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126. At the commencement of business, A had as much money as B; but at the expiration of a year, A having gained 20 per cent., and B having lost $1200, they had equal sums of money. What was the original stock of each?

127. Three persons formed a partnership for the transaction of business. A advanced of the capital stock, B, and C the remainder. It is required to divide the gain, which was $3500, justly among them.

128. Two men purchased a farm in company. A paid $3250, B paid $2750. What yearly income, and what per cent., will each derive from the investment, the farm renting for $625, and the taxer and expenses for repairs being $125 a year?

129. A mechanic hired a large house for one year, with the liberty of letting any part of it. At the end of 3 months he admitted A, and at the end of 6 months he admitted B, as joint tenants, each occupying equal portions of the house. How should the rent, which was $560, be divided among them?

130. If A can reap an acre of wheat in 94 hours, B in 10 hours, and C in 103 hours, in what time can they reap an acre if they work together?

131. A farmer having two equal flocks of sheep, sells 18 sheep from one flock, and 30 from the other; after which he finds twice as many left in one flock as in the other. How many were there originally in each flock?

132. A mechanic hired a certain number of men at $1.75 a day, as many at $1.50, and as many at $1.35 as at $1.50. What was the number of each, the daily wages of the whole being $42?

133. A trader having increased his capital by of itself, lost of what he then had; he afterwards gained a sum equal to of the remainder, when he was worth $5860. What was his capital?

134. The age of A is that of B, and the age of C is that of A and the sum of all their ages is 120 years. What is the age of

ach?

135. A merchant retired from business when he had passed of his life, during of which period he had been engaged in trade, having commenced at the age of 21. At what age did he die? 136. What is a mean proportional number between the numbers 36 and 144?

NOTE. A mean proportional between two given numbers is a number whose second power is equal to the product of those numbers. Hence the square root of their product must be the mean proportional required.

137. What is a mean proportional between 25 and 289 ?

138. A circular pavement contains 15625 square yards; what must be the length of the side of a square which shall contain the same number of square yards?

NOTE. If we extract the square root of any given number, the root must be the length of the side of a square which shall contain the same number.

139. There is a triangular lot of land which contains 5625 square feet; what must be the length of the side of a square lot that shall contain the same number of square feet?

140. It is required to lay out 100 acres of land in the form of a rectangle, which shall be twice as many rods in length as it is in breadth; what must be its length and breadth?

NOTE. If we extract the square root of one half the number of square rods in the given quantity of land, this root must be the required breadth.

141. Suppose I wish to set out an orchard of 600 trees so that the length shall be to the breadth as 3 to 2; how many trees must it be in breadth, and how many in length?

142. There is a right-angled triangle, whose base is 40 feet, and its perpendicular 30 feet; what is the length of its hypothenuse?

143. There is a right-angled triangle, the hypothenuse of which is 60 feet, the base 48 feet; what is the length of the perpendicular? 144. There is a right-angled triangle, the hypothenuse of which is 90 feet, and the perpendicular 54 feet; what is the length of the base?

145. What must be the length of a ladder that will reach a window 24 feet from the ground, the foot of the ladder being placed 7 feet from the wall of the building?

146. A line 244 feet in length will reach from the top of the walls of a fort, situated on the bank of a river, to its opposite side; the river is known to be 240 feet in width; what is the height of the walls of the fort?

147. There is a rectangular school-room 72 feet in length, and 44 feet in width; what is the number of feet from the centre of the room to either corner?

148. A and B start from the same place; A travels 121 miles directly north, and B, in the same time, travels 144 miles directly west. How many miles are they from each other?

149. There is a room 18 feet in length, 16 feet in breadth, and 12 feet in height; what must be the length of a line that will reach from a corner at the bottom to its opposite diagonal corner at the top?

150. The bushel measure is 18.5 inches in diameter, and 8 inches in depth; and contains 2150.4 cubic inches. What must be the length of the side of a cubic box which will contain the same quantity?

NOTE. If we extract the cube root of any given number, the root must be the length of the side of a cube which will contain the same quantity.

151. A carpenter was directed to make a cubical bin that should contain 25 bushels; what was its length, breadth and depth?

152. What must be the length of a bin that will contain 96 bushels of grain, the width being 4 feet, and depth 4 feet 6 inches? 153. What must be the depth of a brick cistern, 6 feet in diameter, that will contain 1260 beer gallons?

154. There is a cylindrical cistern 6 feet in depth, containing 756 gallons of water; what is the diameter of the cistern?

155. If the side of a square piece of land be 72 feet, what must be the side of a square piece 4 times as large?

156. There is a square township of new land, each side of which measures 1920 rods; what must be the side of a square piece of land that shall contain as many square rods?

