3. Find prices of 2, 5, 7, 11, 12 score at 1d., 71⁄2d., 18. 24d.. 3s. 4 d., 5s. 6d. each. 4. Find prices of 5, 7, 10, 24, 100, gross at 7 d., 61⁄2d., 18.54d., 2s. 1 d., 3d. each. 5. Find prices of 720, 320, 600, 360, 160, articles at 1s. 1d., 4s. 2 d., 18. 7 d., 2s. 03d., 5s. 1ğd. 6. Find prices of 10, 100, 1000, 50, 80, things at 18. 44d., 28. 37d., 38. 1 d., 41d., 58. 94d. 7. Find prices of 837, 965, 65, 74, 68, 312, 198, things at 2s. 2 d., 111ď., 3s. 41⁄2d., 5s. 11⁄2d., 3s. 111d., 1s. 111⁄2d., 1s. 103d. 8. Find price of a stone, cwt., ton, pack and sack at 1s. 5d., 9jd., 18. 5d., 28. 91d., 31d. per lb. 9. The price of 12, 20, 80, 64, 1920, things is £3. 10s. Od., £4. 58. 11 d., £18. 98. 6d., £75.0s. 1d., £214. 78. 93d. respectively; find the price of 1. 10. Calculate the cost of a dozen, score, and gross at these prices-3d., 5 d., 64d., 101d., 11ąd., 18. lid., 18. 11⁄2d., 18. 113d., 2s. 1 d., 4s. 11d., 5s. 7d., 7s. 6d. 2. The Method of "Nine Multiples" and "Moving the Points." The construction of small Tables containing 1, 2, 3, 4, 5, 6, 7, 8, 9 times any unit, quantity, price or decimal expression enables us to perform the conversion of quantities from one unit to another, and the calculation of prices and exchanges without further labour than addition by simply moving the decimal points-to any required accuracy. 1o. Conversion of Units. English. (1) Grains to Troy ounces for Bullion Operations. MOVING THE POINTS. (2) lbs. to cwts. for Commerce generally. (3) sq. inches to sq. feet for Engineers etc. (4) cubic ins. to cub. ft. for Engineers etc. 31 8 00462925925 9 00520791666 For English-Metric conversions see the Chapter on the Metric System. Multiples like (2) may also be used to calculate the price per lower unit, given the price of the higher. Example. Suppose price per cwt. is 18s. 9d.-to find price per lb. 18s. 9d.=225d. Now use (2). .. Price per lb. = 1.79 •18 ⚫04 2.11=23d. 2o. Calculation of Prices by Multiples of the Quantities (Inverse Method). The use of Multiples of well-known quantities is not very advantageous with our coinage because it is not a decimal one. By constructing the multiples of these quantities decimalised to certain bases, however, and employing denomination-changes, full advantage may be taken of the principle of moving the points. The best bases to use are 960 (f. as £) and 3840 (16ths as £). We give both sets of multiples, the actual and the decimalised, and the examples are worked in both ways. With the actual multiples it is easiest to use pence -afterwards changing to £, s., d. When we come to metric quantities at foreign prices we shall see the value of the actual multiples. They would be of as great importance with us if we used mils as the division of the £. (1) cwts. to lbs.-base 3840. (2) sacks to lbs. (flour)—base 960. Example 1. Price per lb. is 2ğd. = 101f. 1 280 2916 2= 560 583 3= 840 875 4 1120 1.16 5-1400 1.4583 735d. £3.063 (1s. 3d.). PRICES BY MULTIPLES. 33 These and such similar multiples as may be required should be carried in the pocket-book ready for use. The bases 240 (d. as £) and 1920 (8ths as £) may also be used, but 960 is the most convenient for all kinds of prices. 3°. Calculation of Prices by Multiples of the Price (Direct Method). The Price is first converted into a decimal of a £ and then the nine multiples are taken. With commonly-occurring prices the method is very advantageous as its speed is always great and in many cases the working is instantaneous. It is obvious also that the method can equally well apply to dozens, scores, cwts., gross, or any special quantities in which goods are quoted. 1=£ •168489583 Examples. 1. 4000 oz. = £673·958 1234∞σ •33697916 •50546875 ⚫842447916 1.0109375 7 8 9 1.347916 = £673. 19s. 2d. 2. 3125 oz. = 505.469 16.849 3.370 ⚫842 £526.530 = £526. 10s. 74d. With practice all two-figure quantities can be written down at sight after mental addition. The method can be applied to Sterling Exchanges with great effect. = (3) Rupee 1s. 511⁄2d. 1 £073046875 Example. 8560 rupees=584.375 Such exchanges fluctuate as a rule within very small limits and therefore the Tables required are very few. Hence those whose dealings with the East are frequent can readily make tables of the kind as they are required-keeping them for future use. Find the prices per higher unit at the given prices per lower unit in each case. |