Dividing a School Trip Budget Fairly
A school is planning a trip for 96 students and 8 teachers. The bus company charges a flat fee of AED 1,800 per bus, and each bus holds a maximum of 45 people. The school must also buy entry tickets at AED 25 per student; teachers enter free. Lunch costs AED 18 per person for everyone (students and teachers). The school has collected AED 12,000 from student fees. The principal wants to know whether the trip is affordable and, if there is a shortfall, how much each student would need to pay extra. A parent volunteer claims that if they use fewer buses, they can save money without any problem.
1. Determine the number of buses needed and the total cost of the trip. Show your reasoning.
Read the worked answer
People: 96 students + 8 teachers = 104 people.
Buses: each holds 45. 104 ÷ 45 = 2.31… → need 3 buses (2 buses hold only 90, not enough).
Costs:
- Buses: 3 × 1,800 = AED 5,400
- Tickets: 96 × 25 = AED 2,400 (teachers free)
- Lunch: 104 × 18 = AED 1,872
- Total = 5,400 + 2,400 + 1,872 = AED 9,672
Compare to funds: AED 12,000 collected − AED 9,672 = AED 2,328 surplus.
So the trip is affordable with AED 2,328 left over. No extra payment per student is needed.
2. Evaluate the parent volunteer's claim that using fewer buses saves money 'without any problem'.
Read the worked answer
The claim is false because of the capacity constraint.
- With 2 buses, capacity = 2 × 45 = 90 people, but 104 people are going. That leaves 14 people without a seat - not allowed.
- Saving one bus saves AED 1,800, but it is impossible without either (a) reducing the group to 90 or fewer, or (b) hiring an additional smaller vehicle, which would likely cost more per seat.
Judgement: The volunteer confused 'fewer buses = lower cost' with feasibility. The binding constraint is capacity, not budget. Since the school already has a surplus of AED 2,328, there is no financial pressure to cut a bus. The correct number of buses is 3.