figs at $4.16 per cwt. allowing a deduction of 14 pounds per cwt. for boxes? Ans. $552.37. (0.) $572 will gain in 13 months? 176. In what time will $858 gain as much interest as Ans. 83 months. (0.) 177. If 6 pounds of rice cost 63 cents, and 18 pounds of rice are worth as much as 7 pounds of coffee, what are 78 pounds of coffee worth? Ans. $19.44. (0.) 178. If 83 yards of cloth cost $33.30, what will 62 yards, 2 quarters cost at the same rate? Ans. $253.12. (6.) 179. What will 43 pieces of cloth, each containing 40 yards, come to at 62 cents per yard? Ans. $1075. (0.) 180. How many yards of silk may be bought for $37.62, if of a yard cost 66 cents? Ans. 42 yds. 3 qrs. (3.) 181. If a ship sail 924 miles in 93 hours, in how many hours would she sail 65 miles, at that rate? Ans. 6,913 hours. (13.) 1620 182. If 3 pounds of sugar cost 25 cents, and 15 pounds of sugar are worth 8 pounds of coffee, how much will 96 pounds of coffee cost? Ans. $15. (0.) 183. If 7 cwt. 1 quarter of sugar cost $64.96, what will be the price of 4 cwt. 2 quarters, at the same rate? Ans. $40.32. (3.) 184. How many yards of carpeting, 3 quarters of a yard wide, are sufficient to cover the floor of a room that is 18 feet wide and 60 feet long? Ans. 160 yds. (0.) 185. If 6 yards of cloth cost $23, what will 9 yards, 3 quarters cost, at that rate? Ans. $34.50. (0.) 186. If a man perform a journey in 22 days, when the days are 12 hours long, how many days will it take him to perform the same journey when the days are 15 hours long, if his rate of travelling be the same? Ans. 18 days. (0.) 187. If 144 cwt. be carried 200 miles for $32, how many pounds can I have carried 72 miles for the same money? Ans. 4433 pounds. (5.) 188. A goldsmith sold a tankard for £10 12s. at the rate of 5s. 4d. per ounce; I demand the weight of it. Ans. 39 oz. 15 dwts. (3.) 189. A gave B 5 cwt. of sugar, at 6 cents a pound, for a quantity of cinnamon, at $1.28 a pound; how many pounds Ans. 26 lbs. 4 oz. (3.) of cinnamon did A receive? 190. If $783.42 gain $27.45 in 12.75 months, what principal will gain the same amount of interest in 15.3 months? Ans. $652.85. (0.) The common method will require 70 figures. 191. If a man drink daily a dram which costs 64 cents, how much will he expend in this manner in 20 years of 365 days each? Ans. $456.56, (6.) the transaction? 192. If I invest $1250 in wood, at $4.25 a cord, and sell it at an average of $5.10 a cord, how much do I make by Ans. $250. (0.) 193. Laid out £250 in cloth, at 30s. per yard, and afterwards finding it was damaged, sold it at 26s. 3d. per yard, how much did I lose? Ans. £31 5s. (0.) 194. What is the cost of 37 tons, 14 cwt. 2 quarters, 14 pounds of hemp, at £89 6s. 8d. per ton? Ans. £3370 13s. 2d. (10.) 195. E has flannel worth 50 cents a yard for ready money, but in trade he will charge 56 cents. 314 cents a yard in ready money, at muslin to be rated in trade? H has muslin worth what price ought the Ans. 35 cts. (0.) 196. A bankrupt owes in all $26,789, and delivers пр his whole property amounting to $11,739, how much does that creditor receive to whom he owes $1869 ? Ans. $819. (6.) 197. If 3 times 3 pounds of sugar cost 1 times 12 dolpounds cost? lars, what will of of 12 Ans. 37 cents. (0.) 198. If a mill grind 1811 bushels of corn in one hour and 18 minutes, in what time will it grind 690 bushels? 7 Ans. 48 hours. (0.) 199. A merchant bought of a company's stock, for $89,900, what would be the price of of the stock, at the same rate? Ans. $111,600. (0.) 200. If of a yard of cloth cost £7, what will of a yard come to at the same rate ? Ans. 3s. 4d. (0.) 201. A person having of a sloop, sells of his share for £319, what was the value of the whole sloop, at that rate? £598 2s. 6d. (4.) 159 202. A merchant sold 53 pieces of cloth, each containing 24} yards, at $63 per yard, what did he get for the whole? Ans. $888. (0.) 203. Bought a cask of wine, containing 126 gallons, at 40 cents a gallon; but by accident 18 gallons leaked out; at what price per gallon must the remainder be sold to gain 12 per cent. on the whole first cost? Ans. 52 cts. (0.) 204. How much wine at $1.26 per gallon must I give for 26.cwt. 2 quarters, 14 pounds of raisins, valued at $9.44.4 per cwt.? Ans. 199 gals. 247 qts. (16.) To solve the above question in the ordinary way, and reduce the fraction to its lowest terms, will require 151 figures, being 135 figures more than our solution requires. 205. If a Spanish dollar weighs 17 pennyweights, 6 grains, what will be the weight of $480? Ans. 34 lbs. 6 oz. (0.) 206. The circumference of the earth, measured on the equator, being 24,896.16 miles, what is the length of an arc 57° 17' 45"? Ans. 3962.35065 miles. (20.) Here our solution requires 20 figures, the common method will require 155, making a difference of 135 figures. 