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17. If the multiplier is i of the multiplicand, and the square of the product is 627264, what is the multiplier and what the multiplicand ?

8. If I buy 24 yards of cloth at the rate of 3 yards for a dollar, and 24 yards at $3 per yard, and sell the first lot at the rate of 2 yards for a dollar and the second at $2 per yard, shall I gain or lose, and how many dollars ?

19. The town of B is 36 miles due north from the town of A; C is 27 miles due east from B; D is 20 miles due south from C; E is 39 miles due west from D. How far is each of the abovenamed towns from A?

20. Multiply the sum of and by the difference of and }, divide the result by the product of į and I, and multiply the result last obtained by the quotient of divided by .

21. How many days will it take John and George together, to do a piece of work which John alone can do in 20 days, and which George alone can do in 24 days?

22. A can do a piece of work in 12 days; B can do it in 15. days; A and C together can do it in 8 days; and B and D together can do it in 9 days. In how many days can C and D together do it?

23. By what number must 9 be divided to give 1.6 for a quotient?

24. of a certain number exceeds f of that number by 4 more than to of the number. What is the number?

25. I bought a house for a certain sum, and, after expending $1000 in repairing it, I sold it at an advance of 25 per cent on its total cost, by which I gained a sum equal to 33} per cent of what I bought it for. How many dollars did I gain ?

26. What per cent shall I gain by buying bank stock at 25 per cent below par, and selling it at 10 per cent below par?

27. If a number be multiplied by itself, and the product be added to 47, the result will equal 24 times the square of 16. What is the number?

28. į of my money equals of Mr. Sumner's, and of Mr. Sumner's equals of Mr. Greene's. Now, allowing that Mr. Greene has $50000, how many dollars have I?

29. A's services are worth $1 per day, B’s are worth $1.25 per day, and C's are worth $1.50 per day. They together did a piece of work “by the job" for $75, and they succeeded in performing it in 15 days. How ought the money to be divided ?

30. Edward and William start at the same time to walk a distance of 32 miles. Edward walks at the rate of 4 miles per hour and rests every third hour, while William walks at the rate of 3 miles per hour and rests every fourth hour. Which will reach his journey's end first, and how much first?

31. One of two poles is just as long as the other, and they are set up in a vertical position at a distance apart equal to the sum of their lengths. Moreover, a point in the ground between them, just of the distance from the foot of the longer pole to the foot of the shorter, is 30 feet from the top of each. What is the length of each pole? How far is the foot of one from the foot of the other? How far apart are their tops ?

32. How many cubic inches of iron are there in a spherical shell, of which the outside diameter is 12 inches, and the inside diameter is 11 inches ?

33. A cylindrical pail whose outside diameter and outside altitude are each 1 foot, is made of wood is of an inch thick. How many cubic inches of wood does the pail contain ?

34. How many gallons of water will the pail described in the last problem contain ?

35. I bought a cask of spirits at $2 per gallon, but of it having leaked out, I added 10 per cent of water, and sold the mixture at $2.25 per gallon. Did I gain or lose, and how many per cent?

36. I bought a cask of wine, but of it having leaked out, I poured in s as much water as there was wine remaining, and then sold the mixture for as much per gallon as I had given for the wine? What per cent did I gain on the cost of the wine actually sold ? What per cent did I lose on the cost of the whole ?

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37. By selling goods at 10 per cent below their cost, I lost $100 more than I should have gained by selling į of them at cost, and the other half at 5 per cent above cost. What was the cost of the goods, and how many dollars did I lose ?


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40. I bought a lot of goods for a merchant residing in Havana, for which I charged a commission of 2 per cent. I also insured their safe transportation to Havana, for which I charged a premium of 11 per cent of their cost. My total charges for the goods, my commission, and the insurance, were $7450. What was the cost of the goods? What was my commission ? What was the insurance ?

41. Jan. 1, 1858, Gould and Newman purchased a cargo of grain for $2500, giving in payment their note on 4 months. Jan. 17th, they sold the grain at an advance of 25 per cent, receiving in payment a note due in 5 mo.; and, Jan. 19th, they paid $43.25 in cash for storage and other expenses. When the note which they had given for the grain became due, they got the one which they had received discounted at a bank, and made a complete settlement. Money being worth 6 per cent per year, what was their gain by the transaction ?

