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39. An importer sold cloth to a wholesale dealer, and gained 10 per cent of what it cost him. The wholesale dealer sold it to a retail dealer at an advance of 10 per cent on what it cost him. The retail dealer sold it at an advance of 20 per cent on what it cost him. Now, allowing that the retail dealer received $726 for the cloth, how much did it cost the importer?

40. What must be the diameter of a globe which contains 27 times as many cubic inches as a globe 2 inches in diameter ?

41. A man spent and of his money, and then earned $36, when he had $88 more than of what he had at first. How much money

had he at first?

42. George says that if he should earn as much more money as he now has, as much more, and 371⁄2 dollars, he should have $555. How much money has he?

43. Four men bought a grindstone 4 feet in diameter, paying equal sums, and they agreed that the first should grind off his share, then the second, and so on to the last. What was the thickness of the portion ground off by each?

44. June 1, 1852, I bought for cash 500 casks of oil, each cask containing 42 gallons, at $1.10 per gallon. Oct. 1, 1852, I sold it on 3 months' credit, at a price per gallon equal to 125 per cent of its cost per gallon, deducting 5 per cent of the whole quantity of oil for leakage. I immediately got the note received for the oil discounted at a bank. Allowing that I paid 10 cents per cask for truckage, and $25 for storage and other expenses, and that money was worth 6 per cent per year, did I gain or lose, and how many dollars?

45. A, B, and C trade in company, and gain $100, of which A has $12.50, B has $25, and C has $62.50. C put in $21 more of the original stock than A and B together. What was the original stock?

46. Reuben Aldrich and George Guild bought cloth together, Aldrich paying $6 more than of its cost. They sold the cloth at such rate that Aldrich's share was $39, and Guild's share was $36. What did the cloth cost?

Charles

47. Charles, John, and James were talking of their money. has 50 dollars. James says that if Charles should give him his money, he should have twice as much as John; and John says that if Charles should give him his money, he should have three times as much as James. How much has each ?

48. A speculator borrowed $2000, agreeing to pay interest at the rate of 9 per cent per year, and invested the money in land at $80 per acre. 3 mo. afterwards he sold the land for $900, and the rest at $100 per acre, and expended the proceeds for flour. 2 mo. 15 da. afterwards he sold of the flour for $600, and the remainder for what

he paid for the whole, and immediately paid the amount of the bor rowed money. How much was his gain?

49. If of 12 were 6, what, in the same ratio, would of 50 be?

50. I own a square lot of land measuring 10 rods on a side. How deep a ditch 6 feet wide must I dig around it within its limits to raise its surface 1 foot?

51. A merchant sold a lot of flour at $8.40 per barrel, and thereby gained 20 per cent. He afterwards sold another lot of the same flour

for $203, and thereby gained 16 per cent.

in the last lot?

How many barrels were there

52. What must be the diameter of a sphere to contain as many cubic inches as a cone 1 foot high and having a base of 1 foot in diameter ?

53. Mr. Hicks invested a certain sum in flour, and Mr. Gardiner invested twice as much. It turned out that Mr. Hicks lost 10 per cent, and Mr. Gardiner gained 10 per cent, and that the difference between what Mr. Hicks received for his lot and what Mr. Gardiner received for his was $260. How much did each invest?

54. Jan. 1, 1852, I borrowed $954, agreeing to pay interest at the rate of 5 per cent, and immediately expended it for cloth at $3 per yard. Four days afterwards I sold the cloth at $3.50 per yard, to be paid June 17, 1852. On receipt of the money, I immediately expended it for cloth at $1 per yard. July 1, 1852, I sold the cloth at $1.12 per yard, payable Sept. 22, 1852. As soon as this debt was paid, I put the money on interest at 6 per cent. Jan. 1, 1853, I collected the amount due me, and paid that which I owed. How much had I gained by the transactions ?

55. Wishing to find the distance between two trees, which cannot be directly measured on account of a swamp, I measure due east 80 yards from the foot of one of them; then turning south, I measure 100 yards, when I find that I am just 40 yards to the east of the other How far apart are the trees?

tree.

56. The eaves of a house are at the same height, and 30 feet apart. The ridge pole is 12 feet higher than the eaves, and just midway be tween them. The house is 40 feet long. How many shingles will it take to cover the roof, if each shingle covers a space 6 inches long and 4 inches broad?

57. Multiply any number by 4, add 6, divide by 2, add 7, divide by 2, subtract 5, add twice the original number, divide by the original numher, subtract 1, multiply by the original number, add 3, multiply by 3, add 11, divide by 2, and the result will always be 10 more than 3 times the original number. Why is this? 58. A man spent he had left, and

of his money and a dollar more; then of what of a dollar more; then of what he had left, and

of a dollar more, when he had just 7 dollars. How much money had he at first?

59. A rectangular box is 3 times as long as it is wide, and twice as wide as it is high, and contains 96 cubic feet. How many square feet are there in its surface?

60. Obtained at a bank, on my note payable in 3 months, money enough to buy 20 acres of land at $100 per acre. One month afterwards I sold the land, receiving in payment a note on demand, wi. interest at 6 per cent per year. I collected the amount of this note the day my note became due at the bank, and found that it took pay the latter. For how much per acre did I sell the land ?

of it to

61. Obtained at a bank, on my note payable in 5 months, money enough to buy 20 acres of land at $100 per acre, and at the same time hired of a friend money enough to buy another lot of the same size and price as the first, giving in payment my note payable on demand, with interest at 6 per cent per year. When the note at the bank became due, I sold both lots for cash at the same price per acre, and found that the money received for 16 acres of it was sufficient to pay my note at the bank. How much did I gain by the transactions? How much more on the second lot than on the first?

