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by this ratio, we have in fee: x*x ###. 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 o' feet x #39 × # =4; #9 –56+44 feet, for the answer. 20. If 34 pounds of coffee cost 24 shillings, how much will 10+ pounds cost 7 In this example, 2+=# shillings must be our third term; and since 10+="4 pounds must cost more than 3}=4 pounds, we must divide "4 by 3 for the ratio; making it *x #. Multiplying the third term by this ratio, we obtain # shillings x*x #; which, after cancelling, becomes # of a shilling x *="# shillings=7# shillings. 21. Gave $72 for 11 barrels of fish. How much will

88 barrels cost at the same rate 7 Ans. $576. , 22. If 434 pounds of cheese cost $220, what will 216# pounds cost at the same rate 7 Ans. $11.

23. If I pay $390 for sawing 7 cords of wood, how much ought I to give for sawing 234 cords ' Ans. $13. 24. If so, of a ship is worth $2853, what is the whole worth 7 The ratio of the whole ship, or {}, to so, is 19. Hence, $2853 × 19 = $951 × 10–$95.10 Ans. 25. If I's of my income is $533, what is my whole income? Ans. $1732-25. 26. A person failing in business, finds that he owes $7560, and that he only has $3100 to pay it with. How much can he pay to that creditor whose claim is $756? Ans. $310. 27. If it require 54 bushels of wheat to make one barrel of flour, how many bushels will it require for 100 barrels of flour ! A n.s. 550 hushels.

28. If 7 barrels of flour are sufficient for a family 6 months, how many barrels will they require for 11 months 7 Ans. 12# barrels. 29. If it take 25 yards of carpeting, a yard wide, to cover a certain floor, how many yards of # carpeting would be necessary to cover the same floor 7 Ans. 334 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 7 Ans. $42.85%. 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. 9% inches. 34. If 8 men can mow a field in 5 days, in how many days can 5 men do the same 2 Ans. 8 days. 35. If 274 yards of cloth cost $60, how many yards can I buy for $100? Ans. 45+ yards. 36. If 273 yards of cloth cost $60, what will 45+ yards cost 7 Ans. $100.

37. If { of a ship is worth $9000, what is her whole value 2 The whole ship being a unit, or #, we have the ratio #; hence, the answer is $9000 × #=$14400. 38. If so, of a city lot is sold for $500, what would or of the same lot sell for at the same rate 2 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. 68104r;#r miles. 40. The equatorial portions, by the diurnal rotation of the earth, moves about 24900 miles each day ? How far is that in each hour? Ans. 1037, miles. 41. 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 one second 7 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 7 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 2 Ans. 116 days 44 hours. 45. Admitting the diameter of the earth to be 8000 milés, 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 2 Ans. $4.663. 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.

48. If in 12 months the interest of $100 is $7, how long must $100 be on interest to gain $10% Ans. 174 months. 49. 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. 50. If a staff of 10 feet in length give a shadow of 15 feet, how high is that tree whose shadow measures 90 feet 7 Ans. 60 feet. 51. 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. 34 miles. 52. 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 7 Ans. 18 yards. 53. If the earth move through 12 signs, or 360° in 365+ days, how far will she move in a lunar month of 294 days? Ans. 29%r degrees. 54. Suppose a steamboat capable of making 15 miles each hour, to move with a current whose velocity is 24 miles per hour, what will be the whole distance made during 134 hours ? And what distance will the boat move in the same time against the same current 7 Ans. } With the current, 2364 miles. Against the “ 1683 4 55. If the magnetic influence move through the telegraphic wires at the rate of 200000 miles in one second of time, how many times could it pass around the world in one second, allowing the circumference of the earth to be 24899 miles' Ans. 8.3% of times.

56. If A can do a piece of work in 7 days, and B can do it in 8 days, what part of it can both do in 34 days? Ans. }#} of it. 57. A reservcir, whose capacity is 1000 hogsheads, has a supply pipe by means of which it receives 300 gallons each hour; it also has two discharging pipes, the first of which discharges # of a gallon each minute, the second discharges 14 gallons per minute. The reservoir being empty, in what time will it be filled if the supply pipe alone is opened? In what time, if the supply pipe and the first discharging pipe are opened? In what time, if the supply pipe and the second discharging pipe? And in what time, if all three are opened? Supply pipe only opened, 210 hours= 83 days.

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110. When the quantity required depends upon more than three terms, the operation of finding it is called the Rule of Compound Proportion.

Suppose we have the following example:

If 6 men can mow 30 acres of grass in 5 days, by working 8 hours each day, how many acres can 4 men mow in 9 days of 10 hours each

Had the number of days, as well as hours in each day, been the same in both cases, the question would have been equivalent to the following:

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