18. Bought 3 tons of oil, for 503 dollars 25 cents; 85 gallons of which having leaked out. I wish to know at what price per gallon I must sell the residue, that I may neither gain nor lose by the bargain. 19. If, when the price of wheat is 6s. 3d. a bushel, the penny loaf weighs 9 oz., what ought it to weigh, when wheat is at 8 s. 2 d. a bushel ? .. 20. If 15 yards of cloth yard wide cost 6 dollars 25 cents, what will 40 yards being yard wide cost? 21. What quantity of water must I add to a pipe of mountain wine, for which I gave 110 dollars, to reduce the first cost to 75 cents a gallon? 22. Borrowed of a friend 250 dollars for 9 months; and then, to repay him for his kindness, I loaned him 300 dollars. How long must he keep the 300 dollars, to balance the previous favor ? 23. If 4.cwt. can be carried 36 miles for 51 dollars, how many pounds can be carried 20 miles for the same money? 24. A person owning of a coal mine, sells of his share for 570 dollars. What is the whole mine worth, at the same rate ? ! , 25. If the discount on $106, for a year, be $ 6, what is the discount on $477, for the same time? 26. If, when the days are 13 hours long, a traveller perform his journey in 35 days, in how many days will he perform the same journey, when the days shall be 114 hours long? 27. A regiment of soldiers consisting of 976 men, is to be new clothed; each coat to contain 2 yards of cloth 15 yard wide, and to be lined with shalloons yard wide. How many yards of shalloon will be required ? 28. If 30 men can perform a piece of work in 15 days, how many men would accomplish the same piece of work, in a fifth part of the time ? 29. What is the value of 172 pigs of lead, each weighing 3cwt. 2 qrs. 17 lb., at 29 dollars 58} cents per fother of 19cwt.? 30. A merchant gave his note for 1831 dollars 75 cents, payable in 8 months; but the holder of the note homo.mIf 30 menany yards of the lined within 2 being pressed for money, the merchant paid it in 3 months. Allowing money to be worth 6 per cent. a year, what sum was requisite to redeem the note ? 31. If A can mow an acre of grass in 5 hours, and B can mow 12 acre in 9 } hours, in what time can they jointly mow 84 acres ? 32. How much cambrick may be bought for £8 6 s. 31 d., if 291 yards cost £ 186 2 s. 41 d. ? *33. If a staff 3 feet 3 inches high casts a shadow 51 feet long, what is the height of the steeple of Park street church, in Boston, which, at the same time, casts a shadow of 368 feet 6 inches in length ? 34. A and B hired a pasture for $49.50, in which, A pastured 13 cows, and B 19. What must each pay ? 35. If 220 yards in length and 22 yards in breadth make an acre, what must be the breadth of a lot that is 121 yards in length, to contain an acre ?, 36. If 365 men consume 75 barrels of provision in 9. - months, what number of barrels will 500 men consume during the same time? 37. If 19 yards of linen cost $14.25, what will 435.6 yards come to, at the same rate ? 38. The value of 8.25 pounds of pure silver being $ 128, what is the value of 376.7848 pounds ? 39. Suppose sound to move 1106.3 feet in 1 second; how many miles distant is a cloud, in which lightning is observed 47.5 seconds before the thunder is heard ? 40. It has been found, that 100 cubic inches of alcohol and 82.5 cubic inches of water, when mixed, measures only 177.41 cubic inches. If, then, 125 gallons of alcohol and 103.125 gallons of water be mixed, how many gallons will the mixture compose ? COMPOUND PROPORTION. When proportion is applied to questions, in which the relation of the required quantity to the given quantity of the same kind is traced through two or more proportions, it is called COMPOUND PROPORTION. For example, 16 men dug a trench 54 yards long and 5 yards wide, in 6 days. How many men of equal ability and industry will dig a trench of the same depth, 135 yards long, and 4 yards wide, in 8 days ? In the above question, the number of men required depends upon three circumstances; viz. the length of the trench, its width, and the number of days in which it is to be dug. If we omit the consideration of all the circumstances except the length, the question will be simply this, If 16 men dug a trench 54 yards long, how many men will dig one 135 yards long ?