii +^ + ^V + ffV. -yd rs- - -f + iP(r. 119. If 3 men mow 20 acres in 11 days of 11 hours, how many men will it take .0 mow a rectangular field 384 yards, long and 300 yards wide, in 4 days of 12 hours ? 120. If by selling goods for $272 I lose 15 per cent, how much per cent would I have lost or gained if I had sold them for $336 ? 121. If oranges are bought at the rate of 20 for a d many should be sold for $28 to gain 40 per cent ? a cioiuir, now ARil'HMETJC 13 '72 <^i 122. Add tcgethcT 536.421, 53, 6^1, 5.36421, and subtract the result from 100,000. 123. If 1,000 square yards produce a load of hay, how many loads will 25 acres produce ? 124. Find the simple interest on $281.63 ^^ S'A ]ier cent for four years and 2 months. 125. A freight train is S miles ahead of an express that travels at the rate of a mile in i^ minutes. Twenty minutes later the express runs into the freight train. At what rate is the freight train running ? 126. If Y men, working 16 days, can mow a field 1,320 yards long, and 880 yards wide, what will be the length of the side of a rield 1,320 yards wide, which 4 men can mow in 42 days ? 127. Divide 1.765 h) 2470 to five places of decimals. 128. If 8 acres produce 220 bushels of corn, how much will 22 yards produce ? 129. $19.68;^ is 2^ per cent of what sum ? 130. If 19 men can build 38 yards of wall in 12 days, how many men will build 96 yards, 2 feet, 3 inches in 21^ days ? 131. If 12 men build a wall 60 feet long, 4 feet 'hick, and 20 feet high in 24 days, working 12 hours a day, how many men will It take to build a uall 100 feet long, 3 feet thxk, and 12 feet high, in 18 days, working 8 hours a day? 132. How much per cent above cost must a man mark his goods in order that he may take off 30 per cent from the market price, and still make 30 per cent on the cost ? 133- If a pint contains 28^ cubic inches, how many pints are there in a cubic fool of water? 134. Find .015 of 17 acres, 130 square rods. 14 PROHLEMS IN 135' ^^ 5 needlewomen can finish a certain ({uantity of work in lo;^ (lays of 9;^ hours each, how V>\\<^ would it take 3 needle- women to do twice the same wo'-k, reckoning 10 hours to the day? 136. Find the srjuare root of , 196 to four places of decimals. 137. How many horses will he required to plough 117 acres in 35 (lays, if 10 horses can plough 13 acres in 7 days ? 138. If I buy 3,090 yards of cloth at ()2y2 cents per yard, and sell the whole for $3, 205.87 j^, what is the gain per cent ? 139. How many bricks %% inches long, ^% inches wide, 2^ inches thick, can be stored in a building 17^ yards long, 10 yards wide, and 8)^ feet high ? 140. How many men working for ll cents an hour for 23 days of 9 hours, can earn the same wages as 22 men working for 11 j^' cents an hour for 18 days of 9^ hours ? 141. A can mow | of a held in 7^ days, B can mow f of the same field in 9;^ days. In what time can A and B together mow the field ? 142. 'A train travels a certain distance in 4/5^ hours at the rate of i6| miles an hour. How long will a train going \^% miles an hour take to travel the same distance ? 143. I pay for 180 yards of cloth at 92>^' cents per yard, but it is measured with a yard stick yi of an inch short. How much money does the seller unfairly take ? 144. What will be the price of ^^540 stock at 76? 145. What stock at 95 can be bought for ^855 ? lifO. r» uaL aUiiUai in;-v;mc Xb Cicilvco irutll £i^\'00 %/2 PCF cent stock ? ARITHMETIC 15 147. When stock is at 5 per cent premium I sell out /66cx> nf this stock ; what money do I receive ? 14S. What is the rate of interest when the 3 per cents are at 72 ? 149. How much money shall I receive for ;^"5400 stock at 10 per cent discount ? 150. The 3^ per cents being at 91^, what amount of stock can be had for £^94^ ? 151. The liroker's charge being % per cent what will he re- ceive on ;^2400, 4 per cent stock at 85 ? 