13. Bought two flocks of sheep for £.65. 13s., one containing 5 more than the other. Each sheep cost as many shillings as there were sheep in the flock. Required the numbers in each flock. Ans. 23, and 28. 14. A regiment of soldiers, consisting of 1066 men, is formed into two squares, one of which has four men more in a side than the other. What number of men are in a side of each of the squares? Ans. 21, and 25. 15. What number is that, to which if 24 be added, and the square root of the sum extracted, this root shall be less than the original quantity by 18. Ans. 25. 16. After taking the kings, queens, and knaves out of a pack of cards, the rest were divided into three heaps. The number of pips contained in the second heap was found to be 4 times the square of the number in the first heap; and had the third heap contained 5 more pips than it did, the number in it would have been exactly half of what the first and second heap contained. Required the number of pips in each heap. Ans. 6, 144, and 70. 17. A Tailor bought a piece of cloth for £.147, from which he cut off 12 yards for his own use, and sold the remainder for £.120. 5s. gaining 5 shillings per yard. How many yards were there, and what did it cost him per yard? Ans. 49 yards, at £.3'per yard. 18. A regiment of foot was ordered to send 216 men on garrison duty, each company being to furnish an equal number; but before the detachment marched, 3 of the companies were sent on another service, when it was found that each company that remained was obliged to furnish 12 additional men, in order to make up the complement 216. How many companies were there in the regiment, and what number of men was each company ordered to send at first? Ans. There were 9 companies; and each was to send 24 men. 19. A Poulterer bought 15 ducks and 12 turkeys for five guineas. He had two ducks more for 18 shillings than he had of turkeys for 20 shillings. What was the price of each? Ans. The price of a duck was 3s. and of a turkey 5s. 20. Two men, A and B, entered into a speculation, to which B subscribed £.15 more than A. After 4 months, C was admitted, who added £.50 to the stock; and at the end of 12 months from C's admission they found they had gained £.159; when A withdrawing received for principal and gain £.88. What did he originally subscribe? Ans. £.40. 21. A wall was built round a rectangular court to a certain height. Now the length of one side of the court was two yards less than 8 times the height of the wall, and the length of the adjacent side was 5 yards less than 6 times the height of the wall; and the number of square yards in the court was greater than the number in the wall by 178. Required the dimensions of the court, and the height of the wall. Ans. The sides were 30, and 19, and the height 4 yards. 22. A ship containing 74 sailors, and a certain number of soldiers besides officers, took a prize. The sailors received each one-third as many pounds as there were soldiers, and the soldiers received £.3 a piece less, and £.768 fell to the share of the officers. Had the officers however received nothing, the soldiers and sailors might have received half as many pounds per man, as there were soldiers. How many soldiers were there, and how much did each receive? Ans. There were 36 soldiers, each soldier received £.9, and each sailor £.12. 23. A Poulterer going to market to buy turkeys, met with four flocks. In the second were 6 more than three times the square root of double the number in the first. The third contained three times as many as the first and second; and the fourth contained 6 more than the square of one-third of the number in the third; and the whole number was 1938. How many were there in each flock? Ans. The numbers were 18, 24, 126, 1770, respectively. 24. A body of men are just sufficient to form a hollow equilateral wedge, three deep; and if 597 be taken away, the remainder will form a hollow square, four deep, the front of which contains one man more than the square root of the number contained in a front of the wedge. What is the number of men? Ans. 693. 25. Two men, A and B, undertake to perform a piece of work in four days, for which they are to receive a certain number of shillings; but after some time, finding that they shall not be able to finish it in the time proposed, they call in C to assist them, and upon an equitable division of the money, C receives a sum equal to the square root of the whole number of shillings; but had they been obliged to call in C to their assistance 1+ day sooner, his share of the money would have been two-fifths more. How long did C work, and what did he receive? Ans. He worked 2 days, and received 5 shillings. 26. A cask, whose content is 20 gallons, is filled with brandy, a certain quantity of which is then drawn off into another cask of equal size; this last cask is then filled with water; after which the first cask is filled with the mixture, and it appears, that if 6 gallons of the mixture be drawn off from the first into the second cask, there will be equal quantities of brandy in each. Required the quantity of brandy first drawn off. Ans. 10 gallons. 27. There are three numbers, the difference of whose differences is 5; their sum is 20; and their continual product 130. Required the numbers. Ans. 2, 5, and 13. 28. There are three numbers, the difference of whose differences is 3; their sum is 21; and the sum of the squares of the greatest and least is 137. Required the numbers. Ans. 4, 6, 11. 29. There is a number consisting of 2 digits, which when divided by the sum of its digits gives a quotient greater by 2 than the first digit. But if the digits be inverted, and then divided by a number greater by unity than the sum of the digits, the quotient is greater by 2 than the preceding quotient. Required the number. Ans. 24. 30. A certain sum was to be raised on three estates belonging to A, B, and C, at the rate of one shilling per Now the number of acres A and B had, were as 3 to 7; and if the number of acres in the whole were divided by one-third of the product of the numbers in the first acre. 3 4 and third, the quotient would be Also the sum paid by A and C was 36 shillings less than the sum of three times the money paid by C, and two-sevenths of the money paid by B. Of how many acres did each estate consist; and what was the whole sum to be raised? Ans. A had 12, B 28, and C 20 acres; and the sum was £.3. 31. A Butcher bought a certain number of calves and sheep, and for each of the former gave as many shillings as there were sheep, and for each of the latter one-fourth as much. Now had he given 4 shillings more for each of the former, and 2 shillings more for each of the latter, he would have paid seven pounds more. But had a sheep cost aş much as a calf, he would have expended £.56. 8s. How many did he buy of each; and what were their prices? Ans. 23 calves, and 24 sheep; and their prices were 24, and 6 shillings, respectively. 32. Two persons, A and B, comparing their wages, observe that if A had received per day in addition to what he does receive, a sum equal to one-fourth of what B received per week, and had worked as many days as B received shillings per day, he would have received £.2. 8s.; and had B received 2 shillings a day more than A did, and worked for a number of days equal to half the number of shillings he received per week, he would have received £.4. 18s. What were their daily wages? Ans. A's 5 shillings, and B's 4. 33. There are four towns in the order of the letters, A, B, C, D. The difference between the distances from A to B and from B to C is greater by four miles than the distance from B to D. Also the number of miles between B and D is equal to two-thirds of the number between A and C. And the number between A and B is to the number between C and D as seven times the number between B and C: 26. Required the respective distances. |