-which will make the following proportion; 54 : 135=16 : A, and the fourth term will be found to be 40 men. Secondly, we will consider the width ; and, since the second trench is to be narrower than the first, the number of men required will be proportionally less, and our second proportion will be the following; 5:4=40 : A, and the fourth term will be 32 men. Lastly, we will notice the number of days in the question; and, since the longer the time allowed, the less will be the number of men required to do the work, we shall have the following proportion; 8:6=32 : A, and this gives 24 men for the fourth term, which is the answer to the question. We see in this solution, that 16 is multiplied by 135, and the product divided by 54; the quotient, being made the third term in the second proportion, is multiplied by 4, and the product divided by 5; this. last quotient, being made the third term in the third proportion, is multiplied by 6, and the product divided by 8. The result, therefore, would be the same, if 135 and 4 and 6 were multiplied together, and their product multiplied by 16, and this last product divided by the product of 54 and 5 and 8. The proportion may be thus arranged. 54 ; 135 ) 5: 44=16 : A 8: 6) 2160 : 3240 =16 : A If, instead of calculating the fourth term in each proportion, we only indicate the operation by a fraction, 54 we shall have, in the first of the foregoing proportions, for the fourth term: taking this for the third term of the second proportion, we shall have the following, 5:43 10X130 : A, and the fourth term will be 10X135X4; De 54X5, taking this for the third term in the third proportion, we shall have the following, 8:6= "*4*3** :A, and the fourth term will be ****, which is equal to 24, the number of men required. In this fractional expression, we see at once, that the product of all the second terms is multiplied by the third term, and that this product is divided by the product of all the first terms, and the quotient is the fourth term, or answer to the question. Hence we see, that questions in compound proportion will be accurately solved by the following rule. RULE. Make the number, which is of the same kind with the answer, the third term; of the remaining numbers, take any two of a kind, and write one for a first term and the other for a second term, as directed in simple proportion, then any other two of a kind, and so on, till all are written. Lastly, multiply all the second terms together, and their product by the third term, and divide the result by the product of the first terms; the quotient will be the fourth term, or answer. 41. A wall to be built to the height of 27 feet, was raised to the height of 9 feet by 12 men in 6 days; how many men must be employed to finish it in 4 days? 12 men is the third term, because the answer is to be in men. . 9 : 18 In stating the different lengths l of the wall, the shorter is inade the 36 : 108 =12 : A first term, because, the longer the 12 wall, the greater will be the number of men required to build it. 36)1296(36 Ans. In stating the days, the less num ber is made the first term, because, 216 the less the time, the greater must 216 | be the number of men. 27 4: 6 * =12 : A 108 42. If 120 bushels of corn will serve 14 horses 56 - days, how many days will 94 bushels serve 6 horses ? 43. If a footman travel 130 miles in 3 days, when the days are 12 hours long, in how many days of ten hours in length, can he travel 360 miles ? 44. If 6 laborers dig a ditch 34 yards long in 10 days, how many yards will 20 laborers dig in 15 days ? 45. If a garrison of 600 men have provisions for 5 weeks, allowing each man 12 ounces a day, how many men may be maintained 10 weeks with the same provisions, if each man is limited to 8 ounces a day? 46. If 3 bushels and 3 pecks of wheat will last a family of 9 persons 22 days, in how many days will 6 persons consume 5 bushels ? 47. If 450 tiles, each 12 inches square, will pave my cellar, how many tiles must I have, if they are only 9 inches long and 8 inches broad? 48. If 12 ounces of wool make 2 yards of cloth 6 quarters wide, how much wool is required for 150 yards 4 quarters wide ? 49. If a bar of iron 4 feet long, 3 inches broad, and 11 inch thick, weighs 36 pounds, what will a bar weigh, that is 6 ft. long, 4 in. broad, and 2 in. thick ? 50. If 6 men built a wall 20 feet long, 6 feet high, and 4 feet thick, in 16 days, in how many days will 24 men build a wall 200 feet long, 8 feet high, and 6 feet thick ? 51. If 14 men can reap 84 acres in 6 days, how many men must be employed to reap 44 acres in 4 days ? 52. A ship's crew of 300 men were so supplied with provisions for 12 months, that each man was allowed 30 ounces a day; but after having been 6 months on their voyage, they find it will take 9 months more to finish it, and 50 of their number have been lost. It is required, to find the daily allowance of each man during the last 9 months. 53. A wall was to be built 700 yards long in 29 days; after 12 men had been employed on it for 11 days, it was found they had built only 220 yards. How many more men must be put on, to finish it in the given time? |