A bicycle repair shop offers a voucher that reduces a repair bill to three-quarters of its original value, after which a fixed \(\pounds5\) collection fee i...
Question 1 Report
A bicycle repair shop offers a voucher that reduces a repair bill to three-quarters of its original value, after which a fixed \(\pounds5\) collection fee is added, giving a final bill of \(\pounds41\). Taking the original repair cost as \(y\) pounds, form an equation and solve it to find \(y\). (3)
Answer Details
This question translates a worded description involving a fraction of an unknown and a fixed fee into a linear equation, and solves it.
Reducing the bill to three-quarters gives \(\dfrac{3}{4}y\); adding the fixed \(£5\) collection fee gives the final bill:
\[\dfrac{3}{4}y + 5 = 41\][1 mark]
Subtracting \(5\) from both sides:
\[\dfrac{3}{4}y = 36\][1 mark]
Multiplying both sides by \(\dfrac{4}{3}\):
\[y = £48\][1 mark]
The original repair cost was \(£48\). Checking: \(\dfrac{3}{4}(48)+5 = 36+5=41\), which matches.
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