A festival sets a ticket price of \(£p\) before tax. VAT of 20% is added to this price, and a booking fee of \(£4\), which is not subject to VAT, is then ad...
Question 1 Report
A festival sets a ticket price of \(£p\) before tax. VAT of 20% is added to this price, and a booking fee of \(£4\), which is not subject to VAT, is then added.
- Give an expression, in terms of \(p\), for how much a customer is charged altogether. (2)
- A customer pays a total of \(£70\). Form and solve an equation to find \(p\). (2)
- The organiser decides to absorb the booking fee into the ticket price instead of charging it separately, so that the total a customer pays stays at \(£70\). Work out the new pre-VAT ticket price, giving your answer to the nearest penny. (2)
Answer Details
This question builds an algebraic expression for a total charge, forms and solves a linear equation from it, and then re-solves a related equation under a changed condition.
VAT of \(20\%\) is added to the ticket price \(£p\), giving \(1.2p\). The flat, VAT-free booking fee of \(£4\) is then added, so the total charge is:
\[1.2p + 4\][2 marks]
Setting this equal to the total paid:
\[1.2p + 4 = 70\] \[1.2p = 66\] \[p = £55\][2 marks]
If the booking fee is absorbed into the ticket price so that VAT is charged on the whole \(£70\), the new pre-VAT price satisfies \(1.2p = 70\), so:
\[p = £70 \div 1.2 = £58.33 \text{ (nearest penny)}\][2 marks]
In part (c) the whole \(£70\) is now subject to VAT (since the booking fee no longer sits outside it), so the divisor is applied to the full \(£70\), not to \(£66\) as in part (b).
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