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45. When $ 11.75 are paid for 24 acres, what quantity
will $ 100.00 purchase ? Ans. 19A. IR. 3245 p. 46. John Savory and Thomas Hardy traded in company; Savory put in for capital $ 1000 ; they gained # 123.00; Hardy received for his share of the gains $ 70 ; what was his capital ?
Ans. $ 1206.8915. 47. E. Fuller lent a certain sum of money to C. Lamson, and, at the end of 3 years, 7 months, and 20 days, he received interest and principal $ 1000; what was the sum lent?
Ans. $ 820.79431 48. Lent $ 88 for 18 months, and received for interest and principal $97.57 ; what was the per cent. ?
Ans. 71 per cent. 49. When of a gallon cost $87, what cost 71 gallons ?
Ans. $ 1051.25. 50. When $71 are paid for 184 yards of broadcloth, what cost 5 yards ?
Ans. $ 19.26486 51. How many yards of cloth, at $ 4.00 per yard, must be given for 18tons. 17cwt. 3qr. of sugar, at $ 9.50 per cwt. ?
Ans. 8975 yards. 52. How much grain, at $ 1.25 per bushel, must be given for 98 bushels of salt, at $ 0.45
Ans. 3525 bushels. 53. How many acres of land, at $ 37.50 per acre must be given for 86tons. 18cwt. 3qr. 20lbs. of coal, at $8.50
Ans. 19A. 2R. 335p. 54. A person, being asked the time of day, replied, that 7 of the time passed from noon was equal to it of the time to midnight. Required the time.
Ans. 40 minutes past 4. 55. How many cubic feet of water in a pond, that contains 200 acres, and is 20 feet deep ?
Ans. 174,240,000 feet. 56. On a certain night, in the year 1842, rain fell to the depth of 3 inches in the town of Haverhill ; the town contains about 20,000 square acres. Required the number of hogsheads of water fallen, supposing each hogshead to contain 100 gallons, and each gallon 282 cubic inches. Ans. 13346042hhd. 55gal. 1qt. Opt. 244gi. 57. If the sun pass over one degree in 4 minutes, and the longitude of Boston is 71° 4' west, what will be the
per ton ?
time at Boston, when it is 11h. 16m. A. M. at London ?
Ans. 6h. 31m. 44sec. A. M. 58. When it is 2h. 36m. A. M. at the Cape of Good Hope, in longitude 18° 24' east, what is the time at Cape Horn, in longitude 67° 21' west ?
Ans. Sh. 53m. P. M. 59. Yesterday my longitude, at noon, was 16° 18' west ; to-day I perceive by my watch, which has kept correct time, that the sun is on the meridian at ilh. 36m. ; what is my longitude ?
Ans. 22° 18' west. 60. Sound, uninterrupted, will pass 1142 feet in one second, how long will it be in passing from Boston to London, the distance being about 3000 miles ?
Ans. 3h. 51m. 10+sec. 61. The time which elapsed between seeing the flash of a gun, and hearing its report, was 10 seconds ; what was the distance ?
Ans. 2 miles. 860 feet. 62. If a globe of silver, 2 inches in diameter, be worth
$ 125, what would be the value of a globe 3 inches in diameter ?
Ăns. $ 421.871. 63. J. Pearson has tea, which he barters with M. Swift, at 10 cents per lb. more than it costs him, against sugar, which costs Swift 15 cents per lb., but which he puts at 20 cents per lb., what was the first cost of the tea?
Ans. $ 0.30. 64. Q. and Y. barter ; Q. makes of 10 cents 121 cents ; Y. makes of 15 cents 19 cents ; who makes the most per cent., and by how much ?
Ans. Y. makes 14 per cent. more than Q. 65. A certain individual was born in 1786, September 25, at 27 minutes past 3 o'clock, A. M., how
minutes old will he be July 4, 1844, at 30 minutes past 5 o'clock, P. M. ?
Ans. 30,386,283 minutes. 66. The longitude of a certain star is 3s. 14°. 26'. 14"., and the longitude of the moon at the same time is 8s. 19o. 43' 28'., how far will the moon have to move in her orbit to be in conjunction with the star ?
Ans. 6s. 24°. 42'. 46". 67. From a small field containing 3A. IR. 23p. 200ft., there were sold 1A. 2R. 37p. 30yd. 8ft. ; what quantity remained ?
Ans. 1A. 2R. 25p. 21yd. 5ft. 36in. 68. What part of of an acre is of anacre?
69. My chaise having been injured by a very bad boy, I am obliged to sell it for $ 68.75, which is 40 per cent. less than its original value, what was the cost ?
