Elements of Algebra

204 ELEMENTS SECT. IV. 2. A person being asked what his age was, replied that $\frac{3}{4}$ of his age multiplied by $\frac{1}{12}$ of his age gives a product equal to his age. What was his age? Ans. 16. 3. The sum of 660l. was raised for a particular purpose by four persons, A, B, C, and D; B advanced twice as much as A; C as much as A and B together; and D as much as B and C. What did each contribute? Ans. 60l., 120l., 180l., and 300l. 4. To find that number whose $\frac{1}{3}$ part exceeds its $\frac{1}{4}$ part by 12. Ans. 144. 5. What sum of money is that whose $\frac{1}{2}$ part, $\frac{1}{3}$ part, and $\frac{1}{4}$ part, added together, shall amount to 94 pounds? Ans. 120l. 6. In a mixture of copper, tin, and lead, one half of the whole $-16$lb. was copper; one-third of the whole $-12$lb. tin; and one-fourth of the whole $+4$lb. lead: what quantity of each was there in the composition? Ans. 128lb. of copper, 84lb. of tin, and 76lb. of lead. 7. A bill of 120l. was paid in guineas and moidores, and the number of pieces of both sorts was just 100; to find how many there were of each. Ans. 50. 8. To find two numbers in the proportion of 2 to 1, so that if 4 be added to each, the two sums shall be in the proportion of 3 to 2. Ans. 4 and 8. 9. A trader allows 100l. per annum for the expenses of his family, and yearly augments that part of his stock which is not so expended, by a third part of it; at the end of three years, his original stock was doubled: what had he at first? Ans. 1480l. 10. A fish was caught whose tail weighed 9lb. His head weighed as much as his tail and $\frac{1}{2}$ his body; and his body weighed as much as his head and tail: what did the whole fish weigh? Ans. 72lb. 11. One has a lease for 99 years; and being asked how much of it was already expired, answered, that two-thirds of the time past was equal to four-fifths of the time to come: required the time past. Ans. 54 years. 12. It is required to divide the number 48 into two such parts, that the one part may be three times as much above 20, as the other wants of 20. Ans. 32 and 16. 13. One rents 25 acres of land at 7 pounds 12 shillings per annum; this land consisting of two sorts, he rents the better sort at 8 shillings per acre, and the worse at 5: required the number of acres of the better sort. Ans. 9 of the better. 14. A certain cistern, which would be filled in 12 minutes