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60. What is the compound interest of $17.25 for 2 years and 7 months, at 5 per cent.?

Note. From the table take the amount of 1 dollar for two years, at 5 per cent. 2nd compute the interest on it for 7 months, at 5 per cent. as in simple interest; add this to the amount for two years. This will be the amount of 1 dollar for 2 years and 7 months. Multiply this by 17.25; this will be the amount of $17.25 for the time. Then to find the interest, subtract the principal from the amount.

61. What will $73.42 amount to in 4 years, 3 months, and 17 days, at 6 per cent. compound interest?

62. A note was given 13th March, 1815, for $847.25; how much had it amounted to on the 7th November, 1820, at 6 per cent. compound interest?

63. How much would the sum in the last example have amounted to in the same time, at simple interest? 64. What is the compound interest of $1753 for 11+ years, 10 months, and 22 days, at 6 per cent. ?

65. A note was given 11th May, 1813, for $847, rate 6 per cent. compound interest. The following payments were made: 18th February, 1815, $158; 19th of December, 1816, $87; 5th October, 1819, $200. What was due 8th July, 1822?

66. What will 17£. 13s. 6d. amount to in 5 years, 3 months, at 6 per cent. compound interest?

Note. Change the shillings and pence to decimals of a pound, and proceed as in Federal money. Call the unit in the table 1£. instead of 1 dollar.

67. What is the compound interest of $643, for 7 years, 5 months, and 18 days, at 5 per cent.?

68. What is the compound interest of 143£. 7s. 4d. for 19 years, 7 months, at 5 per cent.?

69. A farmer mixed 15 bushels of rye, at 64 cents per bushel; 18 bushels of corn, at 55 cents per bushel; and 21 bushels of oats, at 28 cents per bushel. How many bushels were there of the mixture? What was the whole worth? What was it worth per bushel?

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70. A grocer mixed 123 lbs. of sugar, that was worth 8 cents per lb.; 87 lbs. that was worth 11 cents per lb.; and 15 lbs. that was worth 13 cents per lb.? What was the mixture worth per lb.?

71. A grocer mixed 43 gallons of wine, that was worth $1.25 per gal. with 87 gals. that was worth $1.60 per gal. What was the mixture worth per gal.?

72. With a hhd, of rum, worth $.87 per gal. a grocer mixed 10 gals. of water. What was the mixture worth per gal.?

73. How many gals. of rum, at $.60 per gal. will come to as much, as 43 gals. will come to, at $.75 per gal. ?

74. How much water must be added to a pipe of wine, worth $1.50 per gal. in order to reduce the price to $1.30 per gal.?

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75. A grocer has two kinds of sugar, one at 8 cents per lb., the other at 13 cents. He wishes to mix them together in such a manner, that the mixture may be worth 11 cents per Ib. What will be the proportions of each in the mixture?

Note. The difference of the two kinds is 5 cents. Therefore if a pound of each kind be divided, each into five equal parts, the difference between one part of each will be 1 cent. If lb. be taken from that at 8 cents, and lb. of that at 13 cents be put in its place, the pound will be worth 9 cents. If 3 lb. be taken from it, and as much of the other be put in its place, the pound will be worth 11 cents, as required. The pound then will consist of, at 8 cents, and, at 13 cents. If 5 lbs. be mixed, there will be 2 lbs. at 8, and 3 at 13 cents. The proportions are 2 lbs. at 8, as often as 3 lbs. at

13 cents.

76. A farmer had oats, at 38 cents per bushel, which he wished to mix with corn, at 75 cents per bushel, so that the mixture might be 50 cents per bushel. What were the proportions of the mixture?

Note. The difference in the price of a bushel is 37 cents. The difference between 7 of a bushel of each

is 1 cent. If of a bushel be taken from a bushel of oats, and of a bushel of corn be put in its place, a bushel will be formed worth 50 cents, and consisting of

oats, and corn. The proportions are 12 of oats Errol to 25 of corn. Coon

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It is easy to see that the denominator will always be the difference of the prices of the ingredients, and the difference between the mean and the lesser price will be the numerator for the quantity of the greater, and the difference between the mean and the greater will be the numerator for the quantity of the lesser value. Take away the denominators, and the numerators will express the proportions.

77. A merchant has spices, some at 9d. per lb. some at 1s., some at 2s., and some at 2s. 6d. per lb. How much of each sort must he mix, that he may sell the mixture at 1s. 8d. per lb.?