152. I want to secure an income of ^600 a year; what amount of 3 per cent stock must I buy to produce it ? 153. What income will be produced by the investment of ^6700 in the 3X per cents at 102^, taking brokerage into account ? 154. If ;^4000 I0.5-. l)e invested in the 3 per cents at 92, what will be gained l)y selling out at 96 ? 155. By investing in the 4)4 per cents at 95 I get an income of jCs^o ; what sum did I invest ? 156. When the 3>^ per cent stock is at 93 j^, how much must be sold out to realize ;^6oo, brokerage being taken into account? 157. Plnd the change in a person's income who transfers ;^2400 from the 3 per cents at 90 to the 3j^ per cents at 96? 158. How much stock is obtained by investing ^{^4500 in bank stock at 210, brokerage being taken into account ? 159. Which is the better investment, the 3^-^ per cents at 86, or interest at 3|^ per cent ? 1 6 PROlUJiMS IN l6o. What nnnunl income will a person receive who invests ^2000 n, 4 per <-ent stock at 95, and ^',000 in 3 per cent stock :u /, 105 ? J's\. *i ' "' '"u ^' '^" ' ^"^'^ "^ ''' *'^^>" ' ^ *^'-^ ^'4 times N^Iiat H docs in the same tim(^ and IJ dcvs 3^" what C does in the same tune. How l„ng would it take each to do the work ? 162. Bo.ght a ninnbcr of cattle for $2000; had I luuud.t 20 head more at a cost of ten dollars per head less, my entire outlay would have been $2800. How many cattle were purchased ? 163. Kind interest on a note for $515.62, dated March isl, ^^11^ and paid July i6th, 1875, at 8%. 164. A man mowing grass v\alks pt the rate of .35 miles an hour and in 70 minutes mows a grass plot of 1056 square yards- how broad does he mow ? 1 / • . 165. A tradesman has a cash price for gooiofJ 2.8 '>. 6^xi of \ ■ 2i.KixA •2 T .16 (1 ARirilMETlC 19 187. Ue» it to A at $So per acre, /, of the remainder to B at $22 for % of an acre;, and the rest, which is 120 acres, to (^ at $75 for % <»f an acre ; what is his gain or loss ? 190. Sold tea at 90 cents per lb., having gained .vV, ' i the cost, finii the selling price per lb. if he had lost nV 191. A man can row a boat from A to H (a distance of 30 miles) in 7j^ hours if there be no current ; how long would it take him to row it if there was a current of I j^ miles per hour from B to A ? 192. When the 3 per cents were at 90, I found lint by selling out and investing in India 4 per cents at 95 I could improve my income by £2^ ds. Find the amount u my stock in the 3 per cents. 193. A own I of a vessel and B the remainder ; the vessel is sold, A receiving Co per cent of his share of the mone) , and B 20 per cent of bis ; B afterwarchi received $4000 fi >m the purchaser, and the balance then due was divided ecpially >etween A and B. What is the ship sold for ? 194. A man sells out \ of stock in a certain railway, )aying 2% half-yearly dividends, and invests in Bank of Con nerce stock at 120 and paying 4% half-yearly dividends ; he fines that \\\% ifjf.cjnie is tlius increased .*'?'J'2'X i find the amount < ; his railway stock. f 20 PROBI.EMS IN 195. A man's income is derived from tlie proceeds of $4550 at a certain rate \^L■: cent, and $5420 at one per cent more than the former rate ; his whole income being $453, find the rates. 196. A farmer gives for a horse a bill of $272, due in two months, and sold him at once for a bill of $316, due in 5 months ; find the farmer's gain or loss, true discount being reckoned at 4^^ per cent. 4 of jJ- -^ c\^ '^ 2 4. 4 _ 1 -=- f of i of % of a rod to the 197. Reduce ^ ■2 fraction of 2 furlongs. 198. A grocer, by selling 10 lbs. of tea for a certain sum, gained 20 per cent ; afterwards he increased his price, giving only 9 lbs. for the same money. How much per cent did he make at his increased price ? 