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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 2 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
* ,95 142
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 66} cwt. of cheese, at $4 per cwt. ; how much will be the balance in his favor ? Ans. $19.
53. Bought 81 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 374 cents per gallon ; how many gallons did he receive ?
Ans. 54,72 gallons. 55. A man exchanged 70 bushels of rye, at $,92 per
per bushel ?
bushel, for 40 bushels of wheat, at $1,37; per bushel, and received the balance in oats, at $,40 per
how many bushels of oats did he receive ?
Ans. 231. 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 534 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 reduced to the same denomination before dividing.
Ans. 3; 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 yard ?
Ans. 1811 gallons. 59. There is a fish, whose head is 4 feet long; his tail is as long as his head and į 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 į the length of the fish.
Ans. 32 feet. 60. A gentleman had 7 £. 17 s. 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, 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 J,B,C, and Dių; at the end of 3 yrs., they had gained $2364 ; what was each one's share of the gain?
B's $ 591
C's $ 394
64. Bought a book, the price of which was marked $4,50, but for cash the bookseller would sell it at 33} 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. to last, $,401
.66. A merchant bought a cask of sugar, containing 740 pounds, for $59,20; how must he selt 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?
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
circle measures about 31 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. 381 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 & part of its diameter.
86. How many solid inches in a ball 7 inches in diame. ter ?
Ans. 1793. 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 30 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