207. How much sugar at 8d. per pound must I give for 20 cwt. of tobacco, at £3 per cwt.? Ans. 16 cwt. 8 lbs. (3.) 208. My tailor informs me it will take 104 square yards of cloth to make me a full suit of clothes. The cloth I am about to purchase is 13 yards wide, and on sponging it will shrink 5 per cent. in width and length; how many yards of the above cloth must I purchase for my new suit? Ans. 66 Solution. Yds. 4 41 A$ 8 19 20 1083 yds. Here 10 yards=41 which we place at the head of the line. Now if the cloth were a yard wide, then every yard in length would contain one square yard; but being 13 yards wide, it will require less in length in the same ratio as the width is greater than a yard, (that is in the ratio of 8 to 15.) This statement would give the proper quantity of cloth were there no other conditions; but in consequence of its shrinking 5 per cent. which is equal to 6, we perceive that 20 parts in length and width, before the cloth is sponged, will only be equal to 19 parts after; hence we must increase Q 1083)6560(6,833 Ans. the quantity which the first part of our statement would give, in the ratio of 20 to 19, both in length and width. The solution of the above question, as indicated in Greenleaf's Key, page 130, will require three statements, which when worked out and the fractional part reduced to its lowest terms, 101 figures will be the smallest number which will complete the work; and unless the pupil is pretty skilful in reducing the fraction, he may not get through much short of 200 figures. In our solution it is unnecessary to make more than 8 figures. COMPOUND PROPORTION. 1. If the wages of 6 men for 14 days be $84, what will be the wages of 9 men for 11 days? would give us the wages of 9 men, but it would be for the same time which 6 men require, to earn $84, that is, 14 days, which would be too much, as we are required to find the wages for only 11 days, which will be less than the first part of the statement would give, in the ratio of 11 to 14; hence we place 11 on the right of the line, and 14 on the left, then 6 times 14 cancels the 84, and we have only to multiply 9 and 11 together for the answer. When the answer to a question depends upon several conditions, as in the last two examples, the process by which we effect the solution is called Compound Proportion. RULE FOR COMPOUND PROPORTION. As in simple proportion, place on the right of a vertical line, that number which is of the same name or kind as the required answer; then of the remaining numbers take any two that are of the same kind, and ascertain from the reading of the question, whether an answer depending upon these alone would be greater or less than the number first written, and place the greater or less on the right of the line accordingly, (as in simple proportion;) then take any other two of the same kind, and again ascertain from the reading of the question, whether an answer depending upon these alone would be greater or less than the number first written, and place the greater or less of these numbers on the right of the line accordingly; and so on until all the numbers are stated, then proceed as in simple proportion. 2. Suppose 4 men in 12 days can mow 48 acres of grass, how many acres ought 13 men to mow in 9 days? Acres. 148 4 13 12 9 Ans. 117 acres. Here you will at once perceive that 48 acres is of the same name as the required answer; then of the remaining numbers, first take the men, and pay no regard to the time; and you will readily perceive that since 48 is the number of acres which 4 men can mow, 13 men should of course mow a greater number of acres; therefore, you place the 13 on the right of the line, and the 4 on the left; in the next place take the days, and pay no attention to the number of men, and say if the mowing of 48 acres will afford labour for 12 days, the mowing of a less number of acres will afford labour for 9 days; therefore, place 9, the less of these two numbers, on the right of the line; then 4 times 12 cancels the 48, and the product of 13 and 9 gives the answer. 3. If 16 men receive $256 for 18 days' work, how much ought 27 men receive for 24 days? 1256 A 16 27 18 36 In this solution, observe 9 and 2 are factors of 18, the 9 we divide (mentally) into 27, and the 2 into 24; the product of their quotients is 36; now to multiply 36 and 16 together, multiply 16 by each figure of 36; thus, 6 times 16 are 96, put down 6 and carry 9, then 3 times 16 are 48, and 9 are 57 This could have been done very conveniently without writing either 16 or 36. 24 Ans. $576 |