The Field Trip Fraction
A class of 32 students is planning a field trip. Permission slips are required, and 3/8 of the class has returned a signed slip so far. The bus company charges $240 for a bus that holds up to 40 passengers, and the museum charges $7 per student who attends. The teacher says, "We have 12 slips, so we're almost halfway - let's book the bus now." A parent volunteer points out that the trip cannot run unless at least 3/4 of the class returns slips by Friday, and that the bus is booked whether or not students attend.
1. Calculate how many students have returned slips, how many more are needed to reach the 3/4 requirement, and explain whether the teacher's "almost halfway" statement is accurate.
Read the worked answer
Slips returned: 3/8 of 32 = 32 ÷ 8 × 3 = 12 students.
Requirement: 3/4 of 32 = 32 ÷ 4 × 3 = 24 students.
Still needed: 24 − 12 = 12 more students.
Is "almost halfway" accurate? Half of 32 is 16. The class has 12, which is 4 short of halfway - so "almost halfway" overstates progress. More importantly, halfway is not the goal; the goal is 24. The class has 12 of the 24 required, meaning it is exactly halfway to the requirement, not almost halfway to the class total. Framing progress against the wrong target makes the situation look more complete than it is.
2. The teacher wants to book the bus now. Using the numbers, explain the financial risk of booking before the 3/4 requirement is met, and state what should happen first.
Read the worked answer
The bus costs $240 regardless of attendance, and the museum adds $7 per attending student.
If the trip is booked and only the current 12 students attend, the cost is $240 + (12 × $7) = $240 + $84 = $324. If the requirement is not met and the trip is cancelled, the $240 bus fee is still owed with no trip - a pure loss.
If all 24 required students attend, the cost is $240 + (24 × $7) = $240 + $168 = $408. The bus holds 40, so 24 fits comfortably; there is no capacity problem.
The risk is committing $240 before knowing whether the 3/4 threshold will be reached. The correct order is: collect the remaining 12 slips first, confirm 24 students by Friday, and only then book the bus. Booking now gambles $240 on an outcome that is currently 12 slips away.