199. Find^ihe expense of papering a room 21 ft. long, 15 wide, and 12 high, with paper 30 inches wide, at 18 cents a yard, allowance being made for a door 7 ft. by 3 ft., and two windows each 5 ft. by 3 ft. 200. An insurance company took a risk at 2^%, and reinsured t of the risk at 2%; the premium received exceeded the premium paid by $42 ; fiml the amount of the risk. 201. Simplify! If + f of ^_-|_|^2,W. 202. A sum of money was divided among A, B, and C ; A received .939 of ^f of it"; B, ^^ of it, and C, $3015.30; find the amount divided. 203. A trench 80 yards long, 10 feet deep, and 9 feet wide, was completed by 20 men in I2>^ days, of ten hours each ; and a trench 76 yarfls long, and twelve feet deep was completed by thirty men in ^% days, of 9^-2 hours each ; how wide was the liUor trench ? ARirHMETfC 21 $4550 204. The cost of carpeting a room 10^-2 yards long, with carpet 27 inches wide, and costing $1.35 a yard, was $93.15 : find the width of the room. 205. A grocer mixes 60 lbs. of tea at 65 cents a lb., with 80 II1S. at 60 cents a lb.; at what rate per lb. must he sell the mixture to gain 30% ? 206. A person loaned $480 for two months and 13 days, at 9% : what interest did he receive ? 207. I send $5250 to a commission merciiant in Montreal, who charges 5% for investing, with instructions to purchase certain goods, deducting his commission from the amount of money sent him : find his commission. 208. A coal dealer bought 784,000 lbs. of coal, at $4.50 a ton (2240 lbs.), and sold 524,500 lbs. of it at the rate of $5.50 per short ton (2000 lbs.), and the balance at $4.20 per short ton : find the whole gain. 209. From a pound Troy are coined 46!^ sovereigns ; find (in £ s. d.) the price per oz. of gold. 210. Divide $29.50 between two persons, so that one shall receive half as much again as the other. * i^ 6-5 IT 211. Simplify i of H-TTT of H + A of -^ 211. The sum paid for 494 gallons oil, inchiding a duty on each gallon which amount§ to \ of the cost price of a gallon, is $1719.12 ; find the duty on a gallon. 213. A person insured a house for | its value at \\% annually; after paying 6 premiums the house was destroyed, llie entire loss being $1945. Find value of the house. 22 PROBLEMS IN 214. A parcel of 12 lbs. weitrht is carried 80 miles by rail for 56 cents, and the rate for the distance over 50 miles is two-thirtls of the rate for the first 50 miles ; how far can a parcel of 8 lbs. be carried for 16 cents ? 215. A and 15 agree to do a certain piece of work for $25 ; A could do it in 8 days, and B in 10; but C joining them, the work is done in 3 days : how should the money i>e divided ? 216. State the difierence between " True " and " Bank " dis- count. I owe a man $575, and gave him a note at 60 days : what must be the face of the note to pay him th<:: exact del)t, when discounted at (iiank discount) i/^/o a month? 217. A drover bought oxen at $40, cows at $30, and sheep at $10 a head ; there were 2^ times as many cows as oxen, and 5 times as many sheep as cows, and the whole cost was $1440 ; how many of each did he buy ? 218. Find the cost of painting a room 20 ft. 3 in. I)y 18 ft. 6 in., and 10 ft. high, having two windows, each 7 ft. by 4 ft., at the rate of 50 cents a square yard. 219. The true discount on $1235.68^^ for 210 days is $31,173^; find the rate per cent. 220. What sum of money must be divided among A, H and C, so that A may have $1.44, and C $2.25, and that B may have as much per cent more than A as C has more than B ? 221. Divide the number 474 into three such parts that three times the first may be equal to 5 times the second and to eight times the third. 222. Simplify, ARiriL\]ETlC 23 223. A wine merchant pays $175 for a hogshead of wine, and bottles it off into an equal number of quart, pint, and half-pmt l)ottles : how many dozen of each has he, and at what must he sell it per dozen to gain 5% of his outlay ? 