A shipping company wants the average weight of four packages in a shipment to be at most 2.5 kilograms. The...

1. TRANSLATE the problem information

• Given information:
  • First three packages: 2.8 kg, 1.9 kg, 2.6 kg
  • Fourth package: w kg (unknown)
  • Company requirement: average weight 'at most 2.5 kg'

• What 'at most 2.5 kg' means: \(\leq 2.5\)

2. INFER how to set up the average

• To find average of four weights: add all weights, then divide by 4
• Average = \(\frac{\mathrm{w + 2.8 + 1.9 + 2.6}}{4}\)

3. TRANSLATE the constraint into an inequality

• The average must be at most 2.5 kg
• So: \(\frac{\mathrm{w + 2.8 + 1.9 + 2.6}}{4} \leq 2.5\)

This matches choice (B) exactly.

Answer: B

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Misinterpreting 'at most 2.5' as 'at least 2.5'

Students sometimes confuse the direction of inequalities, thinking 'at most' means the minimum requirement rather than the maximum allowed. This leads them to use \(\geq\) instead of \(\leq\).

This may lead them to select Choice D (\(\frac{\mathrm{w + 2.8 + 1.9 + 2.6}}{4} \geq 2.5\))

Second Most Common Error:

Poor INFER reasoning: Forgetting to divide by 4 for the average

Some students recognize they need to add the weights but forget that average requires dividing by the count of items. They set up the constraint as just the sum being at most 2.5.

This may lead them to select Choice A (\(\mathrm{w + 2.8 + 1.9 + 2.6} \leq 2.5\))

The Bottom Line:

This problem tests whether students can accurately translate everyday language ('at most') into mathematical symbols and remember that average always involves division by count.