(4032) What did I hhd. ? (2016). What did 1 tierce > (1344) What did I bbl.? (1008) Ans. $84. What did 2 quarts cost? (16) What did 3 pints cost ? (12) What did 4 gills cost ? (4) A. $,32. 33. Bought 6 tuns of wine for $500,50 ; what did 1 pipe cost ? A. $41,708 +. 34. When a merchant compounds with his creditors for 40 cents on the dollar, how much is A's part, to whom ho owes $2500 ? how much is B’s part, to whom he owes $1600 ? A. A's, $1000; B's, $640. 35. A, failing in trade, owes the following sums, viz. to B $1000,60, to © $500, to D $750,20, to E $1000, to F $230 ; and his property, which is worth no more than $1020,20, he gives up to his crcditors; how much does he pay on the dollar? and what is the amount of loss sustained by all? A. 25 cents on $1; and the amount of loss is $3060,60. 36. Bought 4 tierces of rice, each weighing 7 cwt. 2 qrs. 16 lbs.; what do they come to at $9,35 per cwt.? (285842) At $2,50 per qr. ? (305714) At 10 cents per pound? (34240) A. $933,956 to 37. Bought, by estimation, 300 yards of cloth, for $450,60; but, by actual measurement, there were no more than 275 yds. 2 qrs.; for how much must I sell the measured yards per yd., so as to neither make nor lose ? (1635) How much must I sell 20 yds. for, so as to lose nothing? (32111) How much 25 yds. qrs. ? (41707) How much 30 yds. 1 qr. 3 na. ? (49782) A. $125,835 +. 38. If a staff 6 feet long cast a shade on level ground 9 feet, what is the height of that steeple whose shade measures at the same time 198 feet? 4. 132 feet in height. Ratio, 22. 39. If 3 cwt. 2 qrs. 16 lbs. of sugar cost $31, what will 10. cwt. 3 qrs. 20 lbs. cost ? (Ratio, 3 x 51 153) What will 21 cwt. 3 qrs. 12 lbs. ? (6, ratio, X 51 = 306) What will 43 cwt. 2 grs. 24 lbs.? (Ratio, 12; then, 12 x 51 = 612) A. $1071. Note. The following examples may be performed either by analysis, or by finding the ratio, or bv me common rule. Perlaps it would be well to let the pupii 19.50 his choice. The one by ratio is recommended. 40. If $100 gain $6 in a year, how much will $20 gain in the same time? (120. Ratio, $). How much will $10 gain? (30. Racio, tb) How much will $50 gain ? (3. Ralio, ) How 11; uch will $75 gain ? (450. Ratio, 1) What will $200 guin ? (12. Rntin, 2) How much will $300 gain ? (18. Ratio, 3) How nach will $500 gain ? (30. Rutio, 5) How much will $800 pain : (48. Ratio, 8) How much will $1000 gain? (60. Ratio, .), llow much will $1250 gain? (75. Ratio, 121) How much will .32000 gain ? (120. Ratio, 20) Ans. $372,30. 2 At 30 cents ? 41. If 12 men can build a wall in 20 days, how many can do the same in 5 days ? 4. 48 inen. Ratio, 4. 42. If 60 men can build a wall in 4 days, how many men can do the same in 20 days ? A. 12 men. Ratio, } 43. If 4 men can build a wall in 120 days, in how many days will 12 men do the same? (40) Will 16 men? (30) Will C men ? (24) Will 24 men ? (20) A. 114 days. 44. If a man perform a journey in 30 days, by travelling 6 hours each day, in how many days will he perform it by trav. elling 10 hours each day? (10 hours will require a less nunber of days than 6 hours ; that is, the multiplying or 2d terin must be the smallest.) A. 18 days. Ratio, } x 30 =18, the same. 45. If a field will keep 2 cows 20 days, how long will it keep 5 cows ? (8) Will it keep 8 cows? (5) Will it keep 10 cows. (4) Will it keep 20 cows? (2) A. 19 days. 46. If 60 bushels of grain, at $1 per bushel, will pay a debt, how many bushels, at $1,50 a bushel, will pay the same ? (40) How many bushels at $1,20 ? (50) How many at 80 cents (75) At 50 cents (120) At 40 cents ? (150) (200) A. 635 bushels. 