attending him as there were gentlemen; and the number of pounds which each had was double the number of all the servants; and the whole sum of money taken out was £3456. How many gentlemen were there? Ans. 12. 9. Divide the number 49 into two such parts, that the quotient of the greater divided by the less may be to the quotient 10. A detachment of soldiers from a regiment being ordered to march on a particular service, each company furnished four times as many men as there were companies in the regiment; but these being found to be insufficient, each company furnished 3 more men; when their number was found to be increased in the ratio of 17 to 16. How many companies were there in the regiment? Ans. 12. 11. A charitable person distributed a certain sum amongst some poor men and women, the numbers of whom were in the proportion of 4 to 5. Each man received one-third of as many shillings as there were persons relieved; and each woman received twice as many shillings as there were women more than men. Now the men received all together 188. more than the women. How many were there of each? Ans. 12 men, and 15 women. 12. A Gentleman who had a certain number of horses, kept part of them at livery stables, for which he paid £4. 108. per week. The rest he kept at home, and their number was to the number kept at the livery stables as 7 to 3. He found that the expense of keeping 5 at home was just equal to that of keeping 4 at the stables; and the number of shillings that one horse cost him at home was to the number of horses kept at home as 6 to 7. How many horses had he? Ans. 6 at the livery stables, and 14 at home. 13. A city barge, with chairs for the company and benches for the rowers, went a summer excursion, with two bargemen on every bench. The number of gentlemen on board was equal to the square of the number of bargemen, and the number of ladies was equal to the number of gentlemen, twice the number of bargemen, and one over. Among other provisions, there were a number of turtles equal to the square root of the number of ladies; and a number of bottles of wine less than the cube of the number of turtles by 361. The turtles in dressing consumed a great quantity of wine, and the party having stayed out till the turtles were all eaten, and the wine all gone, it was computed, that supposing them all to have consumed an equal quantity, (viz. gentlemen, ladies, bargemen, and turtles,) each individual would have consumed as many bottles as there were benches in the barge. Required the number of turtles. 14. Ans. 19. From two towns, C and D, two travellers, A and B, set out to meet each other; and it appeared that when they met, B had gone 35 miles more than three-fifths of the distance that A had travelled; but from their rate of travelling, A expected to reach C in 20 hours and 50 minutes ; and B to reach Din 30 hours. Required the distance of C from D. Ans. 275 miles. 15. A Farmer bought two flocks of sheep, the first of which contained 18 fewer than the second. If he had given for the first flock as many pounds as there were sheep in the second, and for the second as many pounds as there were sheep in the first, then the price of 6 sheep of the first flock would have been to the price of 7 sheep of the second in the proportion of 7 to 6. Required the numbers in each flock. Ans. 108, and 126. 16. A Poulterer bought a number of ducks and turkeys, the number of ducks exceeding the number of turkeys by 8. For each duck he gave half as many shillings as there were turkeys, and for each turkey half as many shillings as there were ducks. He afterwards bought another small flock of turkeys, containing 4 fewer than the number of turkeys he bought before; and having given for each of them as many shillings as there were turkeys in the flock, he found, that if his former purchase had cost 16 shillings more, it would have cost exactly four times as much as the present one. How many ducks and turkeys did he buy at first? Ans. 12 turkeys, and 20 ducks. 17. Two men, A and B, entered into partnership with stocks, which are in the proportion of 9 to 8; and after trading one year, A found his share of their gain to amount to onethird of his stock. They continued to trade for as many years as are equal to three-fourths of the number of pounds which B contributed to the stock, and found their whole gain amount to £1666. What did each contribute to the stock; and how many years did they trade? Ans. A contributed £63, and B £56; and the number of years is 42. 18. A person wishing to ascertain the area of a certain quadrilateral field, found that he could determine it the most readily by dividing it into two portions, one of which was of the form of a rectangular parallelogram, the shorter side of which measured 60 yards. The other was of the form of a right-angled triangle, whose shortest side was equal to the shorter side of the parallelogram, and the other side containing the right angle, was equal to the diagonal of the parallelogram; and the area of the triangle was to the area of the parallelogram as 5 to 8. What was the area of the field? Ans. 7800 square yards. 19. A Merchant laid out a certain sum upon a speculation, and found at the end of a year that he had gained £69. This he added to his stock, and at the end of another year found that he had gained exactly as much per cent. as in the year preceding. Proceeding in the same manner, and each year adding to his stock the gain of the year preceding, he found at the beginning of the fifth year that his stock was to the original stock as 81 to 16. What was the sum he first laid out? Ans. £138. 20. There is a number consisting of two digits, which being multiplied by the digit on the left hand, the product is 46; but if the sum of the digits be multiplied by the same digit, the product is only 10. Required the number. Ans. 23. 21. From two towns, Cand D, which were at the distance of 396 miles, two persons, A and B, set out at the same time, and met each other, after travelling as many days as are equal to the difference of the number of miles they travelled per day; when it appears that A has travelled 216 miles. How many miles did each travel per day? 22. Ans. A went 36, and B 30. There are two numbers, whose sum is to the greater as 40 is to the less, and whose sum is to the less as 90 is to the greater. What are the numbers ? Ans. 36, and 24. 23. It is required to find two numbers such, that the product of the greater and the cube of the less may be to the product of the less and the cube of the greater as 4 to 9; and the sum of the cubes of the numbers may be 35. Ans. 3, and 2. 24. The paving of two square court-yards cost £205; a yard of each costing one-fourth of as many shillings as there were yards in a side of the other. And a side of the greater and less together measure 41 yards. Required the length of a side of each. Ans. 25, and 16 yards. 25. A person bought a number of apples and pears, amounting together to so. Now the apples cost twice as much as the pears: but had he bought as many apples as he did pears, and as many pears as he did apples, his apples would have cost 10d., and his pears 3s. 9d. How many did he buy of each? Ans. 60 apples, and 20 pears. 26. A person exchanged a quantity of brandy for a quantity of rum and £11. 58.; the brandy and rum being each valued at as many shillings per gallon as there were gallons of that liquor. Now had the rum been worth as many shillings per gallon as the brandy was, the whole value of the rum and brandy would have been £56. 58. How many gallons were there of each ? Ans. 25 gallons of brandy, and 20 of rum. 27. There are two rectangular vats, the greater of which contains 20 solid feet more than the other. Their capacities are in the ratio of 4 to 5; and their bases are squares, a side of each of which is equal to the depth of the other. What are the depths? Ans. 5 feet, and 4 feet. 28. Bought two square carpets for £62. 18.; for each of which I paid as many shillings per yard as there were |