44. What number is that, to which if its third be added the sum will be 48 ? 45. What number is that, to which if its 5th be added the sum will be 54 ? 46. Whal number is that to which if its half and its third be added the sum will be 55 ? 47. A man being asked his age, answered, that if its half and its third were added to it, the sum would be 77 ; what was his age ? 48. What number is that, which being increased by its half, its fourth, and eighteen more, will be doubled ? 49. A boy being asked his age, answered, that if į and of his age, and 20 more were added to his age, the sum would be 3 times his age. What was his age ? 50. A man being asked how many sheep he had, answered, that if he had as many more, į as many more, and 21 sheep, he should have 100. How many had he? 51. A farmer carried his grain to market, and sold 75 bushels of wheat, at $1,45 per bushel, 64 rye, * ,95 142 $ ,50 corn, In exchange he received sundry articles :3 pieces of cloth, each containing 31 yds., at $1,75 per yd. 2 quintals of fish, $2,30 per quin. 8 hhds. of salt, „ $4,30 per hhd. and the balance in money. How much money did he receive ? Ans. $38,80. 52. A man exchanges 760 gallons of molasses, at 371 cents per gallon, for 661 cwt, of cheese, at $4 per cwt. ; how much will be the balance in his favor ? Ans. $19. 53. Bought 84 yards of cloth, at $1,25 per yard; how much did it come to ? How many bushels of wheat, at $1,50 per bushel, will it take to pay for it? Ans, to the last, 70 bushels. 54. A man sold 342 pounds of beef, at 6 cents per pound, and received his pay in molasses, at 37; cents per gallon ; how many gallons did he receive ? Ans. 54,72 gallons. 55. A man exchanged 70 bushels of rye, at $,92 per Ans. 231. per bushel ? yard? bushel, for 40 bushels of wheat, at $1,37; per bushel, and received the balance in oats, at $,40 per bushel ; how many bushels of oats did he receive ? 56. How many bushels of potatoes, at 1 s. 6 d..per bushel, must be given for 32 bushels of barley, at 2.s. 6 d. Ans 53} bushels. 57. How much salt, at $1,50 per bushel, must be given in exchange for 15 bushels of oats, at 2 s. 3 d. per bushel ? Note. It will be recollected that, when the price and cost are given, to find the quantity, they must both be re. duced to the same denomination before dividing. Ans. 37 bushels. 58. How much wine, at $2,75 per gallon, must be given in exchange for 40 yards of cloth, at 7 s. 6 d. per Ans. 18,2 gallons. •59. There is a fish, whose head is 4 feet long; his tail is as long as his head and } the length of his body, and his body is as long as his head and tail; what is the length of the fish ? The pupil will perceive that the length of the body is { the length of the fish. Ans. 32 feet 60. A gentleman had 7 £. 17s. 6 d. to pay among his laborers; to every boy he gave 6 d., to every woman 8 d., and to every man 16 d.; and there were for every boy three women, and for every woman two men; I demand the number of each. Ans. 15 boys, 45 women, and 90 men. 61. A farmer bought a sheep, a cow, and a yoke of oxen for $82,50; he gave for the cow 8 times as much as for the sheep, and for the oxen 3 times as much as for the cow; how much did he give for each ? Ans. For the sheep $2,50, the cow $20, and the. oxen $60. 62. There was a farm, of which A owned 4, and Bf; the farm was sold for $1764; what was each one's share of the money? Ans. A's $504, and B's $1260. 63. Four men traded together on a capital of $3000, of which A put in ,B,C , and Db; at the end of 3 yrs., they had ined $2364 ; what was each one's share of the A's $1182 B's $ 591 C's $ 394 gain? 1 64. Bought a book, the price of which was marked $4,50, but for cash the bookseller would sell it at 334 per cent, discount; what is the cash price? Ans. $3,00 65. A merchant bought a cask of molasses, containing 120 gallons, for $42; for how much must he sell it to gain 15 per cent. ? How much per gallon? Ans. 10 last, $,401 66. A merchant bought a cask of sugar, containing 740 pounds, for $59,20; how must he sell it per pound to gain 25 per cent ? Ans. $,10 67. What is the interest, at 6 per cent., of $71,02 for 17 months 12 days? Ans. $6,178+ 68. What is the interest of $487,003 for 18 months ? Ans. $43,83+ It has been shown that the length of one side of a square multiplied into itself, will give the square contents. Hence to find the area, or superficial contents of a square when one side is given, Multiply the side of the square into itself. 