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(3) Given price of a series of quantities from a Weight or Measure.

Reduce and decimalise the series in terms of the unit whose price is wanted.

Decimalise also the price.
Use Method of Approximation (Division).
Example 1. Price of 324 is £731. 12s. 7d.
324=4.9.9

4 | 731.62916
9 | 182.90729
9 | 20 32303

2.2581
£2. 58. 2d.

Example 2. Price of 1152 is £289. 178.117d.

1,1,5,7,5 | 289.896 | 2:5044

58 39

£2.10s. ld.
51
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Example 3. Price of 8 tons 13 cwts. 1 qr. 7 lbs. is £630.58. 101d.

1,7,3:38 | 630.29 | 3•636
110 3

£3. 12s. 8 d.
6 3
11

1

EXAMPLES. 1. 851 things cost £720. 178. 54d., find cost of 1. 2. 712} things cost £96. 188. 44d., find cost of 1. 3.6314 things cost £325. 98. 41d., find cost of 1. 4, 82% things cost £412. 158. 7}d., find cost of 1. 5. 912 things cost £7315. 198. 11d., find cost of 1. 6. 18 tons 7 cwts. 3 qrs. cost £840. 9s. 6td., find cost of 1 lb.

7. 273 gallons 3 qrs. 1 pint cost £95.78. 11}d., find cost of 1 gallon.

8, 2315 oz. 13 dwts. 11 grains cost £10000, 11s. 1 d., find cost per oz.

9. 3125 qrs. 4 bushels cost £5610. 118. 4d., find cost per qr. 10. 737 yds. 5 inches cost £972. 88. 3}d., find cost per yd.

METHOD OF FARTHINGS.

51

Note 1. The Retailer after deciding the cost per lb. etc. of any purchase has only to add the profit per lb. (etc.) or per cent. to get the corresponding retail price.

Note 2. If price of retail-unit is so small as to fluctuate in 8ths and 16ths of a penny it is advisable to get the answer correct to 5 places and then by the Money-Decimalisation-Extension we can at once find price in 8ths or 16ths. Example. 7 cwts. at £10. 78. 6d., to find price per lb. 7,8,4 | 10•375 | .01323

01323 3 535

5292 183

·0127008 26

:: price=31d.

3

Hence by selling at 3d. there can be no loss, and of course still less so at 31d.

If the dealer wishes to make 20 per cent. profit he would add i to £10.7s.6d. before dividing.

£ 8. d. 10 7 6

2 1 6

12 90
7,8,4 | 12:45 | .0158

461
69

7
:: price=31d. per lb.

EXAMPLES. 1. Price per lb. if 15 cwts, cost £20.58. 6d. 2. Price

per

lb. if 7 tons cost £60. 88. 9d. 3. Price per yd. if 750 yds. cost £42. 88. 4d. 4. Price per yd. if 1000 yds. cost £50. 5. Price per sq. ft. if 192 sq. yds. cost £20. 16s. 8d.

10. The Method of Farthings.

Convert price into farthings and (if necessary) fractions of a farthing.

Multiply by the no. of farthings—mark off 3 places. Add -Answer is in £.

Example 1. 824 articles at 28, 7d. each=127 f.

82400
16480

5768
104.648

4:360

£109.008=0s. 1fd. Example 2. 1256 things at 51%d. each=214 f.

1256 2512

628

314 27.318

1.138

£28.456=98.14d. The difficulty of dividing by 24 may be avoided by using in succession the divisors 4 and 6 and crossing out the line derived from the 4—thus the above examples would appear in this form. (1) 104.648

(2) 27.318 26-169

6-029 4.360

1.138 £109.008

£28.456

11. The Method of Mils.

If we were to adopt the decimal system of coinage which has been repeatedly proposed since 1838, viz. that in which the radical coins are the £, florin, cent, and mil

, each being to of the preceding and the sovereign being the Integer—the calculation of prices is a mere matter of multiplication and moving the point.

Reduce the price to mils (an instantaneous operation)

Multiply by the no. of mils and mark off 3 places.

Example 1. 824 articles at 1 fl. 3 cents 2 mils=132 mils.

82400
24720

1648
£108.768

METHOD OF MILS.

53

Example 2. 1256 things at 2 cents 14 mils=214 mils.

1256 2512

628

314 £27.318

EXAMPLES.

1. 784 arts. at 28. 31d., 18. 7 d., 811d., 121 mils, 45 mils. 2. 1218 arts. at 7 d., 4 d., 9/d., 51 mils, 127 mils. 3. 384 arts. at 2s. 11d., 3s. 14 d., 718d., 18. 31d., 7d. 4. 3000 arts. at 76, 493, 734, 161, 325 mils. 5. 7125 arts. at 241, 1125, 657, 834, 104} mils.

SECTION IIL

THE ENGLISH SYSTEM OF WEIGHTS

AND MEASURES.

The Weights and Measures Act of 1826 (Jan. 1) enacted that

1°. The Brass Standard Yard of 1760 is the Imperial Standard Yard when at a temperature of 62° F. and from it all measures (lineal, superficial, solid) shall be constructed and the 36th part of this yard shall be

an inch.

The length of a Pendulum vibrating seconds in lat. of London in a vacuum at sea-level is 39.1393 such inches—this gives the means of estimating the standard if original is lost.

2°. The Brass weight of one Pound Troy of 1758 is the Imperial standard weight and from it all other weights shall be derived. It is to contain 5760 grains and the Avoirdupois pound 7000 grains.

The weight of a cubic inch of distilled water is 252.458 grains Troy (Barometer 30 inches and Thermometer 62° F.)—this gives the means of recovering the Imperial standard pound if original is lost.

3°. The Imperial Standard Gallon (containing 10 pounds Avoirdupois weight of distilled water at 30 inches and 62° F.) is the standard measure of capacity for Liquids and Dry Goods. The weight of 10 pounds

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