15. A pound sterling is $43; how many dollars in 9 pounds sterling?

16. How many pounds sterling in $800?

17. How many guineas, $4 each, in $1600 ?

Ans. $40. Ans. £180.

Ans. 342 guin. + $4. 18. Bought 20 boxes of sugar, 83 cwt. 2 qrs. 14 lbs., tare 15 per cent; what is the net weight? Ans. 71 cwt. 9 lbs.

19. Bought 40 doz. knives and forks for $56.50; how must I sell them per doz. to gain 30 per cent ? Ans. $1.83625.

20. If I sell goods amounting to £240 10s. New York cur to a man in Conn., for what amount must he credit me on his books, should they be kept in pounds, shillings, and pence? Ans. £180 10s. 21. If 4 men, in of a week, can earn £12 10s., how much will 20 men earn in the same time? Ans. £62 10s.

22. If 4 men, in of a week, can earn $35.75, how much will 20 men earn in 48 weeks? Ans. $1573.

23. The diameter of Mercury is 3200 miles, and the diameter of the Sun is 883000; how many times longer is the diameter of the Sun than that of Mercury?

Ans. 276 times 24. The diameter of Ceres is 1621 miles; how many times is the diameter of Ceres contained in the diameter of the Sun ? Ans. 545 times

25. The distance of the earth from the Sun is 96000000 miles; how long would it take a cannon-ball, flying at the rate of 1000 miles per minute, to go from the earth to the Sun ? Ans. 66 days.

26. What principal, at simple interest, will gain $821 in 3 years, when the rate is 5 per cent ? Ans. $500.

27. If the insurance of two houses, worth $11000, for 1 year, be $110, what will it cost to insure one house, worth $5500, for of a year? Ans. $27.50.

28. If $1200, at a certain rate per cent, gain 3 of itself in 71 years, what will $400 gain in 21 years? Ans. $50.

29. If 32 yds. of carpet, & of a yd. wide, will cover a floor 18 feet long and 12 feet wide, how many yards, 11 yd. wide, will cover a floor 24 feet long and 18 feet wide? Ans. 38 yds.

30. If a barrel of apples contain 23 bushels, how many barrels in 1375 bushels ?

31. How many rods in 1760 yards? 32. How many miles in 8800 yards?

Ans. 500 bbls.

Ans. 320 rods.

Ans. 5 miles.

33. How many nails in 6 yards, 6 ells Hamburgh, 6 ells Flemish, 6 ells English, and 6 ells French?

Ans. 492 nails.

34. How many gills in 4 barrels, 4 hogsheads, and 4 pipes? Ans. 28224 gills.

35. How many pounds in 3 gallons of oil, 3 stone of wire, 3 stone of iron, 3 bushels of salt, 3 firkins of butter, and 3 barrels of flour? Ans. 1020 lbs. 36. How many days from the 14th of January to the 4th of July? Ans. 171 days. 37. How many days from the 4th of July to the 14th of January? 38. How many dollars in £486 12s. Sterling?

Ans. 194 days.

$Ans. 2162.67

39. How many dollars in £100 New Jersey currency? Ans. $266.67

40. How many dollars in £100 New England currency?

Ans. $333.33+

41. How much is of 12 years and 6 months?

Ans. 5 years.

1

42. What is the value of of £362 10s.

Ans. £290.

43. What is the value of 4862 articles at 1s. 8d. for each? Ans. £405 3s. 4d.

44. How much for 6784 bushels at 3s. 4d. per bushel ? Ans. £1130 13s. 4d. 45. How much for 948 yards of silk at £1 2s. 6d. per yard? Ans. £1066 10s..

46. How much for 788 bushels of wheat at 7s. 9d. per bushel? (72s.) Ans. £305 7s. 47. How much for 24 cwt. 2 qrs. and 14 lbs. of sugar at £1 16s. 8d. per cwt.? Ans. £45 2s. 11d. 48 how much for 36 cwt. 3 qrs. and 14 lbs. of rice at £1 9s. 6d. per cwt.? Ans. £54 7s. 93d. 49. If 12 bushels of apples cost 19s. 6d., how much for 37 bushels ? Ans. £3 111d. 50. If I pay $5 for the freight of 2 cwt. and 2 qrs. for 150 miles, how much must I pay for a ton for the same distance? Ans. $40.

51. How many trees can be set on an acre of ground, allowing 4 trees to occupy a space of 5 square yards?

Ans. 968 trees.

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52. If 8 persons use 4 lbs. of coffee in 4 weeks, how much will be sufficient for 100000 persons for one year?

Ans. 650000 lbs.

53. If 3 books cost 8s. 3d., how much for 100?

Ans. £13 15s.

54. If, when wheat is $1 per bushel, the 12 cent loaf weighs 50 ounces, how much should it weigh when the price of wheat is 110 cents per bushel? Ans. 45 oz.

55. What is the value of 4863 acres of land at $12 per

acre?

56. How many yards in 4329 inches ?

Ans. $6206.061.

Ans. 120 yds. 9 in. 57. A man has 3 cwt. 2 qrs. and 14 lbs. of sugar, which he intends to put up into parcels of 31 lbs. each; how many parcels will there be ? Ans. 116 parcels.

