35. How many yards of cloth 3qrs. wide are equal in measure to 30 yards 5qrs. wide ? Ans. 50 yards. 36. A borrowed of his friend B 250l. for 7 months, promising to do him the like kindness: sometime after B had occasion for 300l. how long may he keep it to receive full amends for the favour ? Ans. 5 months and 25 days. 37. If, when the price of a bushel of wheat is 6s 3d. the penny loaf weigh goz. what ought it to weigh when wheat is at 8s. 2d. per bushel ? Ans. 6oz. 13dr. 38. If 4cwt. may be carried 36 miles for 35s. how many pounds can I have carried 20 miles for the same money? Ans. 907lb. 이 39. How many yards of canvas, that is ell wide, will line Ans. 12yds. 20 yards of say, that is 3qrs. wide ? 40. If 30 men can perform a piece of work in II days, how many men will accomplish another piece of work, 4 times as big, in a fifth part of the time? Ans. 600. 41. A wall, that is to be built to the height of 27 feet, was raised 9 feet by 12 men in 6 days: how many men must be employed to finish the wall in 4 days at the same rate of working ? 42. If foz. cost what will roz. cost? 3 Ans. 36. 5 Ans. 11. 5s. 8d. 43. If of a ship cost 2731. 2s. 6d. what is of her worth? Ans. 2271. 125. Id. 44. At il. per cwt. what does-3-lb. come to ? Ans. 10-d of a tun cost? Ans. 1401. 46. A person, having of a coal mine, sells of his share for 1711. what is the whole mine worth ? 45. If of a gallon cost fl. what will 4 Ans. 3801. 47. If, when the days are 13 hours long, a traveller performs his journey in 35 days; in how many days will he perform the same journey, when the days are 18 hours long? Ans. 40 61 days. : 48. A regiment of soldiers, consisting of 976 men, are to be new clothed, each coat to contain 25 yards of cloth that is gyd. wide, and to be lined with shalloon gyd. wide; how many yards of shalloon will line them ? PRACTICE is a contraction of the rule of three, when the first term happens to be an unit, or one; and has its name from its daily use among merchants and tradesmen, being an easy and concise method of working most questions, that occur in trade and business. The method of proof is by the rule of three. An aliquot part of any number is such a part of it, as, being taken a certain number of times, exactly makes that number. GENERAL RULE.* 1. Suppose the price of the given quantity to be 11. Is. or Id. as is most convenient; then will the quantity itself. be the answer, at the supposed price. * 2. Divide The rule, and its application to the following particular Cases, will be rendered very evident by an explanation of the example. In this example it is plain, that the quantity 526 is the answer at 11. consequently, as 3s. 4d. is the of 11. ᄒ of that quantity, or 871. 13s. 4d. is the price at 3s. 4d. In like manner, as 4d. is to of 3s. 4d. so To of 871. 13s. 4d. or 81. 15s. 4d. is the answer at 4d. And by reasoning in this way 41. 7s. 8d. will be shewn to be the price at 2d. and 10s. 11 d. the price at 4.一 Now as the sum of all these parts is equal to the whole price (3s. 101d.) so the sum of the answers, belonging to each price, will be the answer at the full price required. And the same will be true in any example whatever. 2. Divide the given price into aliquot parts, either of the supposed price, or of one another, and the sum of the quotients, belonging to each, will be the true answer required. NOTE. When there is any fractional part, or inferior denomination of the quantity, take the same part of the price, that the given fraction, or inferior denomination, is of the unit, of which the price is given, and add it to the price of the whole number. EXAMPLE. What is the value of 526 yards of cloth at 3s. 107d. per yard ? 101 73 do. at o 3 104 the full price. Ans. 1011. 75. 3d. A few of the many cases, that may occur, will, with their particular rules, be sufficient to illustrate the general rule. Divide by the aliquot parts of a penny, and then by 12 and 20; and it will give the answer required. When the price is an aliquot part of a shilling. RULE. Divide the given number by the aliquot part, and the quotient is the answer in shillings, which reduce into rounds, as before. EXAMPLES. 1. 3d. is 1728 at 3d. 1 When the price' is a part, but not an aliquot part, of a shilling. RULE. Divide the given number by some aliquot part of a shilling, and then consider what part of the said aliquot part the rest is, and divide the quotient thereby ; and the last quotient, together with the former, will be the answer in shillings, which reduce into pounds, as before. When the price is any number of shillings under 20." RULE. 1. When the price is an even number, multiply the given number by of it, doubling the first figure to the right hand for shillings, and the rest are pounds. I 2. When the price is an odd number, find for the greatest even number, as before, to which add of the given number for the odd shillings, and the sum is the answer. 이 1981. 2s. the answer. Ans. 1371. 175 Ans. 3481. 16s. Ans. 2041. 128. Ans. 2501. 163, 70l. Is. the answer. 2. 8cwt. |