we therefore take 650 pounds for the third term. The ratio of 825 sheep to 200 sheep is 25. Hence, we have

200

Cancelling, we have

7. If much will

of a pound of sugar cost of a shilling, how of a pound cost?

In this example, our third term is 23 of a shilling. And since of a pound is less than 1, we must obtain our ratio by dividing by 13, which gives; this, multiplied by the third term, 23 of a shilling, will give 23 of a shilling 11. To reduce this with the least labor, we must resort to the method of cancelling. Thus, cancel· ling the 23, which occurs in both numerator and denominator, also 13 of the numerator against a part of the 26 of the denominator, our expression will, by this means, be come of a shilling xx of a shilling.

NOTE. This method of cancelling should be used when the nature of the question will admit, since it will always simplify the operation.

8. If a tree 38 feet 9 inches in height, give a shadow of 49 feet 2 inches, how high is that trec, which, at the same time, casts a shadow of 71 feet 7 inches?

In this example, our third term is the height of the first tree, which is 38 feet 9 inches=383 feet-155 feet: our ratio will be obtained by dividing 71 feet 7 inches=71 feet=59 feet, by 49 feet 2 inches=491 feet-235 feet: which becomes X5; this multiplied by the third term, 155 feet, gives 155 feet x 85993. Cancelling 6 of the numerator against a part of the 12 of the denomina.

859

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tor, also cancelling 5, a factor of 155 of the numerator, against 5, a factor of 295 of the denominator, we get 31 feet × 859 × 35=26929=56197 feet, for the answer.

9. If 3 pounds of coffee cost 2 shillings, how much will 10 pounds cost?

In this example, 2-3 shillings must be our third term; and since 10162 pounds must cost more than 3}=} pounds, we must divide by for the ratio; making it x; this, multiplied by the third term, shillings, will give shillings x; which becomes, after cancelling, of a shilling 11 shillings=63 shillings.

61
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10. Gave $72 for 11 barrels of fish. How much will 88 barrels cost at the same rate? Ans. $576. 11. If 43 pounds of cheese cost $2.20, what will 2163 pounds cost at the same rate? Ans. $11. 12. If I pay $3.90 for sawing 7 cords of wood, how much ought I to give for sawing 23 cords? Ans. $13. 13. If of a ship is worth $2853, what is the whole worth?

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The ratio of the whole ship, or 18, to, is 10. Hence, $285310$951 × 10=$9510 Ans. 14. If of my income is $533, what is my whole income? Ans. $1732.25. 15. A person failing in business, finds that he owes $7560, and that he only has $3100 to pay it with. much can he pay to that creditor whose claim is $756? Ans. $310.

How

16. If it require 5 bushels of wheat to make one barrel of flour, how many bushels will it require for 100 barrels of flour? Ans. 550 bushels. 17. If 7 barrels of flour are sufficient for a family 6 months, how many barrels will they require for 11 months? Ans. 12 barrels.

18. If it take 25 yards of carpeting a yard wide to cover

a certain floor, how many yards of necessary to cover the same floor?

carpeting would be Ans 33 yards. 19. If a person travel 8 miles in 10 hours, how far will

he travel in 5 days, by travelling 8 hours each day?

N

Ans. 32 miles

20. If 35 pounds of feathers cost $15, what will 100 pounds cost at the same rate? Ans. $42.85. 21. If a man perform a certain piece of work in 18 days, when he works 8 hours per day, how many days will he require if he work 10 hours each day?

Ans. 14 days 4 hours. 22. If a piece of board 12 inches wide and 12 inches long make one square foot, how many inches of length must be taken from a board 15 inches wide to make a square foot? Ans. 93 inches. 23. If 8 men can mow a field in 5 days, in how many days can 5 men do the same?

Ans. 8 days.

24. If 274 yards of cloth cost $60, how many yards can I buy for $100 ? Ans. 45 yards. 25. If 27 yards of cloth cost $60, what will 45 yards cost?

Ans. $100. 26. If of a ship is worth $9000, what is her whole value?

The whole ship being a unit, or, we have the ratio §; hence, the answer is $9000 = $14400.

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27. If of a city lot is sold for $500, what would of the same lot sell for at the same rate? Ans. $1166.

28. Admitting that the earth moves in its orbit about the sun, a distance of 597000000 miles, in 365 days 6 hours, how far on an average does it move in each hour? Ans. 681046 miles. 29. The equatorial portions, by the diurnal rotation of the earth, move about 24900 miles each day? How far is that in each hour? Ans. 1037 miles.

30. If it require 10 years of 365 days for light to pass from a fixed star to the earth, how many miles distant is it, on the supposition that light moves 192000 miles in 1 Ans. 60590592000000 miles. 31. If by a leak of a ship enough water run in in 4 hours to sink her, in what time must she sink?

second ?

Ans. 6hr. 40m. 32. If I pay $25 for the masonry of 4000 brick, how much ought I to pay for the work which requires 100000 brick?

Ans. $625.

33. If a steam-ship require 14 days to sail a distance of 3000 miles, what time, at the same rate of sailing, would she require to sail 24900 miles?

Ans. 116 days 4 hours. 34. Admitting the diameter of the earth to be 8000 miles, and the highest mountain to be 5 miles, what elevation must be made on a globe of 16 inches diameter to represent accurately the height of such mountain?

Ans. of an inch. 35. If $100 in 12 months bring an interest of $7, how much will be the interest of $100 for 8 months?

Ans. $4.663. 36. If the interest of $100 for 12 months is $7, what will be the interest of $75 for the same time?

Ans. $5.25. 37. If in 12 months the interest of $100 is $7, how long must $100 be on interest to gain $10?

Ans. 17 months. 38. If a glacier of 60 miles in length move 50 inches per annum, in what time will it move its whole length? Ans. 76032 years.

39. If a staff of 10 feet in length give a shadow of 15 feet, how high is that tree whose shadow measures 90 feet? Ans. 60 feet.

40. Suppose sound to move 1100 feet in a second; how many miles distant is a cloud, in which lightning is observed 16 seconds before the thunder is heard, no allowance being made for the motion of light? Ans. 3 miles.

41. If it require 30 yards of carpeting which is of a yard wide to cover a floor, how many yards of carpeting which is 14 yards wide, will be necessary to cover the same floor? Ans. 18 yards.

COMPOUND PROPORTION.,

100. When the quantity required depends upon more than three terms, the operation of finding it is called the rule of compound 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, travelling only 6 hours each day, how many miles could he have gone in 15 days, by travelling 10 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 1 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 10 for the second ratio.

Multiplying these two ratios and the odd term together, we get 300 miles 1×10. Cancelling the 6 of the denominator against a part of 300 of the numerator, it becomes 50 miles =441 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 slab, 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 given in pounds; therefore 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 for the first ratio.

The second couplet consists of the widths; and since 4