5. If 4 gallons of vinegar be worth 9 gallons of cider, how many gallons of cider will it require to purchase 36 gallons of vinegar? 9 86x9 = 81 gallons, 4 [Ans. ] 6. If a man travel 765 miles in 1 153 75 days, how far would he travel 1$X765 in 15 days? = 153 miles, 75 [Ans. $ $ 7. If 15 yards of cloth, that is 3 quarters of a yard wide, are sufficient to make a garment, how many yards will it require to line the same that is 5 quarters of a yard wide ? 3 $ 9 yards, [Ans. 8. When $ 200.85 are paid for 66.95 1 39 barrels of flour, what must be gøø.85X18 paid for 13 barrels ? 89 $ 66.95 [Ans. IV. COMPOUND PROPORTION. PERFORMED BY CANCELLING. OPERATION. 1. If a man travel 117 miles in 30 8 20 days, employing only 9 hours a day, g 12 4 how far would he go in 20 days, trav- 117 13 elling 12 hours a day? 104 miles, Ans. In performing this question, we arrange the numbers, that would be the second and third terms in the regular statement of the question on the right hand of a perpendicular line, and the numbers, that would be the first term, on the left. We then divide the product of the uncancelled numbers on the right by the product of the uncancelled numbers on the left. 2. If 6 men in 16 days of 9 hours 24. 6 each build a wall 20 feet long, 6 feet 9 high, and 4 feet thick, in how many 2ø 2øø 10 days of 8 hours each will 24 men 6 build a wall 200 feet long, 8 feet 4 high, and 6 feet thick ? 16 90 days, Ans. 3. If $ 100 gain $ 6 in 12 months, 1$$ 8gø 8 how much would $ 800 gain in 8 12 8 4 months ? 6 $ 32 Ans. 4. If $ 100 gain $ 6 in 12 months, 6 16 2 what must be the sum to gain $ 16 in 8 12 2 8 months ? 100 $ 400 Ans. 5. How long will it take $ 600 bøø 1$ø to gain $ 12, if $ 100 gain $6 in 6 12 2 12 months ? 12 2 4 months, Ans 6 If $ 600 gain $18 in 6 months, 6Ø1Øø what is the rate per cent. ? 6 12 2 18 3 6 per cent. Ans. 7. If 12 men in 15 days can build $ Bø 12 a wall 30 feet long, 6 feet high, and ഉം 800 10 3 feet thick, when the days are 12 B hours long, in what time will 60 men build a wall 300 feet long, 8 feet 12 high, and 6 feet thick, when they work only 8 hours a day? 120 days, Ans. 8. If 8 men spend $ 32 in 13 weeks, 824 3 what will 24 men spend in 52 weeks ? 13 52 4 32 9. If 16 horses consume 84 bush. 16/82 2 els of grain in 24 days, how many 24 48 2 bushels will suffice 32 horses 48 84 days? 336 bushels, Ans. 10. If the carriage of 161 6441865 173 5cwt. 3qr., 150 miles cost 30 180 64 16 $ 24.58, what must be 24.58 paid for the carriage of 68037.44 7cwt. 2qr. 25lbs., 64 miles at the same rate ? 4830 $ 14.087 [Ans. 11. If %oz. 5dwt. of 33 661$Ø 2 bread be bought at 4 d., .19 4.7514 7 when corn is 4s. 2d. 145 per bushel, what weight of it may be bought for 2030 ls. 2d., when the price =llb. 4oz. 312dwt. 6.27 bushel is 58. 6d. ? per (Ans. V. CANCELLING APPLIED TO THE CHAIN RULE. The Chain Rule consists in joining many proportions together; and by the relations which the several antecedents have to their consequents, the proportion between the first antecedent and the last consequent is discovered. This rule may often be abridged by cancelling equal quantities on both sides, and abbreviating commensurables. Note. The first numbers in each part of the question are called antecedents, and the following, consequents. 1. If 20 lbs. at Boston make 23 lbs. at Antwerp, and 150 lbs. at Antwerp make 180 lbs. at Leghorn, how many pounds at Boston are equal to 144 lbs. at Leghorn ? OPERATION BY THE CHAIN RULE. 20 lbs. of Boston = 23 Antwerp, 150 lbs. of Antwerp = 180 Leghorn, 144 lbs. of Leghorn. P 180 144 23 155 It will be per540 720 ceived in this 360 720 144 operation, that 4140 the continued 22320 product of the 20 antecedents is 4140)446400(10749 lbs. Ans. . divided by the 4140 continued pro duct of the con32400 28980 sequents. Hence the fol3420 19 180) lowing 4140 23 Rule.- Write the numbers alternately, that is, the antecedents at the left hand, and the consequents at the right hand ; and, if the last number stands at the left hand, multiply the numbers of the left hand column continually together for a dividend, and those at the right hand for a divisor ; but, if the last number stands at the right hand, multiply the numbers at the right hand column continually together for a dividend, and those at the left for a divisor ; and the quotient will be the answer. OPERATION BY CANCELLING. 23| RØ g 18Ø 155 144 16 2480 = 107 lbs. Ans. 23 2. If 12 lbs. at Boston make 10 lbs. 1Ø 12 at Amsterdam, and 10 lbs. at Amster 12 10 dam make 12 lbs. at Paris, how many 80 pounds at Boston are equal to 80 lbs. 80 lbs. Ans. at Paris ? 3. If 25 lbs. at Boston are equal to 24125 22 lbs. at Nuremburg, and 88 lbs. at 2 92 88 4 Nuremburg are equal to 92 lbs. at 49 46 Hamburg, and 46 lbs. at Hamburg are equal to 49 lbs. at Lyons, how many pounds are equal to 98 lbs. at Lyons ? 100 lbs. Ans. 4. If 24 shillings in Massachu- 2 2482 4 setts are equal to 32 shillings in 6 48 4$ 8 New York; and if 48 shillings in 15 10 New York are equal to 45 shillings 100 in Pennsylvania ; and if 15 shillings in Pennsylvania are equal to 1000 10 shillings in Canada; how many 12 =83;s. Ans. shillings in Canada are equal to 100 shillings in Massachusetts ? 5. If 17 men can do as much work as 25 women, and 5 women do as much as 7 boys, how many men would it take to do the work of 75 boys ? 25/17 =36; men, Ans. 7 6. If 10 barrels of cider will pay for 5 cords of wood, and 20 cords of wood for 4 tons of hay, how many barrels of cider will it take to purchase 50 tons of hay ? $|1Ø 2 7. If 100 acres in Brad- 6 1Rø\1Øø 5 ford be worth 120 in Ha- 13 65 $Ø 10 verhill, and 50 in Haver. 15Ø 25 hill worth 65 in Methuen, how many acres in Brad 1250 =96 acres, Ans. ford are equal to 150 in 13 Methuen ? 8. If 10 lbs. of cheese are 7/10 5 equal in value to 7 lbs. of but- 2 11 ter, and 11 lbs. of butter to 2 8 8 11 bushels of corn, and 11 bushels 14 of corn to 8 bushels of rye, 10 5 3025 cheese are equal in value to 10 7 cords of wood ? 432; lbs. Ans. |