bar. bar. To perform this question by analysis, we say, If 7lbs. cost 56 cents, one lb. will cost 4 of 56 cents, which are 8 cents. Then, if llb. cost 8 cents, 36lbs. will cost 36 times as much ; that is, 36 times 8 cents, which are $ 2.88 Ans. as before. 2. If 76 barrels of flour cost $ 456, what cost 12 barrels? As the answer to this ques76 : 12 :: 4 5 6 tion will be in dollars, we place 4 5 6 $ 456 in the third term ; and, 72 as the answer or fourth term 60 must be less than $ 456, be48 cause 12 barrels will cost less 765472(72 Ans. than 76 barrels, we must, of 532 the other two terms, make the 152 less the second term, and the larger the first term ; that is, 12 152 barrels must be the second term, and 76 barrels the first term. We analyze this question by saying, if 76 barrels cost $ 456, 1 barrel will cost of $ 456, which is $ 6. Then, if I barrel cost $ 6, 12 barrels will cost 12 times as much, that is, $ 72 Ans. as before. 3. If 3 men can dig a well in 20 days, how long would it take 12 men ? days. As the answer will 12 : 3 :: 20 be in days, so the 3 third term will be 12) 60 (5 days, Ans. days. As 12 men will 60 dig the well in less time than 3 therefore, the second term will be less than the first. By analysis. If 3 men dig the well in 20 days, it will take one man 3 times as long, that is, 60 days. Again, we say, If one man dig the well in 69 days, 12 men would dig it in i of 60 days, that is, 5 days, Ans. as before. 4. If 4lbs. of beef cost 36 cents, what cost 87lbs. ? Ans. $ 7.83. 5. What cost 9 gallons of molasses, if 63 gallons cost $ 14.49 ? Ans. $ 2.07 men. men. men, 6. What cost 97 acres of land, if 19 acres can be obtained for $337.25 ? Ans. * 1721.75. 7. If a man travel 319 miles in 11 days, how far will he travel in 47 days? Ans. 1363 miles. 8. If 7lbs. of beef will buy 4lbs. of pork, how much beef will be sufficient to buy 48lbs. of pork ? Ans. 84lbs. 9. Paid for 87 tons of iron $ 5437.50, how many tons will $ 7687.50 buy ? Ans. 123 tons. 10. When $ 120 are paid for 15 barrels of mackerel, what will be the cost of 79 barrels ? Ans. $ 632. 11. If 9 horses eat a load of hay in 12 days, how many horses would it require to eat the hay in 3 days ? Ans. 36 horses. 12. When $ 5.88 are paid for 7 gallons of oil, what cost 27 gallons ? Ans. $ 22.68. 13. When $ 10.80 are paid for 9lbs. of tea, what cost 147lbs. ? Ans. $ 176.40. 14. What cost 27 tons of coal, when 9 tons can be purchased for $ 85.95 ? Ans. $ 257.85. 15. If 15 tons of lead cost $ 105, what cost 765 tons ? Ans. $ 5355.00. 16. If 16hhd. of molasses cost $ 320, what cost 176hhd ? Ans. $ 3520.00. 17. If 15cwt. 3qr. 171b. of sugar cost $ 124.67, what cost 76cwt. 2qr. 191b. ? Ans. $ 601.09. Note. When any of the terms is a compound number, it must be reduced to the lowest denomination mentioned in it; therefore, the hundred weights, quarters, &c., must be reduced to pounds, before the terms are multiplied and divided by each other. 18. If 7s.6d. of the old Pennsylvania currency are equal to $ 1, what is the value of £76. 19s. 11d. ? Ans. $ 205.32. 19. If 8s. of the old currency of New York are equal to $ 1, what is the value of £ 19. 19s. 8d. Ans. $ 49.95+. 20. If 4s. 8d. of the old currency of South Carolina and Georgia are equal to $1, what is the value of £176. 18s. 4d. ? Ans. $ 758.21+. 21. As 4s. 6d. sterling of the English currency are equal to one dollar in the United Sates, how many dollars are there in £769. 18s. 9d. ? Ans. $ 3421.94+. 22. If the cars on the Boston and Portland Railroad go one mile in 2 minutes and 8 seconds, how long will they be in passing from Haverhill to Boston, the distance being 32 miles ? Ans. lh. Gmin. 16sec. 23. If one acre of land cost $ 37.86, what cost 144A. 3R. 17p. ? Ans. $ 5484.25+. 24. If a man travels 3m. 7fur. 18rd. in one hour, how far will he travel in 9h. 45min. 19sec. ? Ans. 38m. 2fur. 32+rd. 25. A fox is 96 rods before a greyhound, and, while the fox is running 15 rods the greyhound will run 21 rods' ; how far will the dog run before he can catch the fox ? Ans 336 rods. 26. If 5 men can reap a field in 12 hours, how long would it take them if 4 men were added to their number? Ans. 6 hours. 