its place, the pound will be worth 11 cents, as required. The pound then will consist of, at 8 cents, and 3, at 13 cents. If 5 lb. be mixed, there will be 2 lb. at 8, and 3 at 13 cents. The proportions are 2 lb. at 8 as often as 3 lb. 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 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 12 corn, and 24 oats. The proportions are 12 of oats to 25 of corn. It is easy to see that the denominator will always be the difference of the prices of the ingredients, und the difference between the mean and the less 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 less 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. The proportions are 10 of the less to 11 of the greater. The proportions are 4 of the less to 8 of the greater, which is the same as I of the less to 2 of the greater. The answer is 10 lb. at 9d. to 11 lb. at 2s. 6d., and 1 lb. at 1s. to 2 lb. at 2s. Other proportions might be found by comparing the first, and third, and the second and fourth. 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 $8.75 per gal.; how many parts water must he put in, that he may afford to sell the mixture at $.65 per gal. ? 81. It is required to mix several sorts of rum, at 5s. 7d., 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? 82. A farmer had 10 bushels of wheat, worth Ss. per 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 14 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 cents per bushel? 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 Part 1. 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. must pay and B1, or, reducing the fractions, and §. A 88. Two men, A and B, traded in company: A put 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 1⁄2 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 which time they had gained 450€ Required each person's share of the gain. ་ 92. The last five are examples of compound or double fellowship. What rule can you make for it? 93. In how long time will 1 dollar gain as much interest as $15 will gain in 1 month? 94. In how long time will 1 dollar gain as much interest as 8 dollars will gain in 3 months? 95. In how long time will 1 dollar gain as much interest as 24 dollars will gain in 5 months? 96. In how long time will 1 dollar gain as much interest as $158 will gain in 11 months? 97. In how long time will 3 dollars gain as much interest as 1 dollar will gain in 24 months? 98. In how long time will 28 dollars gain as much interest as 1 dollar will gain in 157 months? 99. A lent B 8 dollars for 2 months, afterwards B lent A 1 dollar; how long ought he to keep it to satisfy him for the former favour? 100. Clent D 1 dollar for 15 months; afterwards D lent C 5 dollars; how long ought he to keep it to satisfy him for the former favour? 101. A borrowed of B 17 dollars for 11 months, promising him a like kindness; afterwards B lent A 25 dollars. How long ought he to keep it? Note. Find how long he ought to keep 1 dollar, and then how long he ought to keep 25 dollars. 102. I lent a friend 257 dollars, which he kept 15 months, promising to do me a like kindness, but he was not able to let me have more than 100 dollars; how long ought I to keep it ? 103. A owes B notes to be paid as follows: 7 dollars to be paid in 3 months, and 5 dollars to be paid in 8 months; but he wishes to pay the whole at once. In what time ought he to pay it? Note. 7 dollars for 3 months is the same as 1 dollar for 21 months; and 5 dollars for 8 months is the same as 1 dollar for 40 months. 40+21=61, and 7+5=12. He might have 1 dollar 61 months; the question now is how long he may keep 12 dollars. It is evident he might keep it of 61 months. 104. Cowes D $380, to be paid as follows; $100 in 6 months; $120 in 7 months; and $160 in 10 months. He wishes to pay the whole at once. he to pay it? In how long a time ought 105. A merchant has due to him 300£. to be paid as follows; 50€. in 2 months; 100£ in 5 months; and the rest in 8 months. It is agreed to make one payment of the whole. In what time ought he to receive it? 106. Fowes H $1000, of which $200 is to be paid present, $400 in 5 months, and the rest in 15 months. They agree to make one payment of the whole. Required the time? 107. A merchant has due a certain sum of money, of which is to be paid in 2 months, in 3 months, and the rest in 6 months. In what time ought he to receive the whole ? 108. A merchant has three notes due to him as follows: one of $300 due in 2 months.; one of $250 due in 5 months; and one of $180 due 3 months ago; the whole of which he wishes to receive now. What ought he to receive, allowing 6 per cent. interest ? Note. First find the equated time, and then the interest or discount for present payment, as shall be found necessary. $300 for 2 months 1 dol. for 600 months. 1850 The two notes not yet due are the same as I dollar for 1850 months. But he has had $180 3 months after it was due, which is the same as 1 dollar for 540 months. This must be taken out of the other, and there will remain 1 dollar for 1310 months. If he can have 1 dollar for 1310 months, how long can he have $730? 131,0 (73,0 73 580 584 1.8 nearly 1 month and 24 days. As it is not due until 1 month and 24 days after this time, it must be discounted for that time. See Part 1. Art. XXIV., example 130 and following. 6 per cent for 1 year is 9 10 per cent. or .009 for 1 month and 24 days. The fraction then is 1009. $730 is 188% of what? 1000 1009 |