Note. Take one kind, the price of which is greater, and one, the price of which is less than the mean, and find the proportions as above. Then take the other two and find their proportions in the same way.

Less 9d. 9d.

mean

Greater 2s. 6d. 30d. 20.

11d. diff. between less

and mean.
10d. diff. between

greater and mean.

The proportions are 10 of the less to 11 of the greater.

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The proportions are 4 of the less to 8 of the greater, which is the same as 1 of the less to 2 of the greater. The answer is 10 lbs. at 9d. to 11 lbs. at 2s. 6d., and 1 lb. at 1s. to 2 lbs. at 2s.

Other proportions might be found by comparing the first, and third, and the second and fourth.

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78. A grocer has two sorts of tea, one at 75 cents per lb. and the other, at $1.10 per lb. How must he mix them in order to afford the mixture at $1.00 per lb.?

79. A grocer would mix the following kinds of sugar, viz. at 10 cents, 13 cents, and 16 cents per lb. What quantity of each must he take to make a mixture worth 12 cents per lb. ?.

Note. Those at 13 and 16 must both be compared with that at 10 cents separately.

80. A grocer has rum worth $.75 per gal.; how many parts water must he put in, that he may afford to sell the mixture at $.65 per gal.?

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81. It is required to mix several sorts of rum, at 5s. and 9s. per gal. with water, so that the mixture may be worth 6s. per gal. How much of each sort must the mixture consist of?

di 82. A farmer had 10 bushels of wheat, worth 8s. per mack bushel, which he wished to mix with corn, at 3s. per bushel, so that the mixture might be worth 5s. per bushel. How many bushels of corn must he use ?

Note. Find the proportions for a single bushel as before, then find how much corn must be put with 1 bushel of wheat, and then with 10 bushels. The proportions are 2 of wheat to 3 of corn, consequently 1 of wheat to 11⁄2 of corn, and 10 of wheat to 15 of corn.

83. A farmer would mix 20 bushels of rye, at 65 cents per bushel, with barley at 51 cents, and oats at 30 cents per bushel. How much barley and oats must be mixed with rye, that the mixture may be worth 41 bushel?

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84. A grocer had 43 gallons of wine worth $1.75 per gal., which he wished to mix with another kind worth $1.40 per gal., so that the mixture might be worth $1.60 per gal. How many gals. of the latter kind must he use?

85. Three merchants, A, B, and C, freight a ship with wine. A put on board 500 tons, B 340, and C 94; in a storm they were obliged to cast 150 tons overboard. What loss does each sustain ?

See page 59, Art. XVI., example 158 and following.

86. A father dying, bequeathed an estate of $12000 as follows: to his wife, to his eldest son, to his second son, and to his daughter. It is required to divide the estate in these proportions.

Note. Reduce the fractions to a common denominator, and the numerators will show the proportions.

87. Two men hired a pasture for $37, A put in 3 horses for 4 months, and B 5 horses for 3 months. What ought each to pay?

Note 3 horses for 4 months is the same as 4 times 3 or 12 horses for 1 month; and 5 horses for 3 months, is the same as 3 times 5, or 15 horses for 1 month. The question therefore is the same, as if A had put in 12 horses and B 15. A must pay and B 14, or, reducing the fractions, and .

A put

88. Two men, A and B, traded in company: A in $350 for 8 months, and B $640 for 5 months; they gained $250. What was the share of each?

Note. Make the time equal, as in the last example.

89. Four men jointly hired a pasture for 20 English guineas; A turned in 7 oxen for 13 days, B 9 oxen for 14 days, C 11 oxen for 25 days, and D 15 oxen for 37 days. How much ought each to pay

?

90. A family of 10 persons took a large house for of a year, for which they were to pay $500, for that time. At the end of 14 weeks, they took in 4 new lodgers; and after 3 weeks, 4 more; and so on for every 3 weeks, during the term, they took in 4 more lodgers. What must one of each class pay per week of the rent?

91. Three men enter into partnership and trade as follows: A put in 150£, and at the end of 7 months took out 50£.; 5 months after he put in 170£ ;—B put in 205£., and at the end of 5 months, 110£. more, but took out 150£. 4 months after;-C put in 300 guineas, at 28s. each, and when 8 months had elapsed, he drew out 150£., but 5 months after he put in 500£. Their partnership continued 18 months, at the end of

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