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miles in 3 hours : B. goes 54 miles in 2 hours. How far will each travel before they meet ? 164. Three men purchase a vessel. A. pays 1 , B. 3

io and C, the remainder, which was $2550. What was C.'s share, and how much did A. and B. pay?

165. A stone, dropped from the top of a precipice, reached the ground in 3 seconds. What was the height ?

166. What is the least number, which, being divided by 2, 3, 4, 5, 6, 7, 8, or 9, leaves a remainder 1 ?

167. The ages of a man and wife at the time of marriage, were in the ratio of 11 to 9 8 years afterwards they were as 15 to 13. Required the age of each on the wedding day. 168. Find the value of x in the equation,

25 + 4.x3

- 2x2 4. 169. What is the sum of 13 terms of a geometrical progression, whose first term is 2181, and ratio } ?

170. A grazier having two equal flocks of sheep, sells 17 from one, and 95 from the other, when he finds one flock contains three times as many as the other. How many were there originally in each?

171. A footman engaged to serve a year for $72 and a livery, but leaving at the end of 5 months, he received only $24 and the livery. What was the price of the suit ?

172. At the commencement of business, A. had twice as much money as B., but at the expiration of a year, A. hav. ing gained 179 per cent., and B. having lost $500, A.'s stock was 2 times B.'s. Required the original stock of each ?

173. A thief travelling 12} miles in 2} hours, has been absent 7$ hours, when a constable starts in pursuit, going 11 miles to the thief's 10. In what time will the thief be overtaken ?

174. A cistern has 4 pipes, the first of which will fill it in 2 hours, the second in 21 hours, the third in 24 hours, and the fourth in 3} hours. In what time will the cistern be filled, if they are all opened at once ?

175. Bought a piece of cloth, which proved to be but as long as it was marked, but I find that if I sell it at $5.94

per yd, I shall gain 10 per cent on the prime cost. What did I give per yard ?

176. A person left by will to his widow $250 per annum, to his eldest son $6500, to his youngest son $6000, and to his daughter $5500. He had been in business 18 years, commencing with $1500. How much did he save per an. num, his earnings having been invested at 5 per cent. compound interest ?

177. Bought 29 pieces of broadcloth, each 314 yd., at $4.75 per yd., and 37 pieces of cassimere, each 34$ yd., at $1.50 per yd., the whole cost to be divided into 3 equal pay, ments at 4, 8, and 12 months. How much should be de. ducted from the bill upon paying cash, if money is worth 8 per cent. per annum ?

178. My expenditure having exceeded my income by 15 per cent., I find that by saving of my income for the succeeding year, I can supply the deficiency with interest, and have $4.60 left. What is my income ?

179. Find 11 terms of a Harmonical Progression, two of the terms being 4 and 8.

180. Bought goods amounting to $2500, at 12 months credit, at the end of 3 months $400 were paid, at the end of 6 months $500, and at the end of' 8 months $200. When will the balance of $1400 become due ?

181. Two persons of the same age conversing together, one said to the other, “ My eldest son is just half as old as I am, and if 88} is added to the continual product of our three ages, the sum will be 52000.” What was the

age

of each ?

182. What is the present worth of the reversion of an estate valued at $10000, which comes into possession on the death of an individual now 37 years of age, the average duration of life at that age, being 29 years ?

183. What sum of money must a man lay up annually, commencing at 21 years of age, to be worth $30000 when he is 50 years old, the investments being made at 6 per cent, compound interest ?

184. What sum of money at 6 per cent, simple interest,

saved annually, will amount to the same as the preceding example?

185. A., B., and C. meeting on the road, agreed to dine together. A. furnished 5 loaves, B. 3 loaves, and C., having no bread, paid 8 pieces of money for his share. How should the rnoney

be divided between A. and B.? 186. A horse is tied to a stake, so that he can graze & of an acre. What is the length of the rope ?

187. A mechanic hired a certain number of men at $1.00 per day, s as many at 75 cents, and $ as many at 50 cents as at 75 cents. What was the number of each, the daily wages of the whole being $21.00 ?

188. How many drops of water would fill a demijohn that holds 6 gal. 1 qt. 1 pt. ?

189. If 12 oxen eat 3} acres of grass in 4 weeks, and 21 oxen eat 10 acres of the like pasture in 9 weeks, how many oxen will eat 24 acres in 18 weeks, the grass being at first equal on every acre, and growing uniformly ?

