VII. SIMPLE PROPORTION OR RULE OF THREE. In questions of Simple Proportion, quantities of two different kinds are involved, which vary either directly or inversely, as each other. Corresponding values (one of each) of these quantities are given, and a second value of one of them; and it is required to find the corresponding value of the other. This is effected by the Rule of Three, so called, because three quantities are given to find a fourth. Rule-1. Put that quantity for the third term, which is of the same kind with the answer. 2. Put that quantity, which is connected with the third term, as being the value corresponding to the value of the third term, for the first or second term, according as the quantities vary directly or inversely as each other. 3. Put the remaining quantity for the other term. 4. Reduce the first and second terms to the same denomination, and the third to any denomination, or not at all, as may be most convenient. 5. If the first and second, or the first and third, terms have any common divisor, divide them by it. 6. Multiply the second and third terms together, and divide the product by the first. 7. The quotient will be the answer required, in the denomination to which the third term was reduced, and must be expressed, if possible, in higher terms. EXAMPLES. 1. What cost 39 yards of silk at £3: 16: 7 for 13 yards. yds. yds. £. S. d. 2. As 13 : 39 :: 3 16 7 : Ans. lbs. As 17 If 17 lbs. of sugar cost 6s. 6d. what cost 13 cwt. 1qr. 11 lbs. ? 4. The expenses of a parish are £254: 10: 101⁄2 and the rental is £3054: 10:6, how much in the pound must be levied to pay it? 4. If 8 men occupy 9 days in mowing 24 acres, how men occupy in doing the same work? many days will 18 5. If the penny loaf weighs 6 oz. 15 drs. when wheat is at 7s. 6d,, what ought it to weigh when wheat is at 5s. 3d. per bushel? 6. How many yards of drugget 34 yds. wide will cover a room 50 yds. 7. The papering of a room 133 ft. high, and 30 yds. round, cost £2:0:6 what will be the cost of papering a room 10 ft. high, and 20 yds. round? 8. If of an estate be worth £1500, what will 2% of the same be worth? 9. In what time can a man reap a field working 10 hours a day, if he occupies 3 days in reaping it, when he works 12 hours a day? H 10. How many yards may be bought for £12: 12 : 0 if 7 yards cost 19s. 4 d.? In questions of Compound Proportion, several quantities of different kinds are involved, which are all connected with another quantity in such a manner, that they each vary directly or inversely as this other, when all the rest are supposed to remain unaltered. Certain values of the first-mentioned quantities, and the corresponding value of the last-mentioned, are given, and also other values of the first, from which it is required to find the corresponding value of the last. This is effected by the Rule of Compound Proportion, so called, because several proportions are compounded to form a Simple Proportion for the solution of the question. Rule-1. Put that quantity for the 3rd term of a Proportion, which is of the same kind with the answer required. 2. Take any pair of quantities of the same kind, and state them as the 1st and 2nd terms of the Proportion, precisely as though the answer depended entirely on them. 3. Take any other pair of quantities of the same kind, and state them as the 1st and 2nd terms of another Proportion, as though the answer depended entirely on them. 4. Proceed in the same manner with every pair of quantities. 5. Reduce the 1st and 2nd terms of each Proportion to the same name. 6. Multiply together all the 1st terms, and all the 2nd terms; make these respectively the 1st and 2nd terms of another Proportion, and put for the 3rd term the same as before. 7. Solve this Proportion as in Simple Proportion, the result will be the answer required. EXAMPLES. 1. If a man travel 126 miles in 5 days, walking 10 hours a day, in how many days would he travel 756 miles, walking 9 hours a day? 2. If £8793: 4 gain £17: 11: 8 in 5 months, what sum will gain £20 3. If 20 men, working 12 hours a day, earn £54: 7: 6 in 15 days, how many days of 9 hours each must 27 men work to earn £163: 2:6? |
