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bought 3 less for the same money, the price of an orange would have been once and a half of the price he gave. What was the price of an orang??

158. A man divided his estate among his children as follows: to the first he gave twice as much as to the third, and to the second two thirds as much as to the first ; the portion of the second and third together was $1500. What was the portion of each?

159. A man bought 16 bushels of corn, and 20 bushels of rye for $30; and also 24 bushels of corn, and 10 of rye for $27. How much per bushel did he give for each ?

160. A man travelling from Boston to Philadelphia, a distance of 335 miles, at the expiration of 7 days, found that the distance which he had to travel was equal to of the distance which he had already travelled. How many

miles per day did he travel ?

161. A man left his estate to his three sous ? the first had $2000, the second had as much as the first, and į as much as the third, and the third as much as the other two. What was the share of each ?

162. A man when he married was three times as old as his wife ; 15 years afterwurds he was but twice as old. What was the

age of each when they were married ? 163. A grocer bought a cask of brandy, of which leaked out, and he sold the remainder, at $1.80 per gal., and by that means received for it as much as he gave.

How much did it cost him per gal. ?

164. A and B laid out equal sums of money in trade; A gained a sum equal to 1 of his stock, and B lost $225; then A's money was double that of B. What did each lay out ?

165. There is a fish whose head is 16 inches long, his tail is as long as his head and half the length of his body, and his body is as long as his head and tail. What is the length of the fish ?

166 There are three persons, A, B, and C, whose ages are as follows: A is 20 years old, B is as old as A and of the age of C, and C is as old as A and B both. What are the ages of B and C?

167. A person has two silver cups and only one cover. The first cup weighs 12 oz. If the first cup be covered, it will weigh twice as much as the second, but if the second cup be covered, it will weigh three times as much as the first. Required the weight of the cover and of the second cup.

168. Three persons do a piece of work; the first and second together do of it, and the second and third together do 1rWhat part of it is done by the second ?

169. A man bought apples, at 5 cents per doz., half of which he exchanged for pears, at the rate of 8 apples for 5 pears; he then sold all his apples and pears, at I cent each, and by so doing gained 19 cents. How many apples did he buy, and how much did they cost ?

170. A man being asked the hour of the day, answered that it was between 7 and 8, but a more exact answer being required, said the hour and minute hands were exactly together. Required the time.

171. What is the hour of the day when the time past from noon is equal to [ of the time to midnight ?

172. What is the hour of the day when of the time past from midnight is equal to of the time to noon ?

173. A merchant laid out $50 for linen and cotton cloth, buying 3 yards of linen for a dollar, and 5 yards of cotton for a dollar. He afterwards sold of his linen, and of his cotion for $12, which was 60 cents more than it cost him. How many yards of each did he buy?

174. A gentleman divided his fortune among his three sons, giving A 8 as often as B 5, and B 7 as often as C 4; the difference between the shares of A and C was $7500. What was the share of each ?

175. A tradesman increased his estate annually by $150 more than the fourth part of it; at the end of 3 years it amounted to $14811, . What was it at first ?

176. A hare has 50 leaps before a grey-hound, and takes 4 leaps to his 3 ; but two of the grey-hound's leaps are equal to 3 of the hare's. How many leaps must the grey-hound take to overtake the hare ?

177. A labourer was hired for 60 days, upon this condition, that for every day he worked he should receive $1.50 ; and for every day he was idle, he should forfeit $.50; at the expiration of the time he received $75. How many days did he work ?

178. A and B have the same income, A saves of his, but B, by spending 30£. a year more than A, at the end of 8 years finds himself 40£. in debt. What is their income, and what does each spend per year ?

179. A lion of bronze, placed upon the basin of a fountain, can spout water into the basin through his throat, his

eyes, and his right foot. If he spouts through his throat only, he will fill the basin in 6 hours ; if through his right eye only, he will fill it in 2 days; if through his left eye only, he will fill it in 3 days; if through his right foot only, he will fill it in 4 hours. In what time will the basin be filled if the water flow through all the apertures at once ?

180. A player commenced play with a certain sum of money ; at the first game he doubled his money, at the second he lost 10 shillings, at the next game he doubled what he then had, at the fourth game he lost 20 shillings; twice the sum he then had was as much less than 200s., as three times the sum would be greater than 200s. Required the sum with which he commenced play.