224. What must l)e the face of a note so that when discounted at a bank for 4 months and 9 days, at 9 per cent, it will give $240 ? 225. A, B and C having equal shares of a ship, sell respective- ly one-third, one-c|uarter, and one-fifth of their shares to 1), who dies and leaves his share equally among them : If B's and C's interest in the ship be now worth %l1,2PO, what is the value of A's share ? 226. A farmer has 500 bushels of wheat ; he can sell it at once for $1.20 a bushel ; by storing it for six months at a cost of $20 paid in advance, he can realize $1.30 a bushel ; he adopts the former course ; money being worth 8% per annum, determine how much he has gained or lost l^y so doing. 227. Express the value of .83 of 8j. +.65 of 2 guineas + 1.8 of 5^. 228. A merchant bought a number of barrels of flour for $1800 ; he used 20 bbls. and sold -i of the remainder for $1568, which was $224 more than cost. How many barrels did he buy ? 229. When gold is quoted at 133^, what is the gold value of a $10 greenback ? 230.. What is the area of a circle whose diameter is i foot I inch ? 2 ''I, Mow menv Dencils may be bought for $1.00, so that 20% may be gained l)y selling them 4 for i cent ? I 24 PROBLEMS IN 232. A l)oy hired to a mechanic for 20 weeks for $20 and a coat, at the end of 12 weeks the boy quit work and was paid $9 and the coat. Find vakie of coat. 233. At what discount must I buy stocks so that by seHing at 2% premium I may gain 20% on my investment ? 234. What number is that, fV and % of which being multi- plied together will produce the number itself? 235. A and B can build a wall in 4 days, B and C in 6 days, A and C in 5 days ; required the time, if they work together? 236. A makes B a present of $100 on condition that he shall expend it in cows, sheep, and geese ; cows at $10, sheep at $1, and geese at idy^, cents, so as to have just a hundred in the whole. How many must he purchase of each ? 237. A, B and C start from the same point to travel round an island in the same direction, 'J2> miles in circumference; A at the rate of 6, B 10, and C 16 miler, per day, in what time will they be met together ? 238. By selling at 2,1 cents a pound, twice as much is gained as by selling at 29 cents a pound, what per cent is gained by selling at 32 cents a pound ? 239. A house that cost $8250 rents for $750 a year, the insurance is tV%, and repairs >^% every year. What rate of interest does it pay ? 240. A box, with cover, made of board an inch thick, measures on the outside, 20 inches long, 14 inches wide, and 8 inches deep ; tind the cubic contents of the interior, and the cost of painting the outside at 18 cents per square foot, 241. I can obtain $6 more per annum by investing a certain sum in 5 per cents at I2S>4 than in the 3 per cents at 81 ; wiiat is the sum ? ARITHMETIC 25 ANSWERS I. %% of 8.2 ; greatest \ of 23. ' 9^. 24. 2. 40] ? niiles. 25- 3. 2 feet 9f inches. 26. 4. 114 yards. 27. 5- 82H; 28. 6. 37.2748839. .0625. 29. 7. iiX feet. 30. 8. 88 perches. 31- 9. $2,080. 10. 15 acres. 32. II. 2% mills. ZZ- 12. $958.30, 34. 13. $156.81^ 35 14. 1040 feet. 36. 15. $4.77. n 16. $86.40. 38 17. $14.30. 39 18. $3240. 40 19. $17.50. 41 20. $1170. 42 21. 5760 feet. 22. sYl- • « 576. /600. 48 guineas. 3 inches. ;^8,400. ;^2,40o; ^1,200; ^200. 36 minutes. I day 4 hours after C joined A and B. .009984 ;"9Ttwa^ ^%(i9 ^^ £12 los. i}4(i. £S40. £8 2s. •555555- ;^86 8s. 4^% hours. 3 days. 5480 yards. 10 feet. 15 acres, 155 square rods, 23 sejuarc yards, I square foot, 24 square inches. 26 43. 44. 45. 46. 47. 48. 49. 5o. 51. 52. 53 54. 55. 56. 57. 58. 59. 6o. 6i. 62. 63. 64. 65. 66. 67. 68. 69. 70. 71. 72. 73. PROnr.EMS IN 2 weeks, 6 days, 5 hours, 52 minutes, 14 seconds. 18 miles, 230 rods, 8 feet, 10 inches. I s "So" 3 rods, 2 feet, li^^^i in. 100; o.oi. 1 2.045. 0.02 i 35 ; 6.056. 609,840. 25 gallons. 3. 80 rods, 22 yards. 