Prob. 23. A says to B, give me $100, and then I shall have as much money as you. No, says B to A, give me rather $100, and then I shall have twice as much as you. How much has each?

Ans. A $500 and B $700.

Prob. 24. Find two numbers of the following properties. When the one is multiplied by 2, the other by 5, and both products added together, the sum is 31; on the other hand, if the first be multiplied by 7, the second by 4, and both products added together, we obtain 68.

Ans. The first is 8, the second is 3.

Prob. 25. In the composition of a certain quantity of gunpowder, the nitre was ten pounds more than two thirds of the whole; the sulphur was four and a half pounds less than one sixth of the whole; and the charcoal was two pounds less than one seventh of the nitre. How many pounds of gunpowder were there? Ans. 69 pounds.

Prob. 26. Two workmen received the same sum for their labor; but if one had received $24 more, and the other $16 less, then one would have received just three times as much as the other. What did each receive?

Ans. $36.

Prob. 27. Find two numbers of which the less is to the greater as 2 to 3, and whose product is twelve times the sum of the numbers.

Ans. 20 and 30.

Prob. 28. There are two numbers whose difference is 12; and if eight times the less be subtracted from

five times the greater, the remainder will be 6. What are the numbers?

Ans. 18 and 30.

Prob. 29. What number is that, one third, one fourth, and two fifths of which being added together will make 59?

Ans. 60.

Prob. 30. A grocer has two kinds of tea, one of which is worth 57 cents per pound, the other 81.cents. How many pounds of each must he take to form a chest of 104 pounds, which will be worth $67.20?

Ans. 71 pounds of the former and 33 of the latter. Prob. 31. There is a number consisting of two dig its, whose sum is 7; and if 9 be added to the number itself, the digits will be inverted? What is the number? Ans. 34.

- Prob. 32. Out of a hogshead of water which had leaked away one third part, 21 gallons were drawn, and then being gauged, it was found to be half full. How many gallons did it hold?

Ans. 126.

Prob. 33. A pile stands one third in the ground, one half in the water, and three feet above the water. What is its entire length?

to

Ans. 18 feet.

Prob. 34. A and B start at the same time and place

go round an island 600 miles in circumference. A goes 30 miles a day, and B 20. How long before they will both be at the starting point together, and how far will each have traveled?

Ans. In 60 days; and A will have gone three times round the island, and B twice.

Prob. 35. A farmer sold 5 bushels of wheat and 6 of corn for 54 shillings. He afterward sold 4 bushels of wheat and 3 of corn for 36 shillings. What was the price of each per bushel?

Ans. Wheat 6 shillings and corn 4 shillings. Prob. 36. Two persons, A and B, agree together to purchase a house worth $1800. Says A to B, give me two thirds of your money, and I can purchase it alone; but says B to A, if you give me three fourths of your money, I shall be able to purchase it alone. How much had each?

Ans. A had $1200 and B $900. Prob. 37. A father directs that $1125 be divided among his three sons, in proportion to their ages. The eldest is twice as old as the youngest, and the age of the second is one half greater than that of the youngest. How much should each receive?

Ans. The youngest $250, the second $375, and the eldest $500.

Prob. 38. Three regiments are to furnish 603 men, and each to furnish in proportion to its strength. Now the strength of the first is to that of the second as 3 to 5, and the second is to the third as 4 to 7. How many must each furnish?

Ans. The first 108, the second 180, and the third 315 men.

Prob. 39. Divide the number 60 into two such parts that their product may be to the sum of their squares in the ratio of 2 to 5.

Ans. 20 and 40.

Prob. 40. Find a number such that if you subtract

it from 10, and multiply the remainder by the number itself, the product shall be 21.

Ans. 7 or 3.

Prob. 41. A merchant buys several pieces of cloth at the same price for $60. If he had bought three pieces more for the same sum, each piece would have cost him one dollar less. How many pieces did he buy?

Ans. 12.

Prob. 42. What number is that whose half, multiplied by its third part, produces 1176?

Ans. 84.

Prob. 43. The difference of two numbers is 6, and if 47 be added to twice the square of the less, it will be equal to the square of the greater. What are the numbers?

Ans. 17 and 11, or 7 and 1.

Prob. 44. What number is that whose seventh and eighth parts multiplied together, and the product divided by 3, gives the quotient 672?

Ans. 336.

Prob. 45. Find two numbers such that their product shall be 675; and the quotient of the greater, di- . vided by the less, shall be 3.

Ans. 45 and 15.

Prob. 46. There are two numbers, one of which exceeds the other by 8, and whose product is 240. What are the numbers?

Ans. 12 and 20.

Prob. 47. Find two numbers in the ratio of 3 to 5,

and whose product is 375.

Ans. 15 and 25.

Prob. 48. It is required to find two numbers whose product shall be 48, and the difference of their squares 28.

Ans. 6 and 8.

Prob. 49. What two numbers are those whose sum is 41, and the sum of whose squares is 901?

Ans 26 and 15. Prob. 50. What two numbers are those whose sum is equal to a, and the sum of whose squares is equal to b?

Prob. 51. What two numbers are as m to n, and the sum of whose squares is equal to b?

Prob. 52. What two numbers are to each other as m to n, and the difference of whose squares is equal to b?

Prob. 53. There are three pieces of cloth, whose lengths are in the ratio of 3, 4, and 5; and 12 yards being cut off from each, the whole quantity is dimin ished in the ratio of 7 to 4. What was the length of

Prob. 54. There are two boys, the difference of whose ages is to their sum as 1 to 3; and their sum is to their product as 3 to 8.

What are their ages?

Ans. 4 and 8.