157. There is a circular pavement 15 feet in diameter; what must be the diameter of a circle which shall contain 8 times the number of square feet?

158. If a hogshead of water be discharged through a pipe of 2.5 inches in diameter in 12 minutes, what must be the diameter of another pipe, which will discharge 4 hogsheads in the same time?

159. There is a cubic box whose side is 18 inches; what must be the side of a cubic box which shall contain 8 times as many cubic inches?

160. There is a cubic block of granite whose side is 24 inches; what must be the side of a block that shall contain

cubic inches?

as many 161. If the diameter of a globe be 12 inches, what must be the diameter of a globe that shall contain as many cubic inches?

162. If the diameter of a globe be 8 inches, what must be the diameter of a globe that shall contain 64 times as many cubic inches?

163. If a cannon ball 3 inches in diameter weigh 4 pounds, what will a ball of the same metal weigh, the diameter of which is 6 inches?

164. If a cubic block of granite, whose side is 12 inches, weigh 166 pounds, what will a cubic block of the same kind weigh, the side of which measures 36 inches?

165. If a cube of Swedish iron, whose side is 12 inches, weigh 486.876 pounds, what will be the weight of a cube of the same kind of iron, the side of which is 18 inches?

166. What sum of money must a man save annually, commencing at 21 years of age, to be worth $20000 when he is 45 years old. the investments being made at 6 per cent. compound interest?

167. What is the present worth of an estate valued at $12000, which is to come into possession on the death of a person who is now 50 years old, the average duration of life at that age being 21 years?

168. A man has a perpetual annual annuity of $360 dollars, which he wishes to exchange for a life annuity. Supposing money to be worth 6 per cent. a year, what annuity must he receive, it being probable that he will live 21 years?

169. Which is of the greater value, the income of an estate of $650 a year for 12 years, or the reversion of the same estate forever, at the expiration of the 12 years, estimating compound interest at 6 per cent.?

170. A man wishes to give his son, who is now 9 years old, $10000 when he shall be 21 years old. What sum must he invest annually for that purpose, estimating compound interest at 6 per cent. ?

171. What must be the diameter of a circular pond, which shall contain times as much surface as a pond 12 rods in diameter ?

172. A bookseller purchased 20000 quills, for three fourths of which he paid $4.25 a thousand, and for the remainder 75 cents a hundred; he kept 500 for his own use, and sold the rest at $5.62} a thousand. What per cent. profit did he make?

173. A merchant purchased goods to the amount of $1200, which he sold at a loss of 15 per cent.; he then invested the proceeds in other goods, which he sold at a profit of 20 per cent. What per cent. profit did he make on the two transactions?

174. There are two cannon balls, one weighing 32 pounds, and the other 12 pounds. What is the diameter of the greater,-that of the smaller being 5 inches?

175. What will be the expense of painting a conical spire, of which the height is 60 feet, and the diameter at the base is 10 feet, at 15 cents a square yard?

176. A gentleman has a bowling green 300 feet long and 200 feet broad, which he wishes to raise a foot higher by means of the earth dug out of a ditch which surrounds it. To what depth must the ditch be dug, supposing its breadth to be 8 feet?

177. There is an island 60 miles in circumference, and 3 men start together and travel the same way around the island; A travels 4 miles an hour, B 8, and C 9. In what number of hours will they be together again, and what number of miles will each have travelled?

178. What would be the cost of excavating the New York and Erie Canal, supposing it to be 360 miles in length, 40 feet in width at the surface, 32 feet in width at the bottom, and 6 feet in depth, at 25 cents a cubic yard?

179. A market-woman bought a number of apples at 2 for a cent, and the same number at 3 for a cent, and having sold them all at the rate of 5 for 2 cents, found she had lost 4 cents. What number of apples did she purchase?

180. A gentleman purchased 2 pieces of cloth, which together measured 36 yards. Each piece cost as many cents per yard as there were yards in the piece, and their comparative value was as 4 to 1. What was the length of each piece?

181. A shepherd, in time of war, fell in with a party of soldiers, who plundered him of half his flock, and half a sheep over; afterwards, a second party met him, who took half of what he had left, and half a sheep over; and soon after this, a third party met him, and used him in the same manner; and then he had only five sheep left. It is required to find what number of sheep he had at first.

182. A man, to please his children, brings home a number of apples, and divides them as follows: To the first and eldest of his children he gives the half of the whole number, less 8; to the second, the half of the remainder, again diminished by 8; and he does the same with the third and fourth. After this, he gives the 20 remaining apples to the fifth. How many apples did he bring home?

TABLE OF GOLD AND SILVER COINS.

Art. 266. Coins of all nations, met with in circulation, that have been issued within a century; showing their real worth in dollars and cents, also their commercial value in trade.

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