57.8948. , ^ 3,564 yards. J.f^ $4,905. ^*-j 13 feet. 10 yards, 11 inches. T¥T. 20542.5. 524.16231. 0.7003005. ".fiw75v^ 37026 feet? 1015487/ 16.01 16S. 24 lbs. 74. 75. 76. 78. 79. 80. 81. 82. 83. 84. 85. 86. 87. 88. 89. 90. 91. 92. 93- 94. 95. 96. 97. 98. 99 100, lOI. 102. 103. 104. 105. ^tt3^ per cent. $137.50. A, ])y 7^ minutes. 136^ yards. $0.07^. , 6,199. ^ f 176 yards. 3 years. 44 square yards, 5 scjuare feet. 165 men. 3,000 men. $600. 15 days. (iain 3 U per cent. \T,% inoies. 4 horses. 208 A. 0.008. I. I. $5.25. 40.2175. 0.000999. 685?. 0.080026 $551.25. $2,000. 48 cents. ARITHMETIC 27 juare 106. 7 hours. 136. 0.4427. 107. 74 cents. 137. 18 horses. 108. $47.76. 138. 12^4 per cent nearly. j 109. 3 days. 139. 248,832. ' no. 120,000. 140, $S9.i5t^. 7/-^-^-- III. 2340 lbs. 141. ^n^.^ 112. 3 feet, 9 inches. 142. 4 hours. 113. 3 years, 6 months. 143. $2.89^^ 114. 5 men. 144. ;^4I0 8j'. 115- 1834^ per cent gain. 145- ;^900. 116. 26 acres, 126 square rods, 146. ^227 \os. 29 square yards, &c. 147. /6930. 117. 45 men. 148. ^4^. 1 118. 'A- 149. ^4860. 119. 9 men. 150. ^3200. 120. 5% g^in- 151. /3. 121. 400. 152. ;^ 20,000. 122. 45816. 1 1479. 153- ^211 i8.^ 5r%y. ;^i73 18.V. SM 123. 121. ^/ 154. 124. $36.^. 6 /^^ 155- ;^76oo. 125. 24. 156. ^^645 y. 2nd, 126. 1320 yards. 157. £'j los. gain. 127. 0.00071. 158, ^2141 lis. 7\md' 128. 4 quarts. 159. y/2 per cents. 129. $945. 160. ^112 I5.y. 7i^jV. 130. 27 men. 161. A 282^ ; B 351 ; C 26^ 131, iS men. 162. 40 head. 132. 855^ per cent. 163. $97.9 + . ni- 59t?. 164. 49 T51T' 134- 42 square rods, 22 square 165. 50: 53. yards, 6 square feet, 166. tHs-. nt;. 2'7 cn\]n».f; inches. 14 days. — / • 168. 6000 Stock. 28 PROBLEMS IN 169. $20. 206. $8.76. 170. $118.08. $134.40. 207. $250. 171. $744- 20S. $412.32;^. 172. 6,\. 209. /3 I7A-. lO^r/. ^11' $1349.891%. 210. $11.80 $17.70. 174. $400. 211. ^. 180. 7- 216. $593.70. 181. 7^'5. 217. 6 oxen ; 15 cows ; 75 182. =^$1209.30. sheej"). 183. = C()st C $360; W $384; 218. $39. 94a • A $400. 219. 4/2%. 184. A'sgain $3570; B-s'gain 220. $5-49. $3520. 221. 240. 144. 90. 185. $26666^^. 222. 1 ti 4 ;t -2 •J!J1 4!.. 186. c^M '-^t 223. I dozen each, $2.397.5, 187. :; '2 r, ^ $4-79^6, $9.58'''-.' 188. ;['-; of a day. 224. $247,998. 189. $10140. 225. $16700. 190. 6^:^ cents. 226. Loss $5. 191. 227. 17^. 9iV/. 192. ^■3078 stock. 228. 300 barrels. 193- $50,000. 229. $7.50. 194- $41662.^. 230. 132.7326 scjuare inches. 195- 4% 5%. 231. 480. 196. $40. 20. 232. $7.50. 197. ifff, of furlong. 233. 15%. 198. ^iva- 234- 20. 199. $19,512. 235- 3:^V ^i^ys. 200. $4000. 236. 5 cows, 41 sheep, 54 geese 201. ix. 237. 36^ days. 202. $11056.10. 238. 28%. 203. (ifi feet. 239. 8%. 204. 4} -4 yards. 240. 1296 cubic inches, $1.38. 205. Soii. 241. $3078. I Sci anc it a tioi are anc nu] « i ex] ref thi ARITHMETIC 29 APPENDIX 1. Define Arithmetic as a Science and as an Art. As a Science, it logically investigates and philosophically classifies and arranges the principles and rules of the subject ; as an Art it applies these principles to the practical affairs of life. 2. Upon what is Arithmetic founded, and how are its opera- tions carried on ? It is founded on notation, and its operations are carried on by means of addition, subtraction, multiplication and division. 3. What is a Unit ? One, or a single thing. 4. What is a number ? A unit or a collection of units. 5. W'hat is an integer ? A whole number. 6. What is notation ? A method of counting or expressing numbers by characters. 7. What is numeration ? A method of reading numbers expressed by characters. 8. What is an abstract number ? A number used without reference to any particular thing. 9. Concrete number ? One that has reference to a particular thing. I 30 PROBLEMS IN 10. I low are nuniltcrs classified ? They are classified as follows : as even and odd, prime and composite, integral and fractional, abstract and concrete, simple and compound, like and unlike. 