COMPOUND PROPORTION. THE rule for stating and resolving questions belonging to Compound Proportion, has been stated at page 38*. EXAMPLE. If the freight of a ship, of 170 tons, for 3 months, be £90, how much should the freight of a ship, of 118 tons, be for 5 months? As this rule is of the greatest use in comparing the monies, weights, and measures of different countries with each other, the student should make himself perfectly well acquainted with it. MISCELLANEOUS EXERCISES. 1. If 12s. be given for the carriage of 2 cwt. 3 qr. 192 miles, how much should be given, at that rate, for the carriage of 8 cwt. 1 qr. 128 miles ? 2. If the interest of £100, for 12 months, be £3. 10s., how much is the interest of £415, for 5 months? 3. A person put out a sum of money to interest, at 4 per cent, by which he cleared £35, in a year and 9 months; required the sum? 4. If cloth, 5 quarters wide, cost 14s. 6d. a yard, what ought cloth of the same quality, 3 quarters wide, to cost per Scots ell? 5. Bought a cask of butter, containing 50 lb. of 24 oz. each, at 1s. 3d. a lb., how must I retail it, by the Dutch lb. of 174 oz. to clear 3d. on each shilling it cost me? 6. Bought a quantity of Scots cheese, at 54d. a lb. of 22 ounces; how may I retail it, by the avoirdupois lb., to clear 12 per cent.? 7. If 1 lb. of gold be 15 times more valuable than 1 lb. of silver, and the proportion of its weight, to that of silver, be as 196 to 110, what is the value of an ingot of gold, equal in bulk to one of silver, worth 50 guineas? 8. If the interest of £100 for a year be £5, what will the interest of £236, for 78 days, be? 9. If the freight of a ship of 120 tons for 7 months, be £350, what ought to be paid for a ship of 150 tous, for 4 months? 10. If a ship's company of 120 men consume £50 value of wine in three weeks, at 1 pint per day each, when the price is £45 per pipe; how long will £1000 value serve 250 men, when each man is allowed 14 pint per day, and wine at £48 per pipe? RULES FOR PRACTICE. THE rules and observations, contained in the foregoing part of this work, comprehend the whole system of arithmetic, and are sufficient to enable any one, who understands them perfectly, to perform every species of computation that can occur. In many cases, however, the work of calculation may be abridged, by attending to the particular circumstances of the calculations to be performed; such as the kind of numbers that are given, the relation they bear to each, and to certain integers, &c. As this manner of performing computations is of the utmost consequence to those who are engaged in commercial affairs, the most useful methods which practice has suggested, for rendering mercantile computations easy, will be noticed in the remaining part of this work. CASE I. WHEN THE GIVEN PRICE IS AN ALIQUOT PART OF A POUND. RULE. Divide the given quantity or number of articles by that aliquot part, and the quotient is the answer in pounds. If the quantity contain fractional parts, reduce them to a decimal; or take parts of the price for them; or substitute such a part of a pound for them as the fraction is of a unit, considering the integral part of the quantity as pounds. EXAMPLE I. EXAMPLE II. What cost 6841 yards at 6s. 8d. What cost 3564 yards at 8d. per yard? 68. 8d.)6814 £2271 6 8 per yard? 8d.=)3564 £118 16 0 EXERCISES. 1. What cost 4673 yards at 10s.? 3. What cost 4565 yards at 5s.? 1. Multiply the quantity or number of articles by the number of shillings, and divide the product by 20. 2. If the price be an even number of shillings, multiply by half the number and divide by 10; or, which is the same thing, multiply by half the number of shillings, and double the right hand figure of the product for shillings, and the other figures of it are pounds*. This method may be taken when the number of shillings is odd; but in some examples, there will be a remainder of 1 in dividing by 2, which is 18., and must be added to the double of the right hand figure. |