42. Aug. 10, 1858, I purchased for cash 75 bags of coffee, each containing 112 lb., at 9 cents per pound. For how much must I sell it, Sept. 1st, on a credit of 3 months, in order that, if I get the note which I receive for it discounted at a bank, Oct. 1st, the proceeds may be sufficient to give me a clear profit of 10 per cent on the investment, allowing interest at the rate of 6 per cent per year?

43. Robert takes 2 feet, and Charles takes 3 feet, at each step, but Robert takes 4 steps while Charles takes 3. How long will it take Charles to walk as far as Robert can walk in 12 hours ?

44. If $1000 should be so divided between Edward, Arthur, and Daniel, that of Edward's share should equal } of Arthur's, and

that of the sum of the shares of Edward and Arthur should equal 1 of Daniel's share, what would be the share of each?

45. A man made a will, in which he bequeathed į of his estate to his wife, šof the remainder to his son, and the rest in equal shares to his three daughters. He further directed that, in case either heir should die before himself, the property should be divided among the survivors in the proportions indicated by the will. It 80 happened that his wife and one of his daughters died before he did. If the estate was worth $100000, what was the just share of the son and of each daughter ?

46. A lot of land containing 100 acres is dividea, by lines running east and west, into three lots of equal value. If the land in the northern lot is 10 per cent better than that in the middle lot, and that in the middle lot is 127 per cent better than that in the southern, how many acres are there in each lot?

47. A vessel of war left port with provisions enough to last her crew of 700 men 16 months. 2 months after leaving port, she took a prize, on board which she put 50 men, giving them provisions enough to last them l} months. In three months more she made another prize, from which she took 100 men and provisions enough to last 75 men 6 months. In 4 months more, she captured a large Indiaman, on board which she placed 50 prisoners from the former prize, and 25 of her own men. 2 months afterwards she lost 50 men in an engagement with an enemy's vessel, and sprang a leak, so that į of her remaining provisions were destroyed. She reached port the day her provisions were exhausted, but, from the time of her last engagement, each man received only of his usual allowance. How long was her cruise ?

48. There are three numbers, the first and second of which are prime to each other, and so also are the second and third. If the least common multiple of the first and second is 1617, of the second and third is 2156, and of the first and third is 132, what are the numbers ?

49. If A can do şof a certain piece of work in 9 days, and B can do į of it in 10 days, how many days will it take A and B together to do a piece of work 3.22 times as large ?

50. One pipe will fill a cistern in two hours and another will empty it in three. The cistern being empty, in how long time will it be filled if both pipes are left open ?

51. How many balls 3 inches in diameter will be required to weigh as much as a ball 27 inches in diameter, all the balls being of the same material ?

52. Two towns are 108 miles apart. A starts from the first and B at the same time starts from the second. They travel towards each other, and meet in 14 hours. If A travels only as fast as B, how many miles does each travel per hour?

53. A owes B $450 payable in 8 months, and B owes A $600 payable in 10 months. If A pays į of his debt down, and the rest in 15 months, and B pays } of his in 3 months, when ought B to pay the rest of his ?

54. Why is not selling 60 apples at the rate of 5 for 2 cents equivalent to selling 30 at the rate of 2 for a cent and 30 more at the rate of 3 for a cent?

55. If a steamboat whose machinery moves uniformly goes at the rate of 15 miles per hour in descending a river, and at the rate of 4 miles per hour in ascending it, how many miles does the current run per hour, and how many minutes will it take the steamboat to go a mile where there is no current?

56. If 60 men can dig a certain trench in 30 days in summer, how many men will it take in winter to dig in 21 days a trench 1į times as long, 1} times as wide, and f as deep, provided that the men can dig only { as many feet per hour, and only s as many hours per day in winter as in summer?

7. A farmer owns a triangular field, the sides of which are respectively 30, 40, and 35 rods in length. He wishes to divide it into two parts of equal area by a line running parallel to the longest side. What will be the length of each side of the trapezoid thus cut off? (See 141, u.)

58. The town A is situated on the banks of a certain river, and at such a distance below the town B, that a boat which sails 7 miles per hour with the current and 3 miles per hour against it,

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