Ans. $ 114.581. 70. Charles Webster's horse is valued at $ 120, but he will not sell him for less than $ 134.40 ; what per cent. does he intend to make ?
Ans. 12 per cent. 71. Three merchants, L. Emerson, E. Bailey, and S. Curtiss engaged in a cotton speculation. Emerson advanced $ 3600, Bailey $ 4200 and Curtiss $ 2200. They invested their whole capital in cotton, for which they received $ 15000 in bills on a bank in New Orleans. These bills were sold to a Boston broker at 15 per cent. below par, what is each man's net gain?
Ans. Emerson $ 990.00. Bailey $ 1155.00. Curtiss $ 605.00. 72. Bought a box made of a plank 34 inches thick. Its length is 4ft. 9in., its breadth 3ft. 7in., and its height 2ft. llin. How many square feet did it require to make the box, and how many cubic feet does it contain ?
Ans. 700 square feet, 294 cubic feet. 73. How many bricks will it require to construct the walls of a house, 64 feet long and 32 feet wide, and 28 feet high ; the walls are to be ift. 4in. thick, and there are also three doors 7ft. 4ịn, high, and 3ft. 8in. wide ; also 14 windows 3 feet wide and 6 feet high, and 16 windows 2ft. 8in. wide and 5ft. 8in. high. Each brick is to be 8 inches long, 4 inches wide, and 2 inches thick.
Ans. 167,480 bricks. 74. John Brown gave to his three sons, Benjamin, Samuel, and William, * 1000 to be divided in the proportion of }, , and } respectively ; but William, having received a fortune by his wife, resigns his share to his brothers. It is required to divide the whole sum between Benjamin and Samuel.
Ans. Benjamin $ 571.42. Samuel $ 428,574. 75. Peter Webster rented a house for one year to Thomas Bailey for $100; at the end of four months, Bailey rented one half of the house to John Bricket, and at the end of eight months, it was agreed by Webster and Bailey to rent one third of the house to John Dana What share of the rent must each
? Ans. Webster $615, Bailey $275, and Dana $114.
76. Bought 365 yards of broadcloth, for which I paid
£ 576. 17s. 9d.; for how much must the cloth be sold per yard to gain 25 per cent. Ans. £1. 19s. 6,45d. 77. John Brown's house is 40 feet square ; the roof comes to a point over the centre of the house, and this point is 12 feet above the garret floor. Required the length of a rafter, which extends from one of the corners of the house to the highest part of the roof.
Ans. 30.72+ feet. 78. Minot Thayer sold broadcloth at $ 4.40 per yard, and by so doing he lost 12 per cent. ; whereas he ought to have gained 10 per cent. For what should the cloth have been sold per yard ?
Ans. $ 5.50. 79. John Crowell sold cloth at $5.50 per yard, and gained 10 per cent. ; whereas, the cloth having been damaged, he should have sold it 12 per cent. less than the cost. What in justice should he have charged per yard ?
Ans. $ 4.40. 80. Jacob How has cloth, which he purchased for 12 per cent. less than its value ; but he sells it at 10 per cent. more than it is worth, and by so doing he gains $ 1.10 on each yard. What per cent. did he make on his purchase ?
Ans. 25 per cent. 81. A gentleman has five daughters, Emily, Jane, Betsey, Abigail, and Nancy, whose fortunes are as follows. The first two and the last two have $ 19,000 ; the first four $ 19,200 ; the last four $ 20,000 ; the first and the last three $ 20,500 ; the first three and the last $21,300. What was the fortune of each ?
Ans. Emily has $5,000; Jane $ 4,500 ; Betsey $6,000 ; Abigail $3,700 ; and Nancy $5,800.
By the Cancelling Method the scholar is enabled to solve many questions with less than half the labor, that would be required by the usual process. It cannot, however, be applied to all the rules of arithmetic, nor to all the questions under any one rule ; but it is generally used in the operations of those questions which require Multiplication and Division. The system is not new. It has been before the public in some form or other for centuries. John Birks, who published the second edition of his most excellent system of “ Arithmetical Collections” in London, 1764, has made many improvements in the system. Since that period, but little advance has been made in it. Whether the author has made his system more plain and intelligible than has been done by others, the candid public must judge. He has spared no pains to exhibit its applicability and utility to those departments of arithmetical science where it can be advantageously employed. He believes the system can be of but little use to the pupil, until he can perform the questions by the common method. Hence the propriety of deferring attention to this method, until the common rules of arithmetic are thoroughly understood.
1. Equal divisors and dividends cancel each other. 2. When the product of two divisors is equal to the product of two dividends, they cancel each other.