27. Ten men engage to build a house in 63 days, but 3 of their number being taken sick, how long will it take the rest to complete the house ? Ans. 90 days. 28. If a 4 cent loaf weighs 5 oz. when flour is $5 per barrel, what should it weigh when flour is $ 7.50 per barrel ? Ans. 3} oz. 29. If 7 men can mow a field in ten days, when the days are 14 hours long, how long would it take the same men to mow the field, when the days are 13 hours long? Ans. 101$ days. 30. If 29|bs. of butter will purchase 40lbs. of cheese, how many pounds of butter will buy 791bs, of cheese Ans. 57+Alb. 31. If of a yard costs of a dollar, what will it of a yard cost ? Ans. $ 0.765. 8. yd. yd. : 11 :: $ ; X 12 X = = $0.764 Ans. Note. Let the pupil explain, why the first term is inverted in the operation. 32. If It of a gallon of oil cost of a dollar, what cost of a gallon ? Ans. $ 1.121. STATEMENT. CANCELLED. $. gal. gal. 11 7 9 = $ 1.124 Ans. 33. If 47 yards of cloth cost $2}, what will 194 yards cost ? Ans. $11.50. yd. 8. yd. 89 23 47 : 191 :: 2} ; X X = $ 11.50 Ans. 39 2 8 34. If for 471 yards of velvet, there be received 114 yards of calico, how many yards of velvet will be sufficient to purchase 100 yards of calico ? Ans. 3911% yards. 35. If 147 ells English of broadcloth will pay for 54 cwt. of sugar, how many yards will 251 cwi. buy? Ans. 85yd. 3qr. 3na. 36. A certain piece of labor was to have been performed by 144 men in 36 days, but, a number of them having been sent away, the work was performed in 48 days ; required the number of men discharged. Ans. 12 men. 37 James can mow a certain field in 6 days, John can mow it in 3 days ; how long will it take John and James both to mow it ? Ans. 33 days. 38. Samuel can reap a field of barley in 9 hours ; but, with the assistance of Alfred, he can reap it in 4 hours ; how long would it take Alfred to reap it alone ?. Ans. 71 hours. 39. A. Atwood can hoe a certain field in 10 days, but, with the assistance of his son Jerry, he can hoe it in 7 days ; and he and his son Jacob can hoe it in 6 days ; how long would it take Jerry and Jacob to hoe it together? Ans. 97 days. 40. Bought a horse for $ 75 ; for what must I sell him to gain 10 per cent. ? $ 100 : $ 110 :: $ 75 : $ 82.50 Ans. 41. Bought 40 yards of cloth at $ 5.00 per yard ; for what must I sell the whole amount to gain 15 per cent. ? Ans. $ 230.00. 42. My chaise cost $ 175.00, but, having been injured, I am willing to sell it on a loss of 30 per cent. ; what should I receive ? Ans. $ 122.50. 43. Bought a cargo of flour on speculation at $ 5.00 per barrel, and sold it at $ 6.00 per barrel ; what did I gain Ans. 20 per cent. per cent. ? 44. Bought a hogshead of molasses for $ 15.00, but, it not proving so good as I expected, I sell it for $ 12.00; what do I lose per cent. ? Ans. 20 per cent. 45. Sold a pair of oxen for 20 per cent. less than their value, whereas, I might have sold them so as to have gained 20 per cent., and, by so doing, I have lost $ 60.00 ; what was the price for which they were sold ? Ans. $ 120.00. 46. Bought a hogshead of molasses for $ 27.50, at 25 cents per gallon ; how much did it contain ? Ans. 110 gallons. 47. A certain farm was sold for $ 1728, it being $ 15.75 per acre ; what was the quantity of land ? Ans. 109A. 2R. 344p. Section 43. COMPOUND PROPORTION. COMPOUND PROPORTION is the method of performing by one operation, such questions as require two or more operations in Single Proportion. 1. If $ 100 will gain $ 6 in 12 months, what will $ 800 gain in 8 months ? Ans. $ 32.00. $ 100 : $ 800 12 months : :: $ 6 : $ 32 Ans. 8 months } OPERATION. 800 X 8 X 6 = $ 32 Ans. 100 x 12 The pupil will perceive, that the above operation is compounded of two statements in Single Proportion, which are as follows. If $ 100 gain $ 6 in one year, what will $ 800 gain in the same time ? Ans. $ 48. |