Again, dividing 12 of numerator and 2 of denominator

From these two examples, we see that the Rule of Three may be given in the following simple form:

RULE OF THREE.

Of the three quantities which are given, one will always be of the same kind as the answer sought; this quantity will be the third term. Then, if by the nature of the question, the answer is required to be greater than the third term, divide the greater of the two remaining quantities by the less, for a ratio; but if the answer is required to be less than the third term, then divide the less of the two remaining quantities by the greater, for a ratio. Having obtained the ratio, multiply the third term by it, and it will give the answer in the same denomination as is the third term.

NOTE.-Before obtaining the ratio, by means of the first two terms, we must reduce them to like denominations.

17. If 200 sheep yield 650 pounds of wool, how many pounds will 825 sheep yield?

In this example, the answer is required to be in pounds; we therefore take 650 pounds for the third term. The ratio of 825 sheep to 200 sheep is 25. Hence we have

13. If ¦ of a pound of sugar cost of a snilling, how much will of a pound cost?

23

In this example, our third term is of a shilling. And sinc. of a pound is less than 1, we must obtain our ratio by dividing by, which gives×+ Multiplying the third term by this ratio, we have 23 of a shilling. To reduce this with the least labor, we must resort to the method of cancelling. Thus, cancelling the 23, which occurs in both numerator and denomi nator, also 13 of the numerator against a corresponding factor of the 26 of the denominator, our expression will become of a shilling ×× 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

19. If a tree 38 feet 9 inches in height, give a shadow of 49 feet 2 inches, how high is that tree 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 feet, by 49 feet 2 inches 494 feet=25 feet: which thus becomes 52 X. Multiplying the third term

by this ratio, we have 155 feet 852×

Cancelling 6 of the numerator against 6, a factor of the 12 of the denominator, also cancelling 5, a factor of 155 of the numerator, against 5, a factor of 295 of the denominator, we get 2 feet 852×5=2662256197 feet, for the answer. 20. If 3 pounds of coffee cost 24 shillings, how much will 10 pounds cost?

In this example, 233 shillings must be our third term; and since 10 pounds must cost more than 34= pounds, we must divide by for the ratio; making it 1. Multiplying the third term by this ratio, we obtain shillings x; which, after cancelling, becomes of a shilling X-61 shillings=63 shillings.

1. Gave $72 for 11 barrels of fish. How much will 88 barrels cost at the same rate? Ans. $576. 22. If 43 pounds of cheese cost $2.20, what will 216 pounds cost at the same rate? Ans. $11. 23. If I pay $3.90 for sawing 7 cords of wood, how much ought I to give for sawing 231 cords? Ans. $13. 24. If of a ship is worth $2853, what is the whole worth?

The ratio of the whole ship, or 18, to, is 10. Hence, $2853 x8951 x 10-89510 Ans. 25. If of my income is $533, what is my whole income? Ans. $1732.25.

3

26. A person failing in business, finds that he owes $7560, and that he only has $3100 to pay it with. How much car he pay to that creditor whose claim is $756? Ans. $310.

27. If it require 51 bushels of wheat to make one barrel of flour, how many bushels will it require for 100 barrels of flour? Ans. 550 bushels.

28. If 7 barrels of flour are sufficient for a family 6 months, how many barrels will they require for 11 months? Ans. 12 barrels.

29. If it take 25 yards of carpeting, a yard wide, to cover a certain floor, how many yards of 4 carpeting would be necessary to cover the same floor? Ans. 331 yards. 30. If a person travel 8 miles in 10 hours, how far will he travel in 5 days, by traveling 8 hours each day? Ans. 32 miles.

31. If 35 pounds, of feathers cost $15, what will 100 pounds cost at the same rate? Ans. $42.855. 32. 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.

33. 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. 34. If 8 men can mow a field in 5 days, in how many days can 5 men do the same? Ans. 8 days. 35. If 27 yards of cloth cost $60, how many yards can I buy for $100? Ans. 454 yards. 36. If 27 yards of cloth cost $60, what will 455 yards cost? Ans. $100.

37. 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 x=$14400.

38. If of a city lot is sold for $500, what would of the same lot sell for at the same rate? Ans. $11663. 39. 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. 68104

miles. 40. The equatorial portions, by the diurnal rotation of the earth, moves about 24900 miles each day? How fat is that in each hour? Ans. 1037 miles.

41. If it require 10 years of 3654 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 one second? Ans. 60590592000000 miles. 42. If by a leak of a ship enough water run in, in 4 hours, to sink her, how long can she survive?

Ans. 6hr. 40m. 43. If I pay $25 for the masonry of 4000 bricks, how much ought I to pay for the work which requires 100000 bricks? Ans. $625.

44. 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 44 hours. 45. Admitting the diameter of the earth to be 8000 miles, and the highest mountain to be 5 miles, what elevation must be made on the globe of 16 inches diameter to represent accurately the height of such mountain? Ans. To of an inch. 46. If $100 in 12 months bring an interest of $7, how much will be the interest of $100 for 8 months?

Ans. $4.66%.

47. If the interest of $100 for 12 months is $7, what

will be the interest of $75 for the same time?

Ans. $5.25