33. If 45 yards of cloth cost $ 27, what will 194 yards cost ? Ans. $ 11.50. CANCELLED. STATEMENT. yd. yd. 8 39 23 47 : 194 :: 2; Х Х = = $ 11.50 Ans. 89 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. 39148 yards. 35. If 147 ells English of broadcloth will pay for 54 cwt. of sugar, how many yards will 2511cwt. buy ? Ans. 85yd. 3qr. 3? {na. 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 8 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. 9,5 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 :: $ 6 : $ 32 Ans. } 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. Again, we say, If $ 800 will gain $ 48 in 12 months, what will the same sum gain in 8 months ? Ans. $ 32. OPERATION. ner. 12 months : 8 months :: $ 48 : $ 32 Ans. as before. This question may be analyzed in the following man We say, If $ 100 gain $6, $ 800 will gain 8 times as much, $ 48. Again, we say, If 12 months gain $ 48, 1 month will gain is of $ 48, = $4, and, if 1 month gain $4, 8 months will gain 8 times $ 4, = $ 32 Answer, as before. Note. The pupil should analyze each question. From the above illustrations, we deduce the following RULE. Make that number, which is of the same kind as the answer required, the third term; and, of the remaining numbers, take any two, that are of the same kind, and consider, whether an answer, depending upon these alone, would be greater or less than the third term, and place them as directed in Simple Proportion. Then take any other two, and consider, whether an answer, depending only upon them, would be greater or less than the third term, and arrange them accordingly; and so on until all are used. Multiply the continued product of the second terms by the third, and divide by the continued product of the first, and you produce the answer. 2. If $ 100 gain $ 6 in 12 months, in how many months will $ 800 gain $ 32. Ans. 8 months. 3. If $ 100 gain $ 6 in 12 months, how large a sum will it require to gain $ 32 in 8 months ? Ans. $ 800. 4. If $ 800 gain $ 32 in 8 months, what is the per cent. ? Ans. 6 per cent. 5. If 15 carpenters can build a bridge in 60 days, when the days are 15 hours long, how long will it take 20 men to build the bridge, when the days are 10 hours long? Ans. 671 days. 6. If a regiment of soldiers, consisting of 939 men can eat 351 bushels of wheat in 3 weeks, how many soldiers will it require to eat 1404 bushels in 2 weeks ? Ans. 5634 soldiers. 7. If 248 men, in 54 days of 11 hours each, dig a trench of 7 degrees of hardness, and 2324 feet long, 33 feet wide, and 24 feet deep; in how many days of 9 hours each, will 24 meņ dig a trench of 4 degrees of hardness, and 3374 feet long, 5 feet wide, and 34 feet deep? Ans. 132 days. Section 44. COMPANY BUSINESS. COMPANY Business, or Fellowship, is a rule, by which merchants, and others in partnership, estimate their gain or loss in trade. It is of two kinds, single and double. Single Fellowship is, when merchants in partnership employ their stock for equal times. 1. John Smith and Henry Grey enter into partnership for three years, with a capital of $ 6000, of which Smith puts in $ 4000, and Grey $ 2000. They gain 8570. What is each man's share of the gain ? Smith's gain $380. Ans. { Grey's gain $ 190. Proof. $ 570. As the whole stock is $ 6000, of which $ 4000 belongs to Smith, it is evident, that his share of the stock is 4888=; and, as each man's gain is in proportion to his stock, of $ 570 = $ 380 is Smith's share of the gain. Grey's stock is $ 2000, therefore, 4888= } of $ 570 = $ 190 is Grey's share of the gain. Hence, to find any man's gain or loss in trade, we have the following RULE. Multiply the whole gain or loss by each man's FRACTIONAL PART of the stock. 2. Three merchants, A., B., and C., engage in trade. A. put in $ 6000, B. put in $ 9000, and C. put in M And I A.'s gain $ 252. $ 5000. They gain $ 840. What is each man's share of the gain ? B.'s gain $ 378. Proof. $ 840. 3. A bankrupt owes Peter Parker $8750, James Dole $ 3610, and James Gage $ 7000. His effects sold at auction, amount to $ 6875 ; of this sum $ 375 are to be deducted for expenses, &c. What will each receive of the dividend ? (Parker $ 2937.75121. Ans. Dóle $ 1212.03 61: Gage $ 2350.2002r. 4. A merchant, failing in trade, owes A. $ 500, B. $ 386, C. $ 988, and D. $ 126. His effects are sold for $ 100. What will each man receive ? Ans. A. receives $ 25.00, B. $ 19.30, C. $ 49.40, D. $ 6.30. Section 45. When merchants in partnership employ their stock for unequal times, it is called Double Fellowship. 1. Josiah Brown and George Dole trade in company Brown put in $ 600 for 8 months, and Dole put in $ 400 for 6 months. They gain $ 60. What is each man's share of the gain ? Operation by analysis. We say, $ 600 for 8 months is the same as 8 x $ 600 = $ 4800 for 1 month ; and $ 400 for 6 months is the same as 6 x $ 400 = $ 2400 for 1 month. The question is, therefore, the same, as if Brown had put in $ 4800 and Dole $ 2400 for 1 month each. The whole stock would then be $ 4800 + $ 2400 $ 7200, and Brown's share of the gain would be do - of $ 60 = $ 40. Dole's share will be 400 $ 60 = $ 20. Hence the propriety of the following |