Excursion quote with free-adult rule and GST
Year 6 at Rivermere Primary has 26 students. Three adults will attend the museum excursion: the classroom teacher, one education aide and the principal. Museum entry is $12.50 per person, and the museum gives free entry to one teacher for every 10 paying students; any additional adults pay full price. The bus company quotes $600 excluding 10% GST, plus $0.95 per kilometre for the 23 km trip each way. The school subsidises every student by $15. The principal wants every student to pay the same whole-dollar amount, rounded up, and will not accept a plan where the school ends up out of pocket.
1. Calculate the total cost of the excursion, showing the bus and entry components separately.
Read the worked answer
Bus
- Distance: 23 km each way = 46 km
- Distance charge: 46 × $0.95 = $43.70
- Add 10% GST: $600 × 1.10 = $660.00
- Bus total: $660.00 + $43.70 = $703.70
Museum entry
- Free adults: 1 for every 10 paying students, so 26 students gives 2 free adults (you cannot round 2.6 up to 3 - the rule is per full 10 students).
- Paying people: 26 students + 1 adult = 27
- Entry: 27 × $12.50 = $337.50
Total: $703.70 + $337.50 = $1,041.20
2. Work out the per-student charge that meets the principal's two conditions (equal whole-dollar amount, rounded up, and no loss to the school), and state the resulting surplus or shortfall.
Read the worked answer
- Subsidy: 26 × $15 = $390.00
- Amount to be raised from students: $1,041.20 − $390.00 = $651.20
- Per student: $651.20 ÷ 26 = $25.046...
- Round up to a whole dollar (rounding down would leave the school short): $26 per student
Check: 26 × $26 = $676.00. Collected plus subsidy = $676.00 + $390.00 = $1,066.00, against costs of $1,041.20, so the school holds a surplus of $24.80. Rounding to $25 would have raised $650, which is $1.20 short.
3. Two students withdraw, leaving 24 students and the same three adults, and the bus quote does not change. Recalculate the per-student charge and explain why it moves so much.
Read the worked answer
- Bus: unchanged at $703.70 (flat hire plus distance already quoted)
- Free adults: 24 students still gives only 2 free places, so 1 adult pays
- Paying people: 24 + 1 = 25; entry = 25 × $12.50 = $312.50
- Total cost: $703.70 + $312.50 = $1,016.20
- Subsidy: 24 × $15 = $360.00
- To raise: $1,016.20 − $360.00 = $656.20
- Per student: $656.20 ÷ 24 = $27.34 → $28 per student
Why it jumps: costs fell by only $25 while the number of students paying fell by two. The bus hire is a fixed cost, so it is spread over fewer families - a $2 rise per student even though the excursion got cheaper overall.