miles, the distance from A to B is to the distance from C to D as 3 to 2, and one fourth of the distance from A to B, added to half the distance from C to D, is three times the distance from B to C. What are the respective distances? Ans. A to B 72 miles, B to C=14, C to D 48. = 10. A field of wheat and oats, which contained 20 acres, was put out to a labourer to reap for $20; the wheat at $1.20 and the oats $0.95 per acre. Now the labourer falling ill reaped only the wheat. money ought he to receive according to the bargain? Ans. $4.80. How much 11. Three men, A, B, and C, entered into partnership; A paid in as much as B and one third of C; B paid as much as C and one third of A; and C paid in $10 and one third of A. What did each pay in? the sum A contributed. Let Ans. $60, $50, and $30, respectively, 12. A gentleman gave in charity £46; a part of it in equal portions to 5 poor men, and the rest in equal portions to 7 poor women. Now the share of a man and a women together amounted to £8. What was given to the men, and what to the women? Let Then 8 the sum a woman received, &c. Ans. The men received £25, and the women £21. 13. Suppose that for every 10 sheep a farmer kep he should plough an acre of land, and should be allow ed an acre of pasture for every 4 sheep. How many sheep may that person keep who farms 700 acres? of the Let the whole number of sheep. The number of acres ploughed will be number of sheep; and the number of acres of the pasture will be of the number of sheep; both these added together must be the whole number of acres, &c. Ans. 2000 sheep. 14. A, B, and C make a joint stock; A puts in $70 more than B, and $90 less than C; and the sum of the shares of A and B is of the sum of the shares of B and C. What did each put in ? Ans. A put in $215, B $145, and C $305. 15. Divide the number 85 into two such parts that if the greater be increased by 7 and the less be diminished by 8, they will be to each other in the proportion of 5 to 2. Ans. 53 and 32. 75 may portion of 8 to 3. 16. It is required to divide the number 67 into two such parts that the difference between the greater and be to the excess of the less over 12 in the proAns. 43 and 24. 17. A man bought 12 lemons and a pound of sugar for 56 cents, afterwards he bought 18 lemons and a pound of sugar at the same rate for 74 cents. What was the price of the sugar, and of a lemon? Let the price of the sugar. In the same manner, 74 -x the price of a lemon. 18 Ans. Sugar 20 cents, lemons 3 cents apiece. 18. A man bought 5 oranges and 7 lemons for 58 cents; afterwards he bought 13 oranges and 6 lemons at the same rate for 102 cents. an orange and of a lemon? What was the price of x= the price of an orange. = the price of a lemon by the first Ans. Oranges 6 cents, and lemons 4 cents apiece. 19. A footman, who contracted for $72 a year and a livery suit, was turned away at the end of 7 months, and received only $32 and the livery. value of the livery? What was the Ans. 24. 20. A landlord let his farm for £10 a year in money and a certain number of bushels of corn. When corn sold at 10s. a bushel, he received at the rate of 10s. an acre for his land; but when it sold for 13s. 6d. a bushel, he received 13s. an acre. How many bushels of corn did he receive? Let x= the number of bushels. Then 10x+200 the year's rent in shillings; 10x + 200 =x+20= the number of acres. 27x+400= the year's rent at the second rate in sixpences. 27x+400 26 the number of acres, which must be Ans. 120 bushels. equal to the other, &c. 21. A man commenced trade with a certain sum of money, which he improved so well, that at the year's end he found he had doubled his first stock wanting $1000; and so he went on every year doubling the last year's stock wanting $1000; at the end of the third year he found that he had just three times as much money as he commenced with. What was his first stock? Ans. $1400. 22. A man, having a certain sum of money, went to a tavern, where he borrowed as much money as he then had, and then spent a shilling; with the remainder he went to another tavern, where he borrowed as much as he then had, and then spent a shilling, and so he went to a third and a fourth tavern, borrowing and spending as before; after which he had nothing left. How much money had he at first? Ans. 11 pence. 23. It is required to divide the number 60 into two such parts, that one seventh of the one may be equal to one eighth of the other. Ans. The parts are 28 and 32, 24. It is required to divide the number 50 into two such parts that of the one added to % of the other may make 40. Ans. The parts are 20 and 30. 25. It is required to divide the number 100 into two such parts, that if one third of one part be subtracted from one fourth of the other, the remainder may be 11. Ans. The parts are 24 and 76. 26. It is required to divide the number 48 into two such parts, that one part may be three times as much above 20, as the other wants of 20. Ans. The parts are 32 and 16. 27. A man distributes 20 shillings among 20 people, giving 6 pence apiece to some, and 16 pence apiece to What number of persons were there of each the rest. kind? Ans. 8 received 6 pence apiece, and 12 received 16 pence each. 28. A man paid £100 with 208 pieces of money, a part guineas at 21s. each, and a part crowns at 5s. each. How many pieces were there of each sort? Ans. 60 guineas and 148 crowns. 29. A country man had two flocks of sheep, the smaller consisting entirely of ewes, each of which brought him 2 lambs. On counting them he found that the number of lambs was equal to the difference between the two flocks. If all his sheep had been ewes, and brought forth three lambs apiece, his stock would have been 432. Required the number in each flock. Let x= the number in the less. Then 2x the number of lambs. 3x the number in the larger. 4x the number in both, &c. Ans. 27 in the less and 81 in the greater. |