A construction site started with 523,600 tons of sand. After completing 24 sections of a road, 410,800 tons of sand...

1. TRANSLATE the problem information

• Given information:
  • Started with 523,600 tons of sand
  • After 24 sections completed, 410,800 tons remained
  • Need: average sand used per section

• What this tells us: We need to find how much sand was used total, then divide by 24 sections

2. INFER the solution strategy

• Key insight: We don't directly know how much sand was used - we only know starting amount and remaining amount
• Strategy: First calculate total sand used, then find average per section
• This is a two-step problem, not a one-step division

3. Calculate total sand used

\(\mathrm{Total~sand~used = Starting~amount - Remaining~amount}\)

\(\mathrm{Total~sand~used = 523,600 - 410,800 = 112,800~tons}\)

4. Calculate average sand per section

\(\mathrm{Average~per~section = Total~sand~used ÷ Number~of~sections}\)

\(\mathrm{Average~per~section = 112,800 ÷ 24 = 4,700~tons}\)

Answer: A (4,700)

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak INFER skill: Students skip the first step and try to divide one of the given quantities directly by 24, not recognizing they need to find the total sand used first.

If they divide the initial amount: \(\mathrm{523,600 ÷ 24 ≈ 21,817}\)

This leads them to select Choice C (21,817)

If they divide the remaining amount: \(\mathrm{410,800 ÷ 24 ≈ 17,117}\)

This leads them to select Choice B (17,117)

The Bottom Line:

This problem tests whether students can break down a word problem into the correct sequence of steps. The key challenge is recognizing that "average sand used per section" requires first determining how much sand was actually used (the difference between starting and remaining amounts) before calculating the average.