Elements of Algebra

CHAP. III. OF ALGEBRA. 321 QUESTIONS FOR PRACTICE. 1. Given $24x = 13y + 16$, to find $x$ and $y$ in whole numbers. Ans. $x = 5$, and $y = 8$. 2. Given $87x + 256y = 15410$, to find the least value of $x$, and the greatest of $y$, in whole positive numbers. Ans. $x = 30$, and $y = 12800$. 3. What is the number of all the possible values of $x, y$, and $z$, in whole numbers, in the equation $5x + 7y + 11z = 224$? Ans. 60. 4. How many old guineas at 21s. 6d.; and pistoles at 17s. will pay 100l.? and in how many ways can it be done? Ans. Three different ways; that is, 19, 62, 105 pistoles, and 78, 44, 10 guineas. 5. A man bought 20 birds for 20 pence; consisting of geese at 4 pence, quails at $\frac{1}{2}$d. and larks at $\frac{1}{4}$d. each; how many had he of each? Ans. Three geese, 15 quails, and 2 larks. 6. A, B, and C, and their wives P, Q, and R, went to market to buy hogs; each man and woman bought as many hogs, as they gave shillings for each; A bought 25 hogs more than Q, and B bought 11 more than P. Also each man laid out three guineas more than his wife. Which two persons were, respectively, man and wife? Ans. B and Q, C and P, A and R. 7. To determine whether it be possible to pay 100l. in guineas and moidores only? Ans. It is not possible. 8. I owe my friend a shilling, and have nothing about me but guineas, and he has nothing but louis d'ors, valued at 17s. each; how must I acquit myself of the debt? Ans. I must pay him 13 guineas, and he must give me 16 louis d'ors. 9. In how many ways is it possible to pay 1000l. with crowns, guineas, and moidores only? Ans. 70734. 10. To find the least whole number, which being divided by the nine whole digits respectively, shall leave no remainders. Ans. 2520. Y