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10. If it take 30 yards of carpeting, which is of a yard wide to cover a floor, how many yards, which is 14 yards wide, will it take to cover the same floor ? Ans. 18 yards.
11. If an individual receive a salary of $700, how much will that be for each day, counting 365 days for a year?
Ans. 147 dollars. 12. If the circumference of a wheel is 174 feet, what distance will it pass over in revolving 131 times ?
Ans. 2333 feet. 13. If it take 21 yards of cloth for 2 pair of pantaloons, and 12} yards for 5 coats, how many yards will it require for 7 coats and 8 pair of pantaloons? Ans. 271 yards.
14. If 191 yards of cloth cost 137 dollars, how many dol. lars will 14} yards cost ?
Ans. 941 dollars. 15. If 3 bushels of apples cost 13 shillings, how much will 17) bushels cost ?
Ans. £3. 158. 102. 16. How much must be paid for 3 cords of wood, at 2} dollars per cord ?
Ans. $86=$8.4375. 17. If a board 16 feet long and 9 inches wide contain 12 square feet, how long must another board be, which is 8 inches wide, to contain the same number of square feet?
Aus. 18 feet. 18. If the freight of 7 hogsheads of melasses for 18 miles is 9 dollars, what must be paid for the freight of 21 hogsheads the same distance ?
Ans. 27 dollars. 19. If of a vessel is worth $1729, how much is the whole vessel worth?
Ans. $46103. 20. Lent my friend 300 dollars for 6 months; afterwards he lent me 400 dollars. How long may I keep it to balance the favor?
Ans. 44 months.
21. If a piece of land 20 rods long and 8 rods wide make one acre, how wide must it be when it is 50 rods long to con. tain the same?
.. Ans. 3f rods. 22. If a ship sail 90miles in 74 hours, how many hours will it require to sail 60 miles ?
Ans. 479hours. 23. If of an acre of land is worth 54 dollars, what is of an acre worth?
- Ans. $7.20. 24. If I pay of a dollar for sawing one cord of wood, how much must I pay for sawing 5 cords ? Ans. $411.
25. If 16} yards of cloth are worth 3 of 1 of 204 dollars; what is that per yard ?
Ans. $397. 26. A man is 1700 dollars in debt, and his estate amounts to but 870 dollars. How much can he pay on the dollar?
Ans. $0.51 27. How many yards of paper, 3 quarters wide, will paper 375 square yards ?
Ans. 500. 28. If a staff 5 feet long cast a shade 64 feet, what is the height of that steeple whose shade, at the same time, measures 150 feet?
Ans. 11513 feet 29. If 3 paces, or common steps, of a person be equal to 2 yards, how many yards are there in 170 paces?'. Ans. 113). 30. What cost 3 cwt, of coffee at 15d. per pound?
Ans. £21. 31. A garrison of 540 men have provisions for 365 days. How long will those provisions last if the garrison be increased to 1127 men ?
Ans. 1741144 days. 32. What will be the tax upon £763 13s. at the rate of 38. 4d. on one pound sterling ?
33. What is the value of a year's rent of 547 acres of land, at the rate of 15s. 6d. per acre ?
34. Allowing the French metre to be 375 feet in length, how many feet are there in 46 metres ?
35. Suppose a certain quantity of hay will feed 70 sheep 31 days, how long would it keep 131 sheep?
36. If 9 yards of silk, which is of a yard wide, line a cloak, how many yards, that is 5 quarters wide, will it take to line the same?
37. If a barrel of beer last 10 men 16 days, how long will it last 27 men ?
38. If 94 barrels of four be consumed by a company in 18 days, how long will 354 barrels last?
39. If a mill grind 194 bushels of corn in 1 hour 7 minutes, in what time will it grind 100 bushels ?
40. If a barrel of flour will support 13 men for 27 days, how long would it support 9 men?
41. If of an acre of land cost $13, how much can be bought for $39 ?
42. If 1% of a dollar will pay for of a bushel of apples, how many bushels can be bought for 71 dollars ?
43. If 750 barrels of cider cost $2250, how much will 419 barrels cost ?
44. If of a firkin of butter is worth 85 cents, what is of a firkin worth?
45. If a staff 3 feet in length give a shadow 7 feet long, how high is that tree, which at the same time casts a shadow of 90 feet?
46. A regiment of soldiers consisting of 976 men is to be clothed ; each coat to contain 21 yards of cloth 15 yards wide, and to be lined with shalloon 7 yard wide. How many yards of shalloon will be required ? :
47. A person owning of a coal mine, sells of his share for $400.' What is the whole mine worth at the same ratio? · 48. A and B hire a pasture for $50, in which A pastures 13 cows, and B 12. What must each pay?
49. Suppose sound to move 1106 feet in a second ; how many miles distant is a cloud, in which lightning is observed 471 seconds before the thunder is heard, no allowance being made for the progressive motion of light?
50. If A can mow an acre of grass in 58 hours, and B can mow 1} acres in 81 hours, in what time can they jointly mow 84 acres ?
COMPOUND PROPORTION. 61. When the quantity required depends upon more than three terms, the operation of finding it is called the rule of coinpound proportion, which may be thus given.
* RULE. " Among the terms given there will be but one like the answer, which we will call the odd term. The other terms will appear in pairs or couplets. Form ratios out of each couplet in the same manner as in the rule of three ; then multiply all the ratios and the odd term together, and it will give the answer in the same name and denomination as the odd term.
Note. Before forming ratios from the couplets they must be reduced to the same denominate value.
Examples. , 1. If a person travel 300 miles in 17 days, traveling only 6 hours each day, how many miles could he have gone in 15 days, by traveling ten hours each day?
In this example the answer is required in miles, therefore our odd term is 300 miles. :
The first couplet consists of days; and since in 15 days, other things being the same, he could not travel as far as in 17 days, we must divide 15 by 17, which gives for the first ratio.
The second couplet consists of hours; and since in 10 hours he could travel farther than in 6 hours, we must divide 10 by 6, which gives 40 for the second ratio.
Multiplying these two ratios and the odd term together, we + 15 x 10 x 300
9. Canceling the 6 of the denominator 17% 6
15 x 10 x 50 against a part of 300 of the numerator, it becomes
17 =4411, miles, for the answer.
2. If a marble slab 10 feet long, 3 feet wide, and 3 inches thick, weigh 400 pounds, what will be the weight of another blab, of the same marble, whose length is 8 feet, width 4 feet, and thickness 5 inches ?
In this example the answer is required to be in pounds ; there. fore 400 pounds is the odd term. The first couplet consists of the lengths, and since 8 feet in length will give less weight than 10 feet, we must divide 8 by 10, which gives is for the first ratio.
The second couplet consists of the widths; and since 4 feet wide will give more weight than 3 feet, we must divide 4 by 3, which gives for the second ratio.
The third couplet consists of thicknesses ; and since 5 inches thick will give more weight than 3 inches, we must divide 5 by 3, which gives for the third ratio. • Multiplying the odd term and these ratios together, we get