62. Bernard Farwell and Francis Dana traded in company. Farwell's stock was $860, and Dana's $420. On dividing their profits, they found that Farwell's share was $4 more than twice Dana's. How many dollars did each gain?

63. A commission merchant received on consignment 100 bags of corn from A, 150 bags from B, and 75 bags from C, and putting them all into 1 lot sold them for $400. Now, allowing that A's lot is 10 per cent better than B's, and 15 per cent better than C's, what is the just share of each ?

64. Is the reasoning process contained in the following solution true or false? If false, in what does its fallacy consist?

Question. What is the effect of adding 3 to both numerator and denominator of a fraction?

Solution. Since adding 3 to both numerator and denominator of a fraction gives for a result a fraction which expresses 3 more parts than the former, but of such kind that it will take 3 more of them to equal a unit, the addition has both increased and diminished the fraction, and has therefore not altered its value.

65. Show the fallacy, if any, in the following solution:

If the numerator of a fraction is 4 greater than its denominator, what will be the effect of adding the same number to both numerator and denominator?

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nator of a fraction will not affect the difference between them. Hence, the resulting fraction in the case supposed must, like the original one, express 4 more fractional parts than it takes to equal a unit. Therefore, the resulting fraction equals the original one, and the supposed addition has not affected the value of the fraction.

66. Two men, A and B, hired a horse and carriage for $7, to go from Providence to Boston and back, the distance between the cities being 42 miles. At Attleboro', 12 miles from Providence, they took in C, agreeing to take him to Boston and back to Attleboro' for his proportionate share of the expense. At Walpole, 24 miles from Providence, they took in D, agreeing to take him to Boston and back to Walpole for his proportionate share of the expense. What ought each person to pay?

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NOTE. Arithmeticians do not agree as to the correct solution of such examples as the above; some contending that each person should pay in exact proportion to the number of miles he rode, and others that A and B should each pay the expense of the ride from Providence to Attleboro', the expense of the ride from Attleboro' to Walpole, and the expense of the ride from Walpole to Boston; that C should pay the expense of the ride from Attleboro' to Walpole, and the expense of the ride from Walpole to Boston; and that D should pay only of the expense of the ride from Walpole to Boston. Which is the just principle?

67. I sold of a lot of land for 20 per cent more than it cost, and the remainder for 20 per cent less than it cost. What per cent did I gain on the whole ?

68. I sold of a cask of wine for $36, which was 25 per cent more than the part sold cost. I then sold the remainder at an advance of 20 per cent on its cost. What per cent of the cost of the cask did I gain?

69. I sent to my agent in Boston a lot of flour, which he sold for $6075, charging a commission of 2 per cent on the sales. He invested the remainder, after deducting his commission of 14 per cent on the purchase, in cloths, which he shipped to my agent in Savannah. The latter sold them at an advance of 25 per cent on the cost, charging a commission of 5 per cent on the sales, and invested the balance, after deducting a commission of 2 per cent on the purchase, in cotton. The cotton was shipped to my agent in Boston, who sold it at an advance of 20 per cent on its cost, charging a commission of 13 per cent. Allowing that the expenses of freight, insurance, &c., were $1000, what was my gain?

70. A traveller had to pass three toll gates. At the first gate he paid 5 cents less than half the money he had; at the second he paid 2 cents less than half of what he had left; and at the third he paid 1 cent more

than half of what he then had, after which he had only 4 cents left. How much money did he have at first?

71. Lyman Richards and John Dexter traded in company, Richards paying in $9 less than of the whole stock. They gained $200, of which Richard's share was $117. What was the original stock of each?

72. A farmer had his sheep in three pastures. In the first pasture there were twice as many as in the second, and in the second twice as many as in the third. 40 jumped out of the first pasture into the second, and 32 jumped from the second into the third, when the number of sheep in each pasture was equal. How many were originally in each pasture?

73. A water tub holds 73 gallons. The pipe which conveys water to it admits 7 gallons in 5 minutes, and the tap discharges 20 gallons in 17 minutes. Now, suppose that both being carelessly left open, the water is turned on at 4 o'clock, and a servant discovers it at 6, and puts in the tap, at what time will the tub be full ? *

74. A gentleman has two horses, and a carriage worth £100. Now, if the first horse be harnessed in the carriage, he and the carriage together will be worth three times as much as the second horse; but if the second horse be harnessed, he and the carriage will together be worth 7 times as much as the first. What is the value of each horse ? * 75. There is a fish whose head is 10 feet long; his tail is as long as his head and half of his body, and his body is as long as his head and tail together. What is the whole length of the fish? *

76. "If 12 oxen will eat 3 acres of grass in 4 weeks, with all that grows during that time, and 21 oxen eat 10 acres in 9 weeks, with all that grows during that time, how many oxen would eat 24 acres, with the growth, in 18 weeks, the grass all the while growing uniformly?"

77. Jan. 1, 1851, my agent in Buffalo bought for me 1000 barrels of flour at $4 per barrel, for which he charged a commission of 1 per cent. On the 3d of January, I sent him cash to pay for the flour and his commission. It cost me $1 per barrel to have the flour transported to Boston, and I incurred other expenses upon it to the amount of $20. Feb. 1, 1851, I sold the flour to J. Smith & Co., at an advance of 25 per cent on its entire cost, receiving in payment half cash, and their note payable in 6 months for the remainder. I had their note discounted at a bank; but before it became due they failed, so that when it became due, I, as indorser, was obliged to pay it. Jan. 1, 1852, I settled with J. Smith & Co., receiving 50 cents on each dollar they owed me. Allowing that money was worth 6 per cent per year, and that I paid the freight and other expenses of the flour on the 15th of January, what was the amount of my loss?

From Fike's Arithmetic, edition of 1788.

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