(4032) What did 1 hhd.? (2016) What did 1 tierce (1344) What did 1 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 he 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 $1600,60, 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 creditors; 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 + 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? (32711) How much 25 yds. 2 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 fect? A. 182 feet in height. Ratio, 22. 2 39. If 3 cwt. 2 qrs. 16 lbs. of sugar cost $51, what will 10 cwt. 3 qrs. 20 lbs. cost? (Ratio, 3 × 51 153) What will 21 cwt. 3 qrs. 12 lbs.? (6, ratio, × 51306) What will 43 cwt. qrs. 24 lbs.? (Ratio, 12; then, 12 × 51 = 612) A. $1071. Note. The following examples may be performed either by analysis, or by finding the ratio, or by the common rule. Perhaps it would be well to let the pupil take 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? (C). Ratio,) How much will $50 gain? (3. Ratio, ) How ich will $75 gain? (450. Ratio, ) What will $200 gain? (12. Ratio, 2) How much will $300 gain? (18. Ratio, 3) How much will $500 gain? (30. Ratio, 5) How much will $800 gal (46. Ratio, 8) How much will $1000 gain? (60. Ratio, 1) How much will $1250 gain? (75. Ratio, 124) How much $2000 gain? (120. Ratio, 20), Ans. $372,30. 41. If 12 men can build a wall in 20 days, how many can do the same in 5 days? A. 48 men. 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, §. Will 20 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) 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 travelling 10 hours each day? (10 hours will require a less number of days than 6 hours; that is, the multiplying or 2d term must be the smallest.) A. 18 days. Ratio, × 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) At 30 cents? (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 breadth make 1 square foot; then, 6 inches in breadth will require more in length; that is, 6:12:: 12) (24) How many inches in breadth? (36) How many 8 inches in breadth? (18) HCw many 16 inches in breadth? (9) A. 87 inches. 48. If a man's income be $1750 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 currency, how much will 4 s. 6 d. make, in federal money? (,75) Will 2 s 6 d.? (,41) Will 1 s. 6 d. ? (,25) Will 3 s. 9 d. ? (,624) A. $2,044. 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 containing 600 gallons, from which, by 1 pipe, 20 gallons run out in 1 hour, and by another 50 gallons, in what time will the cistern 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. 54. A borrowed of B $600 for 3 years; how long ought A to lend B $800 to requite the favour? (2-3) How long ought he to lend him $900? (2) How long $500? (3-7-6) How long $1200? (1-6) A. 9 years, 4 mo. 6 days. 55. A gentleman bought 3 yards of broadcloth 14 yards wide; how many yards of flannel, which is only yd. wide, will line the same? It is evident it will take more cloth which is only yd. wide, than if it were 14 yd. wide; hence 1 must be the middle term. A. 6 yds. Ratio, 2. 56. A regiment of soldiers, consisting of 800 men, are to be clothed, each suit containing 43 yds. of cloth, which is 13 yd wide, and lined with flannel yd. wide; how many yards of flannel will be sufficient to line all the suits? A. 8633 yds. 1 qr. 1 na. FRACTIONS. 57. If of a barrel of flour 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 of a barrel cost of a dollar,, or 1 barrel, will cost 8 times as much, that is, 8X5 40 X 3 Ans. OR, as is more than }, we may make 3 the 2d, or multiplying term, as in the foregoing examples, thus 6 X 5 16 OR, multiplying by the ratio, thus; the ratio of} to } is { ÷ ==6, ratio ; then, fore pro OR, which is obviously the same, having inverted the 1st, or dividing term, multiply all the fractions together; that is, ceed as in Division of Fractions, (¶ XLVII.) thus, 1×4×16 8X3 X5 The 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 ib.? 17 A. $16. 59. If of a bushel of wheat cost of a dollar, what will 1 bushel cost? A. 16. 60. If 14 yds. of cloth cost $12, what will 1 yd. cost? A. $ 63. If will $5 buy? 65. If 4. $1,80. 66 If 16 for 1 coat? a pound, what will 40 pounds cost? A. $2. A. $2,823 yd. cost $2, what is it a yard? A. $5. apples. oz. of gold be worth $1,50, what is the cost of 1 oz.? 67. If of A. $9. yds. will make 8 coats, how many yards will it take A. 264 yds. of a gallon cost $, what will 5 gallons cost? 68. If 6 yds. cost $53, what will 14 yds. cost? A. $1333. 69. If of cwt. of sugar cost $ro, what will 40 cwt. cost? A. $824. 70. If yd. of silk cost of $3, what is the price of 50 yds.? A. $31. 71. If 1 cwt. of flour cost $15, what will A. $1732. cwt. cost? 72. If 3 yds. of cloth, that is 2 yds. wide, will make a cloak, how much cloth, that is only yd. wide, will make the same garment? The narrower the cloth, the more yards it will take; hence we make the greater the second term, thus; yd. : 24 yds. : : 3 yds.: 10 yds., Ans. 73. If I lend my friend $960 for 3 of a year, how much ought he to lend me of a year to requite the favour? He ought not to lend me so 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 6 days? A. 24 men. Ratio, 2. 75. A merchant, owning of a vessel, sells $500; what was the whole vessel worth? of his share for 3 of 3 = f = 3; then, as of the vessel is $500, is $250, and, or the whole vessel, is 5 × 250-$1250. Or thus; of: 1 :: 500: $1250, Ans., as before. 76. If 1 lb. indigo cost $3,84, what will 49,2 lbs. cost at the A. $125,952. same rate? 77. If $293 buy 59 yds. of cloth, what will $60 buy? A. 120 yds. 78. How many yds. of cloth can I buy for $75, if 267 yds. cost $37? A. 535 yds. Ratio, 2. COMPOUND PROPORTION. ¶ 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, will reap of 200 acres, that is, 5 acres in 10 days; and in 1 day, he will reap acre a day; then 14 men in 1 day will of 5 acres = += 1 an reap 14 times as much; which is, 14 x } = 7 acres. and in 24 days, 24 times 7 acres, 168 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 1 man will mow 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? Â. $320. 4. If a man travel 60 miles in 5 days, travelling 3 hours each day, how far will he travel in 10 days, travelling 9 hours each day? of 60=12, and † of 12 = 4 miles, the distance which he travels in 1 hour; then, 4 miles X 9 hours = 36 × 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 he 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 days? This will give the following proportion, to which, and the next following proportion, the answers, or fourth terms, are to be found by the Rule of Three; thus, 5 days 10 days: 60 miles : miles; which gives for the fourth term, or answer, 120 miles. In the next place, we will consider the difference in hours; then the question will be, If a man, by travelling 3 hours a day for a certain number of days, travel |