11. What is the minuend? The number to be subtracted from. 12. What is the subtrahend? The number which is sub- tracted. 13. What is factoring? The process of separating numbers into factors. 14. What is a prime number? One that cannot be resolved into factors. 15. When are numbers prime to each other? When the" have no common divisjr. 16. What is a common divisor ? One that will divide two or more num])ers without a remainder. 17. The greatest common factor ? Is the greatest factor that will divide two or more numbers without a remainder, 18. What is a least common multiple? Is the least number that is exactly divisible by two or more given numbers. 19. What is a vulgar fraction ? A part of a unit. 20. What is a decimal fraction ? A fraction whose denom- inator is increased or decreased in ten fold ratio. 21. Upon what does the value of a decimal depend? Its place from the decimal point. 22. What arc circulating decimals ? A decimal in which a figure or set of figures are continually repeating. { 1 ARITIIMETJC I 23. What is the difference l)ctvveen decimal fra* u , id common fractions? The first has a denominator u tood, showing that a unit is divided into ten equal parts, or sub- divided into a ten-fold ratio ; the second has a denominator shewing that a unit is divided into any number of equal parts. 24. What is currency ? The medium of circulatitjn. 25. From what was the sign % derived ? From the initial letters of the United States. U. S. joined together as a monogram. 26. What is a standard unit ? A unit of measure from whicli the other units of the same kind may be derived. 27. What is the standard unit of value ? Money is the standard unit of value and is of two kinds, coin and paper money. In Canada and the United States the standard unit is the dollar. In English money it is the pound. 28. What is the standard unit of weight ? Troy pound. 29. What is the standard unit of length ? Yard, &c. 30. VVhat is the standard unit of surface ? Square yard for ordinary measurement, and acre for land. 31. What is the standard unit of volume? Cubic yard for ordinarv measurement, and cord for wood. 32. What is the standard unit of capacity ? Gallon for fluids and bushel for dry measure. 33. What is the standard unit of time ? Day, this is deter- mined by revolution of the earth. 34. What is the difference between a lb. Troy and a lb. Avoirdupois ? Troy has 5760 grains, Avoirdupois has '^OOCi grains. 32 PROBLEMS IN 35. What is linen r measure ? That which is used in measur- ing lines or distances. 36. What is a s(|uare ? A figure having four cfjual sides and four e(|ual angles. yj. What is a cube ? A figure having six equal sides. 38. IIovv many inches in a wine gallon? 231 cubic inches. 39. 1 hnv many inches in a beer gallon ? 282 cubic inches. 40. How many inches in a bushel? 2,150.4 cubic inches. 41. What is commission? Per centage allowed an agent or commission merchant. 42. What is brokerage ? The fee paid a broker for the trms- uction of business. 43. What is insurance ? Security on property guaranteed by one party to another, for a stipulated sum, against the loss of that property by any casualty. 44. What is a policy ? A written contract between the parties. 45. What is a premium ? Sum paid for insurance. 46. W^liat is interest ? A sum paid for the use of money. 47. W' hat is usury ? Illegal interest. 48. What is the difference between simple and compound interest ? Simple interest is the interest on the principal only. Compound interest is the interest on the amount. 49. What is discount ? An allowance made for the payment of a debt before it is due. 50. W- hat is the present worth of a debt ? The present worth of a debt is such a sum which, 'oeing put ai. legal interest would amount to the debt when due. '«!