A car workshop charges a call-out fee plus an hourly labour rate. The total bill, in pounds, for a repair is \(B = 45 + 32h\), where \(h\) is the number of ...
Question 1 Report
A car workshop charges a call-out fee plus an hourly labour rate. The total bill, in pounds, for a repair is \(B = 45 + 32h\), where \(h\) is the number of hours worked. One customer's final bill came to 269.
- Find \(h\) in terms of \(B\). (3)
- Work out how many hours the mechanic worked on this repair. (3)
Answer Details
This question tests rearranging a linear formula to make the number of hours the subject, then substituting a target bill to find how long a job took.
(a) Subtract 45 from both sides, then divide by 32:
\[B=45+32h \Rightarrow 32h=B-45 \Rightarrow h=\frac{B-45}{32}\ \text{<b>[3]</b>}\](b) Substituting \(B=269\) into the rearranged formula from part (a):
\[h=\frac{269-45}{32}=\frac{224}{32}=7 \text{ hours}\ \text{<b>[3]</b>}\]The call-out fee of £45 is a fixed cost that does not depend on the hours worked, so it must be subtracted before dividing by the hourly rate; dividing the whole bill by 32 without first removing the £45 would give an incorrect number of hours.
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