47. How much in length that is 6 inches in breadth will make a square foot ? (12 inches in length and 12 in breadih make I square foot; then, 6 inches in breadth will require more in length; that is, 6 : 12 :: 12). (24) How many 4 inches in breadih (36) How many 8 inches in breadth ? (18) FICw many 16 inches in breadth? (9) A. 87 inches. 48. If a man's income he $17504 a year, how much may he spend each day to lay up $400 a year? A. $3,70. 49. If 6 shillings make $1, New England curren ency, how much will 4 s. 6 d. make, in federal money ? (,75) Will 2 s 6 d. ? (,413) Will 1 s. 6 d. ? (,25) Will 3 s. 9 d.'? (,62}) A. $2,04 50, A merchant bought 26 pipes of wine on 6 months' credit: but, by paying ready money, he got it 3 cents a gallon cheaper; how much did he save by paying ready money? A. $98,28. 51. Bought 400 yards 2 qrs. of plaid for $406,80, but could sell it for no more than $$300; what was my loss per ell French ? A. $,40. 52. If 120 gallons of water, in 1 hour, fall into a cistern con taining 600 gallons, from which, by 1 pipe, 20 gallons run out :n 1 hour, and by another 50 gallons, in what time wiīl the cis. tern be filled ? A. 12 hours. 53. A merchant bought 40 pieces of broadcloth, each piece containing 45 yards, at the rate of $6 for 9 yards, and sold it again at the rate of $15 for 18 yards, how much did he make in trading? A. $300. 64. A bacon sd of B $600 for 3 years; how long ought A l. lend 800 to requite the favour? (2-3) How long ought he to lend him $900 (2) How long $500? (3-7-6) Ilow lony $1900 ? (1-6) A. 9 years, 4 mo. 6 days. 55. A gentleman bought 3 yards of broadcloth 15 yards wido; how many yards of flannel, which is only & yd. wide, will lino the same? It is evident it will take more cloth which is only, 1 yd. wide, than if it were 14 yd. wide ; hence it must be the middle terın. A. 6 yds. Ratio, 2. 56. A regiment of soldiers, consisting of 800 men, are to be clothed, each suit containing 48 yds. of cloth, which is 11 yd w.de, and lined with flannel yd. wide ; how many yards of dasınel will be sufficient to line all the suits ? A. 8633 yds. 1 gr. na 16 15 1 15 X ) 120 64 x 64 FRACTIONS. 57. If } of a barrel of four cost of a dollar, what will of a barrel cost ? By analysis. It is plain, that if we knew the price of 1 barrel, of a barrel would cost as much. If t of a barrel cost 18 of a dollar, , or 1 barrel, will cost 8 times as much, that is, 8 X 5 40 X 3 $13, Ans. OR, as is more than }, we may make the 2d, or multiplying 181 m, as in the foregoing examples, thus : bbls.bbls. $ 5 X 3 $:f:: 7. Then, 16 xĀ 64 •(Inverting : by 1 XI.VII. there, $13, Ans. OR, multiplying by the ratio, thus ; the ratio of } to fist 6 X 5 3*=6, ratio ; then, 16 $13, Ans., as bee fore Or, which is obviously the same, having inderted the 1st, or, dividing term, muitiply all the fractions together, that is, proceed as in Division of Fractions, (1T XLVII.) thus, 8 X 3 TX7X16 $13, Ans., as before. Thu pupil may perform the following examples by either of the preceding methods, but the one by analysis is recommended, it being the best exercise for the mind. 58. If 3 lbs. of butter cost of a dollar, what cost s lb. ? A. $.it 30 120 64 A. $51. 186 ARITHMETIC. 59. If } of a bushel of wheat cost is of a dolla. what will I bushel cost? A. 16. 60. If if yds. of cloth cost $17, what will 1 yd. cost? A. 61. At $ Tb a pound, what will 40 pounds cost ? 62. If tyd. cost $275, what will 1 yd. cost ? A. $2,823 63. If sof & yd. cost $2, what is it a yard ? 64. If of off of $1 buy 20 apples, how many applos will $5 buy? A. 4872 i apples. 