58. A man owes a laborer £9 for work, at 7s. 6d. per day; how many days did he work?

Ans. 24 days. 59. Bought sheep for $2 each, calves for $21, cows for $121, and oxen for $171, an equal number of each; how many did I get for $276?

60. What per cent is 3s. 4d. on a pound?

Ans. 8 of each.

Ans. 163 per cent.

61. If of a chest of tea cost $24, how much for a whole chest?

Ans. $60. Ans. $437.50.

62. How much is 3 of of $750? 63. What principal, at 6 per cent per annum, simple interest, will amount to $960 in 10 years?

Ans. $600. 64. In what time will $500, at 5 per cent per annum, simple interest, yield an amount of interest equal to itself?

65. If $400 will yield $50 interest in 2 $1200 yield in 71⁄2 years?

Ans. 20 years.

years, what will Ans. $450.

66. If I hold a note against C. D., due the 1st of Jan. 1848, for $700, and he pay $50 on the 1st of each month, commencing the 1st of Feb. following, how much will he owe me on the 1st of Jan. 1849, interest 6 per cent per annum?

Ans. $175.50. 67. Bought 4 ceroons of indigo, weighing 419 lbs., tare 10 per cent, for $565.50; how must I sell it per lb. to gain 12 per cent ? Ans. $1.68 68. What is the value, in Federal money, of a bill of exchange for £450 sterling, when the premium is 91 per cent? Ans. $2185.

69. What is the compound interest on $1000 for 4 years, at 6 per cent per annum? Ans. $286.466+

70. What sum at simple interest, for 4 years, at 7 per cent per annum, will yield sufficient to pay for a horse and wagon worth $196. Ans. $700. 71. Find the interest on $1000000 for one day, at 6 per cent per annum. Ans. $164.38 + 72. What is the present worth of an annuity of 300 dollars, due one year hence, discount 6 per cent? Ans. $283.02 73. What difference is there between the simple interest, and the discount on $500, at 6 per cent, for 4 years?

Ans. $23.23

74. A. owes B. $200, payable in 3 months, $200 payable in 4 months, and $200 payable in 5 months; if he give him one note for the whole, at what time must it be drawn?

Ans. 4 months. 75. If, by selling cloth at 88 cts. per yard, 10 per cent is gained, what will be the gain per cent, if sold at one dollar per yard? Ans. 25 per cent.

76. L., M., and O. formed a connection in business. L. put in $200 for 6 months, M. put in $200 for 8 months, and O. put in $200 for 10 months; they gained $600: what is the share of each? Prove your work.

Ans. 396.

77. Bought 2644 yards of stuff; sold of the quantity, and afterwards sold of the remainder; how much have I left? Ans. 1487 yds. 78. What number, divided by 161, will produce 24 for the quotient? 79. If the and the of a sum of money be $601.20, what is the whole sum? Ans. $721.44. 80. What is the difference between 10 square yards and 10 yards square? Ans. 90 sq. yds.

81. How many times is 14 feet 9 inches contained in one Ans. 358 times

mile?

$500

(82)

New York, Nov. 25, 1849. Three months after date, value received, we promise to pay to Messrs. Hope & Co., or order, Five hundred dollars. Crawley & Marstin.

If the above note were discounted in the bank, at the rate of 6 per cent per annum, on the day it was drawn, for my account, for how much money would the bank credit me? (See note after Discount.) Ans. $492.25.

83. If a wheel make 4 turns in going 62 feet, how many turns will it make in going a mile ? Ans. 341 turns

84. Five industrious boys, în a week, did sums as follows on Monday they did 275; on Tuesday 270; on Wednesday 265; on Thursday 260; and on Friday 255: what was the average number done by one boy in a day? Ans. 53 sums.

85. How much cloth at $1.25 and $2.25 per yard, and a like quantity of each, can be bought for $700 ?

Ans. 200 yds. of each kind.

86. A ship being overtaken by a gale of wind, in order to save the ship, and the lives of the persons on board, the crew were obliged to throw $5500 worth of the cargo into the sea. The ship and cargo were valued at $68750: what fractional part of the whole value was thrown overboard; and how much did it amount to on a dollar; and how much must a merchant bear of the loss, who owned $12500 worth of the cargo?

Ans. 1st,; 2d, 8 cents; 3d, $1000. 87. Bought of H., H. & Co., a lot of goods amounting to $728.50; for which I am to pay cash, and give my note at 4 months, with interest at 6 per cent per annum added for the rest: how much money must I pay him, and what will be the amount of the note ? Ans. $291.40; $445.84.

INVOLUTION.

INVOLUTION is the method of raising powers from a given number, called the root.

A power is the product arising from multiplying a number by itself, and the product thence arising by the root, as often as is required. Thus, 8 is the third power of 2, because 2×2×2=8; and 81 is the fourth power of 3, because 3×3×3×3=81. The number denoting the power is called the index, and is sometimes written thus, 4, the second power of 4; 6, the third power of 6.

The product of two powers will always equal the power denoted by the sum of their indices; as 53 = 3125; so 5a×53 = 3125.

What is Involution? What is a power? What is the number denoting the power called? What will the product of two powers always equal? What is the rule for involving the root to the required power 2