INTERCHANGES. Example 1. 1754 arts. at 1s. 94d.=213d. =87f. 45 48 200 4 8 Interchanges may be calculated for common quan tities and kept for use. e.g. 500=02018 (Formula), i.e. 2 × 240+1 × 12+8. EXAMPLES. 1. Prices of 15 score, 30 dozen, 3 gross at 31d., 91d., 1s. 11d. each. 2. 18. 9 d. Prices of 912 articles at 1s. 21d., 3s. 11⁄2d., 4s. 23d., 1s. 93d., 28. 101⁄2d. 1845 articles at 71d., 8d., 9 d., 18. Od., 2s. 1d. 9764 articles at 21d., 3d., 4 d., 5d., 18. 74d., Is. 8d. 3126 articles at 11дd., īs. Ožď., 61⁄2d., 73d., 53d., 20d. 640 articles at 1s. 41d., 1s. 24d., ls. 3 d., 18. 51d., 18. 64d., 852 articles at 81d., 9 d., 7d., 111d., 18. 3 d., 18. 4fd. 900 articles at 101d., 7d., 3s. 21d., 45. 31d., 5s. Od., 48. 11 d. 800 articles at 1s. 71d., 1s. 9 d., 2s. 51d., 3s. 7 d., 4s. 11d. 1264 articles at 9ąd., 1s. 21d., ls. 1fd., 191d., 10ąd. 3. Prices of 720, 192, 72, 100, 2880 things at 11d., 2d., 1s. 3 d., 18. 71d., 9td. 4. Cost of 1 cwt., 5 Lisbon Pipes, 1 acre, 1 year's wage, 1 pint at 1s. 11d. per lb., 9s. 74d. per gallon, 5s. 44d. per sq. yd., 30s. 101⁄2d. per week, 31d. per grain. 6. To find the Price of any whole Number of Articles at a given price per Article. (1) Multiply the price as it stands by the number of Articles in the compact form given below. (2) Decimalise the price and multiply, using the Method of Approximation. (3) Use Direct Aliquotation with Decimal working. These methods apply to Weights and Measures when the quantities are all of one kind or are easily reduced to one kind. They also apply to quantities quoted by the dozen, gross, score, at so much per dozen etc. Example. 7316 articles at £3. 178. 9 d. each. 1. 8614 things at £2. 15s. 74d. each. GENERAL METHODS. 47 7. To find the Price of any mixed (Integer with Fraction) Number of Articles given price of a single Article. part. (1) With 1,1, or any aliquot. Multiply by whole number and add the aliquot (2) With,, or any fraction whose numerator and denominator differ by 1. Multiply by whole number increased by 1 and subtract,... etc. (3) With any other fraction—aliquotise it if con venient. Multiply by whole number and add the successive aliquot parts. (4) With any fraction-Decimalise it if convenient. Multiply by the price in any form desirable (Practice etc.). Example 1. 3 qrs. 5 bush. 2 pecks at 138. 9d. per bushel. i.e. 29 bushels at 13s. 9d. each. Example 2. 84g articles=84-24 (Aliquot Notation) at £3. 18. 5§d. £3.072916 48 245833 12292 £258.125 1.536 £260-045 (08. 11d.) These methods are applicable chiefly in the case of Weights and Measures reducible to a whole number and a fraction in the unit whose price is given. EXAMPLES. 1. 87 things at £2. 11s. 74d. 2. 93 things at £1.78. 111d. 3. 121 things at £2. 98. 8d. 4. 10 qrs. 7 bush. 3 pecks at 9s. 24d. per bush. 5. 3201 things at £2. 6s. 8d. 6. 119 cwt. 1 qr. at £1. 16s. 5d. per cwt. 7. 700 yds. 2 ft. at 22s. 7 d. per yd. 8. 874 ac. 3 roods at £4. 78. 9åd. per acre. 9. 1126 sq. yds. 5 sq. ft. at £1. 1s. 31⁄2d. per sq. yd. 10. 712 lbs. 10 oz. at 8s. 4 per lb. 8. To find Price of a Series of Quantities (belonging to any Weight or Measure) given price of one of the Units. (1) Use Ordinary Aliquots of the quantities with Decimals of the Price. (2) Convert (by Reduction and Decimalisation) the given quantities into that of which the price is given. Then use Practice for the money—ensuring accuracy to three places. (3) Convert quantities and price into decimals. Multiply correct to 3 places by the Method of Approximation. Example 1. 367 cwt. 3 qrs. 14 lbs. at £17. 8s. 9d. per cwt. GENERAL METHODS. 49 Example 2. 13 lbs. 9 oz. 7 dwts. 13 grains at £3. 168. 41d. per lb. 1. 371 oz. 13 dwts. 19 grs. at 778. 10d. per oz. 2. 84 tons 12 cwts. 3 qrs. at £1. 58. 74d. per ton. 3. 713 acres 3 roods 15 poles at £4. 9s. 5d. per acre. 4. 515 sq. yds. 7 sq. ft. 110 sq. inches at £1. 7s. 41d. per sq. yd. 5. 271 cubic yds. 13 c. ft. at £5. 18s. 9d. per cub. yd. 6. 125 cwts. 79 lbs. at £2. 158. 4 d. per cwt. 7. 13 furlongs 8 poles 3 yds. at £41. 5s. 6d. per furlong. 8. 7864 galls. 3 qts. 1 pt. at 11s. 91d. per gallon. 9. 8450 qrs. 7 bush. at 33s. 74d. per qr. 10. 971 tons 17 cwts. I qr. at £21. 98. 71d. per ton. 9. To find the price of one Article or Unit. (1) Given price of a whole number of such articles. Decimalise the money and divide in succession by the factors of the given number (Short Division) or use Method of Approximation (Division). (2) Given price of a mixed number of such articles. Decimalise the mixed number and the price. Use Method of Approximation (Division). |