An algebra problem by Eric Zhu
A machine that cost £35,000 is operated 8 hours a day in a 5-day week but one hour each day is used for test purposes. For use of the machine, there are three scales of charges, the first at the rate of £5 an hour for private use, the second at £15 an hour for research work and the third at £40 an hour for commercial work. It is estimated that the number of hours charged at the first, second and third rates is in ratios 4:2:1. What percentage of total receipts do receipts from commercial work represent?
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1 solution
The information about the cost of the machine and the hours of operation is irrelevant. For every 7 hours of use, 4 hours go to private use, 2 hours to research work and 1 hour to commercial work. Thus a total of £ 4 × 5 + £ 1 5 × 2 + £ 4 0 × 1 = £ 9 0 . The £ 4 0 of receipts from commercial work account for £ 9 0 £ 4 0 ≈ 4 4 . 5 % of total receipts.