Museum Field Trip: A Compliant Plan, a Budget, and a Fragile Assumption
Whitfield Middle School is taking 187 eighth graders to a science museum. District policy requires at least one chaperone for every 10 students, and chaperones pay the student rate. Charter buses seat 52 passengers each and cost $850 per bus; museum admission is $12 per person. The school has budgeted $6,200. A teacher's draft plan reads: "199 people total (187 students + 12 volunteers), so 4 buses. Cost = 4($850) + 199($12) = $5,788. Under budget." The 12 volunteers signed up before anyone re-read the chaperone policy, and the office expects late enrollment to add up to 8 more students.
1. Does the draft satisfy district policy? Determine the minimum number of chaperones required and the resulting head count, then confirm the bus count.
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Policy check: 187 ÷ 10 = 18.7, so at least one chaperone per 10 students requires 19 chaperones. Twelve volunteers equals roughly 1 per 15.6 students (187 ÷ 12 = 15.6), which violates the ratio. The draft is not compliant.
Head count: 187 + 19 = 206 people.
Buses: 206 ÷ 52 = 3.96. Buses are indivisible and cannot be overfilled, so round up to 4 buses = 208 seats, leaving 2 seats.
Note that the bus count is unchanged - 4 buses cover both 199 and 206 - which is exactly why the policy violation could have gone unnoticed. The seat chart looks fine while the supervision ratio is not.
2. Recompute the cost for the policy-compliant plan and state the remaining budget. Then test whether the plan still holds if 8 more students enroll.
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Compliant plan (206 people)
- Buses: 4 × $850 = $3,400
- Admission: 206 × $12 = $2,472
- Total = $5,872, leaving $6,200 − $5,872 = $328.
With 8 more students (195 total)
- Chaperones: 195 ÷ 10 = 19.5 → 20
- Head count: 195 + 20 = 215
- Seats: 215 ÷ 52 = 4.13 → 5 buses (a fifth bus is triggered by only 7 people over capacity)
- Cost: 5 × $850 + 215 × $12 = $4,250 + $2,580 = $6,830
Conclusion: $6,830 exceeds the $6,200 budget by $630. The plan is not robust - a modest enrollment increase forces a whole additional bus, a step change of $850 plus admission. The $328 cushion covers admission for about 27 more people but cannot absorb a bus.
3. Identify the most consequential unstated assumption in the draft plan, and describe one contingency that would make the plan defensible to the principal.
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The critical assumption: that 187 is the final enrollment. Every number in the draft - 12 chaperones, 199 people, 4 buses, $5,788 - is downstream of a head count that the office already expects to grow. Because bus capacity is a step function, this assumption sits directly on the one variable that can break the budget, as shown by the 215-person scenario costing $6,830.
Other assumptions worth naming: that all 12 volunteers remain available (volunteers are not guaranteed, and losing them worsens the ratio problem); that museum admission stays at $12 and no group rate or PTA chaperone subsidy applies; that no driver gratuity or fuel surcharge is billed.
A defensible contingency: set a hard enrollment cutoff - the date and the number of students beyond which the trip is re-costed - and hold the $328 reserve plus a written request for a $700 contingency transfer, since $630 is the known exposure if a fifth bus is needed. Alternatively, cap registration at 200 students (20 chaperones, 220 people) and pre-approve the fifth bus before advertising the trip. Either way, the plan should state the enrollment number it depends on and what triggers a revision.