Prom night budget and ticket pricing
The Year 11 prom committee at a school in County Down is planning its end-of-year event. The venue charges £480 plus VAT at 20%, and the caterer charges £18.50 per head with VAT already included. A DJ costs £260 plus VAT, and a photographer has quoted £600 plus VAT. The committee expects 96 students to attend. School policy requires 12 staff to be present, and they must be given the same meal, but staff attend free of charge. Tickets are currently advertised at £32 each. A parent has offered to cover any shortfall up to £250, but only if the committee can show that the event would otherwise break even on ticket sales alone apart from that donation. A non-refundable deposit of 25% of the total cost has already been paid. The committee meets next week to fix the final ticket price and needs a clear recommendation.
1. Calculate the total cost of the event including VAT, and state how much of that total has already been paid as the 25% deposit.
Read the worked answer
Work through each cost separately, applying VAT only where it is quoted as extra.
- Venue: £480 × 1.20 = £576.00
- Catering: 96 students + 12 staff = 108 meals; 108 × £18.50 = £1,998.00 (VAT already included, so do not add 20%)
- DJ: £260 × 1.20 = £312.00
- Photographer: £600 × 1.20 = £720.00
Total = 576 + 1,998 + 312 + 720 = £3,606.00
Deposit = 25% of £3,606 = 0.25 × 3,606 = £901.50, leaving £2,704.50 still to pay.
The common error is to add VAT to the catering figure as well; the wording 'VAT already included' means it is already inside the £18.50.
2. Work out the lowest whole-penny ticket price for the 96 students that covers the full cost. Explain why £37.56, the answer to the division, is not correct.
Read the worked answer
Divide the total cost by the number of paying students:
3,606 ÷ 96 = 37.5625
Rounding this to the nearest penny gives £37.56, but that is not enough:
96 × £37.56 = £3,605.76, which is 24p short of £3,606.
Because the shortfall must be covered, round up to the next penny: £37.57.
Check: 96 × £37.57 = £3,606.72, which covers the cost with 72p spare.
In practice the committee would probably choose £38 as a sensible ticket price, but the minimum that mathematically breaks even is £37.57. The judgement being tested is that money answers must be rounded up, not to the nearest penny, when the question asks for the lowest price that covers a cost.
3. Show whether £32 tickets can work. Then find the minimum whole-pound ticket price needed if the parent's £250 is used.
Read the worked answer
At £32: 96 × £32 = £3,072.
Shortfall = 3,606 − 3,072 = £534.
After the parent's £250: 534 − 250 = £284 still missing. So £32 does not work even with the donation.
With the donation, the amount to be raised from tickets is 3,606 − 250 = £3,356.
3,356 ÷ 96 = 34.9583...
To the next penny this is £34.96 (check: 96 × 34.96 = £3,356.16). The lowest whole-pound price is therefore £35, which raises 96 × £35 = £3,360, leaving £4 spare.
Recommendation: £35 is the lowest whole-pound price that works with the donation; without the donation the committee needs £38.