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 money 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, 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? Stating the question by proportion, we obtain (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? 211 The answer, found as before, is 21 × 6 = 251. 6 24105 Now, if 191 oxen in 18 weeks, eat 24 acres with 4 weeks' growth, and 251 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, (3.) If 6 oxen in 18 weeks eat 5 weeks' growth, how many oxen in the same time will eat 9 weeks' growth? 6 The answer is 104. We have already found that 251 oxen in 18 weeks, will eat 24 acres with 9 weeks' 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 4 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 196. The square root of of 3 times age is 4. What is his age ? turn in 17 miles? of 3 times a man's * Any number that is equal to the sum of all its aliquot parts, is called a PERFECT NUMBER. The only perfect numbers known, are, 28 8128 33550336 8589869056 137438691328 2305843008139952128 2417851 639228158837784576 9903520314282971830448816128 197. What is the difference between the area of a circle whose circumference is 1572 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. 663 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 13 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, 204. Two vessels are 30 miles apart, and are sailing, the first with, and the second against a current of 2 miles per hour. In still water, each would sail 7 miles per hour. In what time will they meet, and what will be the distance of each from its present position? 205. At 6 per cent, compound interest, what annual payment will extinguish a debt of $3500000 in 50 years? 206. The Winchester bushel is 18 inches wide and 8 inches deep. What are the dimensions of a tub of similar form that holds 64 bushels? 207. How much should an annual rent be increased, to amount in 17 years, to the same as $2500 at 6 per cent. compound interest? 208. At what time between half past 7 and 8 o'clock, are the hour and minute hands exactly 13 minutes apart? 209. An estate of $4896 is to be divided in that the widow shall receive as much as the son of 2 times as much as the daughter. each receive? such manner son, and the What must 210. Three men bought a grindstone 50 inches in diameter, for which A. paid 75 cents, B. $1.50, and C. $2.00. What part of the diameter ought each to wear away, allowing the diameter of the axle to be 2 inches? 211. A vessel of 400 tons has a keel 48 feet long. What length of keel has a vessel of 750 tons, that is built on the same model? 212. The commissioners of a certain county are about building a new court house, which will cost $75000. They hire money for the purpose at an annual interest of 5 per cent, and propose to pay the debt thus incurred by 50 equal annual instalments. What amount must be paid each year? 213. Sold a quantity of sugar for $150, thereby losing 15 per cent., but I ought to have gained as much per cent. as the sugar cost. What was my total loss? 214. An estate of $20000 is to be divided between two sons in the following manner: the elder is to receive $100 the first month, $300 the second month, &c., in arithmetical progression and the younger is to receive $1000 per month, until the whole is paid. What is the share of each, and how long will they be in receiving it? 215. What is the quotient of 90g times half a dozen dozen, divided by 1214 times six dozen dozen? 216. A ladder standing upright against a wall reaches the top, but the foot being removed 12 feet from the wall, it reaches to a point 6 feet from the top. Required the length of the ladder, and the height of the wall. 217. There are two cannon balls, one weighing 28 pounds, and the other 9 pounds. What is the diameter of the greater that of the less being 5 inches? 218. If one-third of six were three, What would the fourth of twenty be? 219. A man has a perpetual income of $350 per annum, which he desires 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 16 years? 220. A man hires a farm for 15 years, and expends $1200 on improvements which yield him 7 per cent. per annum. What is the present worth of the gain or loss on his expenditure? 221. Find the value of x from the equation x = 5. 222. A merchant received on consignment, three bales of sheeting, marked A., B., and C. A. contained 420 yards of a quality 15 per cent. better than B., B. contained 380 yards of a quality 10 per cent. poorer than C., and C. contained 450 yards. The whole were sold together at 12 cents per yard; how much should be credited to each, after deducting 2 per cent. commission? 223. An estate was offered for sale for $12000, but the price appearing too high, the tenant took a lease for 25 years at $800 per annum. How much did he gain or lose, estimating compound interest at 6 per cent.? 224. Reduce √4 × √7 to a continued fraction. 225. A man wishes to give his son, who is now 5 years old, $20000 when he is 21 years old. How much must he invest annually for that purpose, at 6 per cent. compound interest? 226. A farmer has a stack of hay, from which he sells a quantity which is to the quantity remaining, as 4 to 5. He |