This example, which is taken from Newton's Universal Arithmetic, can be solved most readily by making three distinct questions.

(1.) If 12 oxen eat 10 acres of grass, with the growth, in 4 weeks, how many oxen will eat 24 acres, with 4 weeks' growth, in 18 weeks ? 8

Stating the question by proportion, we obtain 12 x 4 x 2

19 oxen, for 12

5 418

the answer.

2 R4 165 (2.) If 21 oxen eat 10 acres with the growth, in 9 weeks, how many oxen will eat 24 acres with 9 weeks' growth, in 18 weeks ? 21

The answer, found as before, is 18

21 x 6

5 6 84195

Now, if 191 oxen in 18 weeks, eat 24 acres with 4 weeks' growth, and 25} oxen in the same time, eat the same number of acres with 9 weeks' growth, 5 weeks' growth on 24 acres will support 6 oxen 18 weeks. Then,

253

(3.) If 6 oxen in 18 weeks eat 5 weeks' growth, how many oxen in the same time will eat 9 weeks' growth ? 61

The answer is 104. We have already found that

25} oxen in 18 weeks, will eat 24 acres with 9 weeks' 95

growth, and if we add the number which would eat the growth of the remaining 9 weeks, we obtain 36 oxen for the answer sought.

190. A road has been constructed through a farmer's land, taking 14 acres, worth $75 per acre. In addition to the loss of his land, he is obliged to expend $100 in building a fence, which must be renewed every 12 years.

What damages should he receive, money being worth 6 per cent. compound interest ?

191. If 15 oxen eat 43 acres of grass in 2 weeks, and 24 oxen eat 14% acres in 5 weeks, how many oxen will eat 48 acres in 8 weeks, the grass being at first equal on every acre, and growing uniformly ?

192. Find 6 weights with which any number of pounds, from 1 to 364, can be weighed.

193. What is the sum of all the divisors of 33550336 ?*

194. Four men bought a grindstone 40 inches in diameter, each contributing an equal amount. How much of the diameter ought each to grind away?

195. If the wheel of a carriage turn once and a half in going a rod and a half, how often will it turn in 177 miles ?

196. The square root of } of 3 times of 3 times a man's age is 4. What is his

age

?

* Any number that is equal to the sum of all its aliquot parts, is called a PERFECT NUMBER. The only perfect numbers known, are,

6 28 496 8128 33550336 8589869056 137438691328 2305843008139952128 2417851639228158837784576 9903520314282971830448816128

197. What is the difference between the area of a circle whose circumference is 157,

To feet, and the area of the greatest square that can be inscribed in it ?

198. A. and B. are on opposite sides of a field that is 120 rods in diameter, and commence travelling around it in the same direction. How many times will each go round the field before the slower is overtaken, A. going 39 rods in 3 minutes, and B. 66; rods in 5 minutes ?

199. What number is that which is divisible by 11, but if divided by any number less than 11, leaves 1 remainder ?

200. The Peak of Teneriffe is about 2} miles high. How far may it be seen at sea from the main-top of a vessel, 60 feet above the surface of the water ?

201. A wall 5} ft. high, and 1} ft. thick, is to be built around a garden that is 180 ft. long, and 60 ft. wide, leaving space for two gates, each 6} ft. wide. How many bricks, each 8 in. long, 4 in. wide, and 2 in. thick, will be required ? · 202. A man sold a horse for $65.25, thereby gaining as much per cent. as the horse cost him.

What did he give for the horse ?

203. “One evening I chanced with a tinker to sit, Whose tongue ran a great deal too fast for his wit : He talked of his art with abundance of mettle, So I asked him to make me a flat bottomed kettle. Let the top and the bottom diameters be In just such proportion as five is to three : Twelve inches the depth I proposed, and no more, And to hold in ale gallons, seven less than a score. He promised to do it, and straight to work went, But when he had done it he found it too scant. He altered it then, but too big he had made it, And when it held right, the diameters failed it : Thus making it often too big and too little, The tinker at last had quite spoiled his kettle, But declared he would bring his said promise to pass, Or else that he'd spoil every ounce of his brass. Now to keep him from ruin, I pray find him out The diameter's length, for he'll ne'er do't without.” 204. Two vessels are 30 miles apart, and are sailing, the

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