63. If oz. of gold be worth $1,50, what is the cost of oz.? A. $1,80. 66 If 16% yds. will make 8 coats, how many yards will it take for 1 coat? A. 2377 yds. 67. If ļ of f of a gallon cost $&, what will 55 gallons cost : A. $98. 68. If 6 yds. cost $5%, what will 144 yds. cost? A. $1378. 69. If sof} cwrt. of sugar cost $16, what will 40 cwt. cost ? A. $824. 70. If & yd. of silk cost of $$, what is the price of 50 yde.? .A. $314. 71. If 1 cwt. of four cost $16, what will tiz cwt. cost ? A. $1752 72. If 3 yds. of cloth, that is 21 yds. wide, will make a cloak, how much cloth, that is only & yd. wido, will make the samo garment? The narrower the cloth, the more yards it will take; hence we make tho greater the second term, thus; yd. : 24 yds. : • 3 yds. : 10 yds., Ans. 73. If I lend my friend $960 for of a year, how much ought he to lend me of a year to rcquite the favour? He ought not lo lend me much as I lend him, because I am to keep the money longer than he; therefore, make the middle term. A. $853). 74. If. 12 men do a piece of work in 124 days, how many men will do the same in 68 days ? A. 24'men. Ratio, 2. 75. A merchant, owning of a vessel, sells $ of his share for $500; what was the whole vessel worth? of = 15$ ; then, as of thee vessel is $500, $ is $250, and f, or the whole dessel, is 5 X 250 = $1250. Or thus; šof ? :1: : 500. : $1250, Ans., as before 76. If 14 15. indigo cost $3,84, what will 49,2 lbs. cost at land samo rale? 4. $125,932. 77. Ir buy 594 yds. of cloth, what will $60 buy? 1. 120 yus 78. how many yds. of cloth can I buy for $754, if 2674 yds 374 ? A. 5351 yds. Ratio, 2. cost COMPOUND PROPORTION. 1 LXXIV. 1. If 40 men, in 10 days, can reap 200 acres of grain, how many acres can 14 men reap in 24 days ? By analysis. if 40 men, in 10 days, reap 200 acres, 1 man, in the same time, roill reap to of 200 acres, that is, 5 acres in 10 days; and in 1 day, he will reap Ib of 5 acres = Po= an acre a day; then 14 men in 1 day will reap 14 times as much, rohich is, 14 x1=7 acres, and in 24 days, 24 times 7 acres,= 198 acres, Ans. Perform the following sums in the same manner. 2. If 4 men mow 96 acres in 12 days, how many acres can 8 men mow in 16 days? First find how many acres i man will moro in 12 days ; then, in 1 day A. 256 acres. 3. If a family of 8 persons, in 24 months, spend $480, how much would 16 persons spend in 8 months ? A. $320. 4. If a man travel 60 miles in 5 days, travelling 3 hours each day, how far will ho travel in 10 days, travelling 9 hours each day? 3 of 60=12, and 5 of 12=4 milcs, the distance which he tradels in 1 hour; then, 4 miles x 9 hours = 36 X 10 days = 360 miles, the Ans. It will oftentimes be found convenient to make a statement, as in Simple Proportion. Take the last example.- In solving this question, we found the answer, which is miles, depended on two circumstances; the number of days which the man travels, and the number of hours le travels each day. Let us, in the first place, find how far he would go in 5 days, supposing he travelled the same number of hours each day. The question will then be : If a man travel 60 miles in 5 days, how many miles will he travel in 10 layo? This will give the following proportion, to which, and the next fol. lowing proportion, tne answers, or fourth terms, are to be found by the Rule of Three ; thus, 5 days : 10 Isovs : : 60 miles : which gives for the fourth too. . answer, 120 miles. In the next place. we will consider the difference at nours ; then the question will be, If a man, by travelling 3 Lours a day for a certain number of days, travel miles; |