A school is organizing transportation for a field trip. They will use large buses that can hold 40 students each...

1. TRANSLATE the problem information

• Given information:
  • Total students to transport: 360
  • Large buses hold: 40 students each
  • Small vans hold: 20 students each
  • Number of vans being used: 4
  • Find: Number of large buses needed

2. INFER the solution approach

• Key insight: Since some students will ride in vans, we need to find how many students are left for the buses
• Strategy: First calculate van capacity, then find remaining students, finally determine bus requirements

3. Calculate students transported by vans

• \(\mathrm{4 \times 20 = 80}\) students

4. SIMPLIFY to find remaining students

• \(\mathrm{360 - 80 = 280}\) students still need transportation

5. SIMPLIFY to find buses needed

• \(\mathrm{280 ÷ 40 = 7}\) buses

Answer: A (7)

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak INFER skill: Students don't recognize this as a multi-step problem requiring sequential calculations. Instead, they might try to work with total capacity of all vehicles at once, such as thinking "4 vans + some buses need to hold 360 students total."

This approach leads to setting up incorrect equations like: \(\mathrm{4(20) + x(40) = 360}\), which gives \(\mathrm{80 + 40x = 360}\), so \(\mathrm{40x = 280}\), and \(\mathrm{x = 7}\). While this actually yields the correct answer by coincidence, it reflects flawed reasoning about the problem structure.

Second Most Common Error:

Poor TRANSLATE execution: Students misread the problem and think they need to find the total number of vehicles (vans plus buses) rather than just the number of buses.

This leads them to calculate \(\mathrm{7 + 4 = 11}\) total vehicles, then look for this number among the choices. Since 11 isn't available, this causes confusion and guessing.

The Bottom Line:

This problem tests whether students can break down a multi-vehicle transportation scenario into logical steps, recognizing that you must account for one type of vehicle before determining needs for another.