AlgebraMediumSolving a linear model for the input
Algebra practice question
A bicycle repair shop charges a fixed booking fee of $45 plus $15 for each hour of labour. The total charge, in dollars, for a repair taking h hours is given by C(h) = 45 + 15h.
A repair was charged $135 in total. How many hours of labour did it take?
- A. 6Correct
- B. 9
- C. 12
- D. 90
Answer: A. 6
Set the model equal to the total and solve: 135 = 45 + 15h. Subtract the booking fee first: 90 = 15h. Then divide by the hourly rate: h = 6. (Check: 45 + 15(6) = 45 + 90 = 135.)
Why the other answers are wrong
- B. 9
- You divided the whole total by the hourly rate, 135 / 15 = 9, which ignores the $45 booking fee. Take the fee off before dividing.
- C. 12
- You added the booking fee instead of subtracting it: (135 + 45) / 15 = 12. The fee is part of the 135 already, so it comes off.
- D. 90
- 90 is the labour portion of the bill in dollars, not hours. Divide it by the $15 hourly rate to get the hours.
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