Calculations and evaluation of formulae
4.3 Conversion tables and charts It is often necessary to make calculations from various conversion tables and charts. Examples include currency exchange rates, imperial to metric unit conversions, train or bus timetables, production schedules and so on.
Problem 14. Currency exchange rates for five countries are shown in Table 4.1 Table 4.1 France Japan Norway Switzerland U.S.A.
£1 = 1.50 euros £1 = 175 yen £1 = 11.25 kronor £1 = 2.20 francs £1 = 1.82 dollars ($)
£27.80 = 27.80 × 1.50 euros = 41.70 euros (b) £1 = 175 yen, hence £23 = 23 × 175 yen = 4025 yen (c) £1 = 11.25 kronor, hence 6412.5 = £570 6412.5 kronor = £ 11.25 (d) £1 = 1.82 dollars, hence £90 = 90 × 1.82 dollars = $163.80 (e) £1 = 2.20 Swiss francs, hence 2794 = £1270 2794 franc = £ 2.20 Problem 15. Some approximate imperial to metric conversions are shown in Table 4.2 Table 4.2
capacity
(a) the number of millimetres in 9.5 inches, (b) a speed of 50 miles per hour in kilometres per hour, (c) the number of miles in 300 km, (d) the number of kilograms in 30 pounds weight, (e) the number of pounds and ounces in 42 kilograms (correct to the nearest ounce), (f ) the number of litres in 15 gallons, and
(a) 9.5 inches = 9.5 × 2.54 cm = 24.13 cm 24.13 cm = 24.13 × 10 mm = 241.3 mm (b) 50 m.p.h. = 50 × 1.61 km/h = 80.5 km/h (c) 300 km = (d) 30 lb =
300 miles = 186.3 miles 1.61
30 kg = 13.64 kg 2.2
(e) 42 kg = 42 × 2.2 lb = 92.4 lb 0.4 lb = 0.4 × 16 oz = 6.4 oz = 6 oz, correct to the nearest ounce. Thus 42 kg = 92 lb 6 oz, correct to the nearest ounce. (f ) 15 gallons = 15 × 8 pints = 120 pints 120 pints =
(a) £1 = 1.50 euros, hence
weight
Use the table to determine:
(g) the number of gallons in 40 litres.
Calculate: (a) how many French euros £27.80 will buy, (b) the number of Japanese yen which can be bought for £23, (c) the pounds sterling which can be exchanged for 6412.5 Norwegian kronor, (d) the number ofAmerican dollars which can be purchased for £90, and (e) the pounds sterling which can be exchanged for 2794 Swiss francs.
length
25
1 inch = 2.54 cm 1 mile = 1.61 km 2.2 lb = 1 kg (1 lb = 16 oz) 1.76 pints = 1 litre (8 pints = 1 gallon)
120 litres = 68.18 litres 1.76
(g) 40 litres = 40 × 1.76 pints = 70.4 pints 70.4 pints =
70.4 gallons = 8.8 gallons 8
Now try the following exercise Exercise 15
Further problems conversion tables and charts (Answers on page 272)
1. Currency exchange rates listed in a newspaper included the following: Italy Japan Australia Canada Sweden
£1 = 1.52 euro £1 = 180 yen £1 = 2.40 dollars £1 = $2.35 £1 = 13.90 kronor
Calculate (a) how many Italian euros £32.50 will buy, (b) the number of Canadian dollars that can be purchased for £74.80, (c) the pounds sterling which can be exchanged for 14 040 yen, (d) the pounds sterling which can be exchanged for 1751.4 Swedish kronor, and (e) the Australian dollars which can be bought for £55