181. What is the circumference of a wheel of which the diameter is 5 feet ?

The circumference of a circle is 3.1416, or more exactly 3.1415926 times the diameter.

182. What is the diameter of a wheel of which the circumference is 17 feet ?

[blocks in formation]

D

E

A parallelogram is a figure with four sides in which the opposite sides L are parallel or equidistant F throughout their whole extent. In the adjacent figure A B C p is a parallelogram, and also A B E F. A B E F is a rectangular parallelogram, or a rectangle, and is measured as explained page 79. It is easy to see that A B C D is equal to A B EF, because the triangle B CE is equal to AD F. The contents of a parallelogram, then, is found by multiplying the length of one of its sides as a B, by the perpendicular which measures the distance from that side to its opposite, as e E.

The area

The triangle a is half the parallelogram A B C D. of a triangle, therefore, will be half the product of the base a B, by the perpendicular c E. If the perpendicular should fall without the triangle it will be the

A

E

B

same.

To find the area of any irregular figure, divide it into tri. angles.

To find the area of a circle, multiply half the diameter by half the circumference. Or multiply half the diameter into itself, and then multiply it by 3.1415926.

To find the solid contents of a round stick of timber, find the area of one end, and multiply it by the length.

If a round or a square stick tapers to a point, it contains just s as much as if it were all the way of the same size as at the largest end. If the stick tapers but does not come to a point, it is easy to find when it would come to a point, and what it would then contain, and then to find the contents of the part supposed to be added, and take it away from the whole.

183. What is the area of a parallelogram, of which one side is 13 feet, and the perpendicular 7 feet?

Ans. 91 square feet. 184. How much land is in a triangular field, of which one side is 28 rods, and the distance from the angle opposite that side to that side, 15 rods ?

Ans. 210 sq. rods, or 1 acre and 50 rods. 185. How many square inches in a circle, the diameter 10 inches ?

Ans. 78.54 + in. 186. How many solid feet in a round stick of timber 10 inches in diameter and 17 feet long ?

Ans. 9.272 + ft. 187. How many cubic feet of water will a round cistern hold which is 3 ft. in diameter at the bottom, 4 st. at top, and 5 ft. high?

Ans. 48.433 ft.

Geographical and Astronomical Questions.

188. The diameter of the earth is 7911.73 miles ; what is its circumference ?

189. The earth turns round once in 24 hours ; how far are the inhabitants at the equator carried each hour by this motion ?

190. The circumference of the earth is divided into 360 degrees ; how many miles in a degree ?

191. How many degrees does the earth turn in 1 hour ?

192. How many minutes of a degree does the earth turn in 1 minute of time?

193. What is the difference in the time of two places whose difference of longitude is 23° 43' ?

194. The longitude of Boston is 71° 4' W. of Greenwich, England. What is the time at Greenwich when it is 11 h. 13 min. morn. at Boston ?

195. The long. of Philadelphia is 759 09' W., that of Rome 12° 29 E. What is the tiine at Philadelphia, when at Rome it is 6 h. 27 min. even. ?

196. 'The earth moves round the sun in 1 year, in an orbit nearly circular. Its distance from the sun is about 95,000,000 of miles ; what distance does the earth move

every hour ?

197. The lat. of Turk's Island is 21° 30' N. and the long, is about the same as that of Boston. The lat. of Boston is 42° 23' N. How many miles apart are they?

198. The mouth of the Columbia river is about 1250 W. long., and Montreal is about 73} W. long., they are in about the same lat. A degree of longitude in that latitude is about 48.3 miles. How many miles are they apart, measuring on a parallel of latitude ?

Examples in Exchange. It is not necessary to give rules for exchange. There are books which explain the relative value of foreign and American coin, weights, and measures. The one may be exchanged to the other by multiplication or division.

199. What is the value of 13£. 14s. 8d. English or sterling money, in Federal money ?

It will be most convenient to reduce the shillings and pence to the decimal of a pound. For the value, see the table. 200. What is the value of $153.78 in sterling money

? 201. What is the value of 853 francs, 50 centimes, in Federal money?

202. What is the value of $287.42, in French money ?

203. What is the value of 523 Dutch gelders or florins, at 40 cents each, in Federal money ?

204. What is the value of $98.59 in Dutch gelders.

205. What is the value of 387 ducats of Naples, at $777) each, in Federal money?

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