Coach, Minibus and Budget Decision
Year 6 is planning a museum visit for 84 pupils and 9 adults. The coach company hires whole coaches only; each coach has 48 seats and costs £310. The museum charges £7.50 per pupil and £11 per adult. The school has a budget of £2,400. A parent offers to drive 6 pupils in a minibus with 7 seats including the driver; the parent would enter the museum as an adult. The organiser must decide whether to accept the minibus offer before booking coaches. The coach company also says that loading takes 20 minutes and the journey takes 55 minutes. The museum wants the group to arrive by 10:15. One pupil says, ‘If we take the minibus, we can use one coach and save money.’ Another says, ‘The minibus saves nothing because we still need two coaches.’ The teacher asks the group to check the numbers before deciding.
1. Without the minibus, how many coaches are needed, and what is the total cost? Show every step.
Read the worked answer
Answer: 2 coaches; total £1,349.
- Total people: 84 pupils + 9 adults = 93.
- Coach seats: 93 ÷ 48 = 1 remainder 45, so 1 coach is not enough. Whole coaches only means 2 coaches, giving 96 seats.
- Coach cost: 2 × £310 = £620.
- Pupil admission: 84 × £7.50 = £630.
- Adult admission: 9 × £11 = £99.
- Admission total: £630 + £99 = £729.
- Grand total: £620 + £729 = £1,349.
The total is below £2,400 by £1,051, so the trip is affordable without the minibus.
2. Does accepting the minibus reduce the number of coaches? Does it save money? Explain carefully, using the seat counts and the admission charges.
Read the worked answer
Answer: It does not reduce the number of coaches, but it does save £34.
The minibus has 7 seats including the driver, so it can carry 6 pupils. The people still needing coach seats are 78 pupils + 9 adults = 87. Since 87 > 48, one coach is still not enough, so 2 coaches are still required. The pupil who says one coach will do is wrong because even after the minibus takes 6 pupils, 87 people remain.
Cost with the minibus:
- Coaches: still 2 × £310 = £620.
- Pupils: 78 × £7.50 = £585.
- Adults: 9 original adults + the parent = 10 adults; 10 × £11 = £110.
- Total: £620 + £585 + £110 = £1,315.
Saving: £1,349 − £1,315 = £34. The minibus removes six pupil tickets but adds one adult ticket, so the saving is £45 − £11 = £34.
3. The coach company proposes to begin loading at 9:05. Using the timings, will the group arrive by 10:15? What is the latest time loading must begin?
Read the worked answer
Answer: No, they would arrive 5 minutes late. Loading must begin by 9:00.
If loading begins at 9:05 and takes 20 minutes, the coach departs at 9:25. The journey takes 55 minutes, so arrival is 9:25 + 55 minutes = 10:20. That is 5 minutes after the 10:15 deadline.
To find the latest loading time, work backwards:
- Latest arrival: 10:15.
- Latest departure from school: 10:15 − 55 minutes = 9:20.
- Latest start of loading: 9:20 − 20 minutes = 9:00.
So the teacher should say that loading cannot start later than 9:00 if the group is to arrive on time.