A shipping company uses two sizes of rectangular boxes that each have a height of 15 inches and a width...

1. TRANSLATE the problem information

• Given information:
  • Both boxes: \(\mathrm{height = 15\text{ inches}}\), \(\mathrm{width = 12\text{ inches}}\)
  • Box A: \(\mathrm{length = 20\text{ inches}}\)
  • Box B: length is 30% shorter than Box A's length
  • Need: volume of Box B

• What "30% shorter" means: subtract 30% of the original length from the original length

2. INFER the solution approach

• We need Box B's length before we can find its volume
• Strategy: First calculate Box B's length, then use the volume formula

3. SIMPLIFY to find Box B's length

• 30% of Box A's length = \(\mathrm{0.30 \times 20 = 6\text{ inches}}\)
• Box B's length = \(\mathrm{20 - 6 = 14\text{ inches}}\)

4. SIMPLIFY to find Box B's volume

• \(\mathrm{Volume = length \times width \times height}\)
• Volume of Box B = \(\mathrm{14 \times 12 \times 15 = 2,520\text{ cubic inches}}\)

Answer: B. 2,520

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Misinterpreting "30% shorter than Box A"

Students might think this means "30% of Box A's length" rather than "Box A's length minus 30% of Box A's length." This leads them to calculate \(\mathrm{0.30 \times 20 = 6\text{ inches}}\) as Box B's length, then find volume as \(\mathrm{6 \times 12 \times 15 = 1,080\text{ cubic inches}}\). Since this isn't among the choices, it leads to confusion and guessing.

Second Most Common Error:

Poor INFER reasoning: Forgetting to modify Box A's length and using it directly for Box B

Students understand they need to find volume but skip the length calculation step entirely. They use Box A's length (20 inches) for Box B, calculating \(\mathrm{20 \times 12 \times 15 = 3,600\text{ cubic inches}}\). This leads them to select Choice D (3,600).

The Bottom Line:

This problem tests whether students can accurately translate percentage language into mathematical operations and follow a logical sequence of calculations. The key insight is recognizing that you can't find the volume until you first determine the correct length measurement.