The Field Trip Bus Count
A grade level of 148 students is going on a field trip. Each bus holds 44 students. The trip coordinator writes the division 148 ÷ 44 = 3 remainder 16 on the board and announces, "So we need 3 buses." A teacher objects, saying the remainder means something important here. The coordinator also has a budget line that pays for buses in whole units only, and each bus costs $310. Two chaperones ride free on each bus, but chaperones do not count toward the 44-student limit. One class of 27 students will arrive late and must still be seated. The coordinator wants to know both the correct number of buses and whether the budget of $1,000 is enough.
1. Determine the correct number of buses needed and explain what the remainder represents in this context.
Read the worked answer
The division 148 ÷ 44 gives 3 full buses carrying 132 students, with 16 students left over. The remainder of 16 is not a reason to drop buses - it means 16 students still need seats. Since a bus cannot be split, the coordinator must round up: 3 + 1 = 4 buses.
Checking: 4 buses hold 4 × 44 = 176 seats, which is at least 148, so 4 buses work. Three buses hold only 132 seats, which is less than 148, so 3 buses fail. The remainder tells us there is a partial group that still requires a whole bus.
2. The late class of 27 students is already included in the 148. Does the answer change? Justify with reasoning, then decide whether $1,000 covers 4 buses at $310 each.
Read the worked answer
The 27 late students are part of the 148 total, so they do not add to the count. The answer stays at 4 buses because 148 students still need 176 seats' worth of capacity across 4 buses. If the 27 had been additional students, the total would be 175, and 175 ÷ 44 = 3 remainder 43, still requiring 4 buses - so the conclusion is robust either way.
Cost check: 4 × $310 = $1,240. The budget is $1,000, so it is not enough; the coordinator is short $1,240 − $1,000 = $240. Rounding down to 3 buses would save money but leave 16 students without seats, so cost cannot override the seating requirement.