B. Fellowship. ANALYSIS. 203. 1. Two men, A and B, trade in company; A puts in $100, and B 8200, and they gain $30. What is each man's share of the gain? Each man's gain must evidently have the same relation to the whole gain, that the money which he puts in, has to the whole amount put in. In other words, the whole amount put in, will be to the whole gain as each man's share of the amount put in, is to his share of the gain, i. e. $300: $30 :: $100 : $10 A's share. $200 $20 B's share. Ans. 204. 2. A and B hired a pasture for 12 dollars; A put in 3 cows for 8 weeks, and B put in 4 cows for 9 weeks; what part of the rent ought each to ? Three cows 8 weeks are equal to 1 cow (3X8) 24 weeks, and 4 cows 9 weeks are equal to 1 cow (4×9) 36 weeks; their shares, then, of the pasturage are 24 weeks and 36 weeks, equal to 60 weeks' pasturage. Then, as the whole pasturage is to the whole rent, so is each man's share of the pasturage to his share of the rent; that is, 60 w. : $12 :: (3X8-24w.: $4.30 A's share. Ans. 4×9—36w.: $7.20 B's share. To prove the correctness of the work, we add together the shares, and find them to amount to (4.80+7.20=) $12, the whole rent (54). DEFINITIONS. 205. Money, or property employed in trade, is called capital, or stock,-gain to be divided, the dividend. Fellowship is a general rule, by which merchants, or others, trading in company with a joint stock, compute each person's particular share of the gain or loss. RULE. 206. When the stocks are employed for equal times, say: As the whole stock: is to the whole gain or loss:: so is each man's share of the stock to his share of the gain or loss (203). When the times are unequal, multiply each man's stock by the time of its continuance in trade; then say, As the sum of the products is to the whole gain, or loss :: so is each man's product to his share of the gain, or loss (204). 160 proof. 7. A person dying, bequeathed his estate to his 3 sons; to the eldest he gave $560, to the next $500 and to the other $450; but when his debts were paid, there were $950 left; what was each son's share? $352.317+1st.) 8. Two merchants entered into partnership for 18 months. A at first put in £100, and at the end of 8 months put in £50 more; B at first put in £275, and at the end of four . months took out £70; at the 4. Alligation. ANALYSIS. 207. 1. If I mix 6 quarts of currants, which are worth 8 cents a quart, with 2 quarts worth 12 cents a quart, what will a quart of the mixture be worth? (60) Six quarts at 8 cents are worth (8×6=) 48 cents, and 2 quarts at 12 cents are worth (12×2=) 24 cents; then 48+24-72 cents, the worth of B. Fellowship. ANALYSIS. 203. 1. Two men, A and B, trade in company; A puts in $100, and B 8200, and they gain $30. What is each man's share of the gain? Each man's gain must evidently have the same relation to the whole gain, that the money which he puts in, has to the whole amount put in. In other words, the whole amount put in, will be to the whole gain as each man's share of the amount put in, is to his share of the gain, i. e. $300: $30 :: $100. $10 A's share. Ans. $200 : $20 B's share. 204. 2. A and B hired a pasture for 12 dollars; A put in 3 cows for 8 weeks, and B put in 4 cows for 9 weeks; what part of the rent ought each to pay? Three cows 8 weeks are equal to 1 cow (3X8=) 24 weeks, and 4 cows 9 weeks are equal to 1 cow (4×9) 36 weeks; their shares, then, of the pasturage are 24 weeks and 36 weeks, equal to 60 weeks' pasturage. Then, as the whole pasturage is to the whole rent, so is each man's share of the pasturage to his share of the rent; that is, 60 w. : $12 :: Ans. (3X8-24w.: $4.80 A's share. (4X9-36w.: $7.20 B's share. S To prove the correctness of the work, we add together the shares, and find them to amount to (4.80+7.20) $12, the whole rent (54). DEFINITIONS. : RULE. 206. When the stocks are employed for equal times, say: As the whole stock: is to the whole gain or loss:: so is each man's share of the stock to his share of the gain or loss (203). When the times are unequal, multiply each man's stock by the time of its continuance in trade; then say, As the sum of the products is to the whole gain, or loss: so is each man's product to his share of the gain, or loss (204). 207. 1. If I mix 6 quarts of currants, which are worth 8 cents a quart, with 2 quarts worth 12 cents a quart, what will a quart of the mixture be worth? (60) Six quarts at 8 cents are worth (8×6=) 48 cents, and 2 quarts at 12 eents are worth (12×2=) 24 cents; then 48+24-72 cents, the worth of the whole mixture, and 72-8 (6+2, the whole mixture) 9 cents, the worth of 1 quart of the mixture. When the prices and quantities of the simples are given, and it is required to find the price of a given quantity of the mixture, as in the preceding example, it is called ALLIGATION MEDIAL. RULE. 208. Multiply each quantity by its price, and divide the sum of the products by the sum of the quantities, the quotient will be the rate of the compound required. QUESTIONS FOR PRACTICE. lons of wine at 4s. 10d. a gal- 4. If 5lb. of tea at 6s. per lb., 8lb. at 5s., and 4lb. at 4s. 6d., be mixed together, what is a pound of the mixture worth? Ans. 5s. 2d. 5. A goldsmith melted together 10 oz. of gold 20 carats fine, 8 oz. 22 carats fine, and 1 lb. 8 oz. 21 carats fine; what the fineness of the mixture? Ans. 2018 carats fine. ALLIGATION ALTERNATE. ` 209. When the prices of the simples, and also the price, or rate of the mixture, are given, the method of finding the proportion, or quantities of the several simples, is called Alligation Alternate. 1. A person has tea worth 40 cents a pound, which he wishes to mix with tea worth 60 cents a pound, in such manner that the mixture shall be worth 50 cents a pound; in what proportion must it be mixed? Ans. Equal quantities of each; for the price of one kind exceeds the mean just as much as the price of the other falls short of it, the difference between the given rate and the mean being 5 in each case. 2. In what proportion must I mix currants worth 9 cents a pound, with currants worth 12 cents a pound, in order that the mixture may be worth 10 cents a pound? Here a pound at 9 cents falls one cent short of the mean, and a pound at 12 cents exceeds the mean 2 cents; hence, 2 lb. at 9 cents will fall short of the mean by the same quantity that one lb. at 12 cents exceeds it; we must therefore take twice as many of the 9 cent currants as we do of those worth 12 cents, in order that the mixture may be worth 10 cents. |