chickens; for the turkeys he received $1.10 apiece, and for the chickens 50 cents apiece, and for the whole he received $51 60: how many were there of each? 84. A person hired a man and two boys; to the man he gave 6 shillings a day, to one boy 4 shillings, and to the other 3 shillings a day, and at the end of the time he paid them 104 shillings: how long did they work ? 85. Divide $6471 among three persons, so that as often as the first gets $5, the second will get $6, and the third $7. 86. Two partners have invested in trade $1600, by which they have gained $300; the gain and stock of the second amount to $1140: what is the stock and the gain of each? 87. What is the height of a tower that casts a shadow 75.75 feet long, at the same time that a perpendicular staff 3 feet high, gives a shade of 4.55 feet in length ? 88. A can do a certain piece of work in 3 weeks; B can do 3 times as much in 8 weeks; and C can do 5 times as much in 12 weeks in what time can they all together do the first piece of work? 89. Two persons pass a certain point, at an interval of 4 hours; the first traveling at the rate of 11, and the second 171⁄2 miles an hour: how long, after passing the fixed point, and how far, will the first travel before he is overtaken by the second? 90. Three persons engage in trade, and the sum of their stock is $1600. A's stock was in trade 6 months, B's 12 months, and C's 15 months; at the time of settlement, A receives $120 of the gain, B $400, and C $100: what was each person's stock? 91. A, B, and C, start at the same time, from the same point, and travel in the same direction, around an island 73 miles in circumference. A goes at the rate of 6 miles, B 10 miles, and C 16 miles per day in what time will they all be together again? 92. What length of wire, of an inch in diameter, can be drawn from a cube of copper, of 2 feet on a side, allowing 10 per cent. for waste? 93. A person having $10000 invested in 6 per cent. stocks, sells out at 65, and invests the proceeds in 5 per cents at 82: what will be the difference in his annual income? 94. In order to take a boat through a lock from a certain river into a canal, as well as to descend from the canal into the river, a volume of water is necessary 46 yards long, 8 yards wide, and 2 yards deep: how many cubic yards of water will this canal throw into the river in a common year, if 40 boats ascend and 40 descend each day, except Sundays and eight holidays? 95. A company numbering sixty-six shareholders have constructed a bridge which cost $200000: what will be the gain of each partner at the end of 22 years, supposing that 6400 persons pass each day, and that each pays one cent toll, the expense for repairs, &c., being $5 per year for each shareholder? 96. Five merchants were in partnership for four years, the first put in $60, then, 5 months after, $800; the second put in first $600, and 6 months after $1800; the third put in $400, and every six months after, he added $500; the fourth did not contribute till 8 months after the commencement of the partnership; he then put in $900, and repeated this sum every 6 months; the fifth put in no capital, but kept the accounts, for which the others agreed to allow him $800 a year, to be paid in advance, and put in as capital. What is each one's share of the gain, which was $20.000? 97. A general arranged his army in a solid mass, aud in a square form, and had 44 men over. If he increases the side of the square by 1 man, and makes a new square on this line. he will require 49 men to complete it: how many men had be? 98. A, B, and C, are to share $987 in the proportion of ,, and respectively; but by the death of C, it is required to divide the whole sum proportionally between the other two: what will each have? 99. A lady going out shopping, spent at the first place she stopped, one-half her money, and half a dollar more; at the next place, half the remainder, and half a dollar more; and at the next place, half the remainder, and half a dollar more, when she found that she had but three dollars left: how much had she when she started? 100. If a pipe of 6 inches discharges a certain quantity of fluid in 4 hours, in what time will 4 pipes, each of 3 inches bore, discharge twice that quantity? 101. A man bought 12 horses, agreeing to pay $40 for the first, and in an increasing arithmetical progression for the rest, paying $370 for the last what was the difference in the cost, and what did he pay for them all? 102. A bill for goods, amounting to $15000, is to be paid for in three equal payments without interest; the first in 4 months, the second in 6 months, and the third in 9 months, money being worth 7 per cent.: how much ready money ought to pay the debt? 103. If an iron bar 5 feet long, 24 inches broad, and 13 inches thick, weigh 45 pounds, how much will a bar of the same metal weigh, that is 7 feet long, 3 inches broad, and 24 inches thick? 104. A market woman bought a certain number of eggs at the rate of 4 for 3 cents, and sold them at the rate of 5 for 4 cents, by which she made 4 cents: what did she pay apiece for the eggs? What did she make on each egg sold? many did she sell to gain 4 cents? 105. A person passed youth, 5 years more than How of his life in childhood, of it in of it in matrimony; he then had a son, whom he survived 4 years, and who reached only } the age of his father: at what age did he dic? 106. A well is to be stoned, of which the diameter is 6 feet 6 inches, the thickness of the wall is to be 1 foot 6 inches, leaving the diameter of the well within the wall 3 feet 6 inches; if the well is 40 feet deep, how many cubic feet of stone will be required? 107. A surveyor measured a piece of ground in the form of a rectangle, and found one side to be 37 chains, and the other 42 chains 16 links: how many acres did it contain? 108. A farmer bought a piece of land for $1500, and agreed to pay principal and interest in 5 equal annual instalments: if the interest was 7 per cent., how much was the annual payment? E, F, and G hours; G, H, 109. A fountain has four receiving pipes, A, B, C, and D; A, B, and C will fill it in 6 hours; B, C, and D in 8 hours; C, D, and A in 10 hours; and D, A, and B in 12 hours: it has also 4 discharging pipes, E, F, G, and II; will empty it in 6 hours; F, G, and II in 5 and E in 4 hours; II, E, and F in 3 hours. fountain full of water, and all the pipes open, in what time would it be emptied ? Suppose the 110. If a ball 2 inches in diameter weighs 5 pounds, what will be the diameter of another ball of the same material that weighs 78.125 pounds? 111. A gives B his bond for $5000, dated April 1st, 1861, payable in ten equal annual instalments, the first payment of $500 to be made April 1st, 1862. Afterward, A agreed to take up his bond on the first day of April, 1863. He was to pay, on that day, the instalment due on the first of April, 1862, with interest at 7 per cent., the instalment due April 1st, 1863, and to be allowed compound interest, at 7 per cent., to be computed half-yearly, on each of the subsequent payments: what sum, on the first day of April, 1863, will cancel the bond? MENSURATION. 405. MENSURATION is the art of measuring, and embraces all the methods of determining the contents of geometrical figures. It is divided into two parts, the Mensuration of Surfaces, and the Mensuration of Volumes. MENSURATION OF SURFACES. 1 foot. 406 Surfaces have length and breadth. They are measured by means of a square, which is called the unit of surface. A SQUARE is the space included between four equal lines, drawn perpendicular to each other. Each line is called a side of the square. each side be one foot, the figure is called a square foot. If The number of small squares that is contained in any large square, is always equal to the product of two of the sides of the large square. As in the figure, 3 × 3 = 9 square feet. The number of square inches contained in a square foot is equal to 12 × 12 = 144. 1 foot. If the sides of a square be each four feet, the square will contain sixteen square feet. For, in the large square there are sixteen small squares, the sides of which are each one foot. Therefore, the square whose side is four feet, contains sixteen square feet. Triangle. 407. A TRIANGLE is a figure bounded by three straight lines. Thus, ACB is a triangle. The lines BA, AC, BC, are called sides; and the corners, B, A, and C, are called angles. The side AB is the base. When a line like CD is drawn, making the angle CDA equal to the angle CDB, then CD is said to be at right angles to D |