manner in which questions may be prepared, whose answers shall be free from fractions. 40. Three men, A, B and C, trade in company, and gain $1350. Now, if A put into the joint stock $7 as often as B put in $6, and B put in $6 as often as C put in $5, what is each man's share of the gain? x Therefore, ≈ +*+5 = 1350, by the question, 6 x 7 or 7 x + 6 x + 5 x = 9450, by multiplication. ANS. A, $525; B, $450; C, $375. To generalize this question, we will suppose A put in a dollars as often as B put in b dollars; and that B put in b dollars as often as C put in c dollars; that is, we will use the letters a, b, c, instead of the numbers 7, 6, 5. Let the amount gained be represented by g. a x + bx + c xa g, by multiplication, That is, To find each man's share of the gain, we must multiply the whole gain by his share of the stock, and divide the product by the whole stock. If there has been a loss, instead of a gain, each man's share of the loss can be ascertained in a similar manner. This is a general rule for Fellowship, when all the stock has been employed the same time. 11. Divide 8736 dollars among three men in such a manner, that their shares shall be to each other as the numbers 3, 4 and 5, respectively. 42. Two traders, A and B, found that they had gained, at the end of the year, 3792 dollars. A having put $5000 and B $7000 into the joint stock, what is each man's share of the gain? 43. Three merchants, A, B and C, made up a joint voyage, by which they lost 2595 dollars. A furnished $300 of the capital, as often as B furnished $500, and C, $700. What is the loss of each? 44. The premium on a policy of insurance is $513, which is to be divided between three underwriters. A took 3 shares of the risk, B 7 shares, and C 9 shares. What part of the premium belongs to each? 45. Three merchants, A, B and C, traded in company, and gained $8840. They severally contributed to the joint stock, in the proportion of 5, 6 and 7; and A's money was used 4 months; B's, 3 months, and C's, 2 months. What part of the gain belongs to each? Now, as A furnished x dollars for 4 months, he furnished what was equal to 4 x dollars for one month. 6 x And B's dollars for 3 months = dollars for one 5 18x month; and C's 7 dollars for 2 months = 14* dol Therefore, 4 x = A's share of the gain, 5 18x = B's share, =C's share. =8840, by the question. 5 + 14 x 20 x + 18x + 14 x 44200, or 52 x = 44200, and x 850. Then 4 x 3400, A's share of the gain, Let us now suppose that the sum gained was s dol lars; that A put in a dollars; B, b dollars; and C, c dollars; and that A's money was in h months; B's, m months; and C's, n months. Let x A's share of the stock. Now, if we multiply each man's stock by its time, a h x + b m x + c n x = a s, by multiplication, or (a h + b m + c n) x = a s, Having found the value of x, we obtain the formulas for the shares of A, B and C, by substitution. For instance, A's share of the gain being. h x, we multiply the value of x by h, and obtain Ꮖ and so with the others. ahs a h + bm + c n Hence, to find the share of either of the copart ners, Multiply the sum to be divided by the product of his share of the stock and the time it was used, for a dividend. Multiply the several shares by their respective times, and divide the dividend by the sum of their products. 46. Three men, A, B and C, traded in company, and gained 2160 dollars. A put in $400 for 5 months; B, $500 for 2 months; and C, $600 for 4 months. What is each man's share of the gain? 47. Three men, A, B and C, hired a pasture in common, for 82 dollars. A put in 3 horses for 4 months; B, 4 horses for 2 months; and C, 7 horses for three months. How much must each man pay? 48. Two merchants, A and B, engaged in a speculation, by which they gained 2100 dollars. The capital employed was $14000, of which A furnished $5000, and B, $9000; but A's money was used a year, whereas B's was used only 5 months. Required the gain of each. 49. A farmer would mix corn at a shillings per bushel with oats at b shillings per bushel, so that a bushel of the mixture may be worth c shillings. How many bushels of each sort must he take, to make a composition of n bushels? Let Then n Also, ax the bushels of corn. x the bushels of oats. the value of the corn, bn. b x = the value of the oats, and cn the value of the mixture. Then a x+bnbx cn, by the question. |