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 are 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 is equal to $1, what is the value of 76£. 19s. 11d. ?

Ans. $205.32. 19. If 8s. of the old currency of New York is 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 is equal to $ 1, what is the value of 176£. 18s. 4d. ? Ans. $758.21+. 21. As 4s. 6d, sterling of the English currency is equal to one dollar in the United States, 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. 1h. 8min. 16sec.

23. If one acre of land cost $37.86, what cost 144A. 3R. 17p.? Ans. $5484.25+. 18rd. in one hour, how 19sec. ?

24. If a man travels 3m. 7fur. far will he travel in 9h. 45min.

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 engaged 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

K*

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. 1019 days.

30. If 29 lbs. of butter will purchase 40 lbs. of cheese, how many pounds of butter will buy 79 lbs. of cheese?

31. If of a yard cost of a dollar, yard cost?

Ans. 571 lb. what will

of a

Ans. $0.76.

$0.76 Ans.

21: 1 × 11 × 8 = 238

NOTE. Let the pupil explain, why the first term is inverted in the

operation.

32. If

of a gallon of oil cost of a dollar, what

33. If 4 yards of cloth cost $23, what will 19 yards

34. If for 4

yards of velvet, there be received 11

yards of calico, how many yards of velvet will be suf ficient to purchase 100 yards of calico?

Ans. 391 yards. 35. If 147 ells English of broadcloth will pay for 5 cwt. of sugar, how many yards will 25 cwt. buy? Ans. 85yd. 3qr. 32 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. 3 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. 7 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 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 per cent. ? Ans. 20 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. 34 p.

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.

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.

OPERATION.

$100 : $800 :: $6:$48.

Again, we say, If $800 will gain $48 in 12 months, what will the same sum gain in 8 months? Ans. $32.

OPERATION.

12 months 8 months :: $48: $32 Ans. as before.

ner.

This question may be analyzed in the following manWe 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 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. 674 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 5 days of 11 hours each, dig a trench of 7 degrees of hardness, and 232 feet long, 3 feet wide, and 2 feet deep; in how many days of 9 hours each, will 24 men dig a trench of 4 degrees of hardness, and 337 feet long, 5 feet wide, and 3 feet deep? Ans. 132 days.