69. There is a room 18 feet square ; how many yards of carpeting 1 yard wide will cover it ? Ans. 182=324 ft.=36 yards. 70. The length of one side of a square room is 31 feet; how many square feet in the whole room? Ans. 961 71. If the floor of a square room contain 36 square yards, how many feet does it measure on each side ? Ans. 18 ft. Note. This answer is obtained by finding the square root of the area 36 feet. A parallelogram, or oblong, is a four sided figure, having its opposite sides equal and parallel. To find the area of a parallelogram, 72. A garden in the form of a parallelogram is 96 feet long and 54 wide ; how many square feet of ground are contained in it? Ans. 5184 sq. ft. 73. What is the area of a parallelogram 120 rods long and 60 wide ? Ans. 7200 sq. rods. 74. If a board be 21 feet long, and 18 inches broad, how many square feet are contained in it? Ans. 31} sq. ft. A triangle is a figure bounded by three lines. If a line be drawn from one corner of a parallelogram to its opposite, (as in the Fig. A B,) it will divide it into two B equal parts of the same length and breadth as the parallelogram, but containing only half its surface. These two parts are triangles. Now supposing the А length of this parallelo. gram to be 6 feet, and its breadth 2, the area would be 12 feet. But the triangle will contain only half the surface, or 6 feet. Hence to find the area of a triangle, Multiply the length by half the breadth, or the breadth by half the length. 75. In a triangle 32 inches by 10, how many square inches? Ans. 160 sq. inches. 76. What is the area of a triangle whose base is 30 rods and the perpendicular 6 rods ? Ans. 90 rods. It has been shown that the length of one side of a cube raised to its third power will give the solid contents of the cube. Hence to find the solid contents of a cube, when one side is given, Multiply the given side into itself twice, or raise it to its 77. The side of a cubic block is 12 inches; how many solid inches does the block contain ? Ans. 123=1728. 78. One side of a cube is 59 feet; what are its solid contents ? Ans. 205379. 79. If a cube contains 614,125 cubic yards, what is the length of one side ? Ans. 85 yards. Note. This answer is obtained by finding the cube root of 614125. A circle is a figure contained by one line called the cir. cumference, every part of which is equally distant from a point within called the centre. The diameter of a circle, is a line drawn through the centre, dividing it into two equal parts. It is found by calculation, that the circumference of a third power: circle measures about 34 times as much as its diameter, or more accurately in decimals, 3,4159 times. Hence to find the circumference of a circle when the diameter is known, Multiply the diameter by 31. 80. If the diameter of a wheel is 4 feet, what is its cir. cumference ? Ans. 124 feet. 81. What is the circumference of a circle, whose di. ameter is 147 feet ? Ans. 462 feet. 82. What is the diameter of a circle, whose circum. ference is 462 feet ? Ans. 147 feet. 83. What is the area of a circle, whose diameter is 7 feet, and its circumference 22 feet? Ans. 384 sq. feet, 84. What is the area of a circle, whose circumference is 176 rods? Ans. 2464 rods. The area of a globe, or ball, is 4 times as much as the area of a circle of the same diameter. Hence, to find the area of a globe, 85. What is the number of square miles on the surface of the earth, supposing its diameter 7911 miles ? Ans. 7911 X 24863=196,612,083. To find the solid contents of a globe, or ball, Multiply its area by à part of its diameter. 86. How many solid inches in a ball 7 inches in diame. ter ? Ans. 1794. A cylinder is a round body, whose ends are circles, and which is of equal size from end to end. To find the solid contents of a cylinder, 87. There is a cylinder 10 feet long, the area of whose ends is 3 square feet ; how many solid feet does it contain ? Ans. 30. Solids which decrease gradually from the base till they come to a point, are called pyramids. The point at the top of a pyramid is called the vertex. A line drawn from |