A print shop completes a batch of 800 flyers. The manager reserves 12.5% of the flyers for a mailing list,...

1. TRANSLATE the problem information

• Given information:
  • Total flyers: 800
  • Reserved for mailing: \(12.5\%\) of total
  • Find: Number distributed at event (the rest)

• What this tells us: We need to find what's left after removing the reserved portion

2. INFER the approach

• Since we want "the rest," we need to find: \(\mathrm{Total - Reserved}\)
• First calculate the reserved amount, then subtract from total

3. Calculate the reserved amount

• SIMPLIFY: \(12.5\% \times 800\)
• \(12.5\% = 0.125\) (or recognize \(12.5\% = \frac{1}{8}\))
• \(0.125 \times 800 = 100\) flyers reserved

4. Find the distributed amount

• SIMPLIFY: \(800 - 100 = 700\) flyers

Answer: C. 700

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students misinterpret "the rest will be distributed" and try to calculate \(87.5\%\) directly instead of recognizing they should subtract the reserved portion from the total.

They might calculate \(12.5\% \times 800 = 100\) and then think this IS the answer (the distributed amount rather than the reserved amount).

This may lead them to select Choice A (100).

Second Most Common Error:

Inadequate SIMPLIFY execution: Students correctly identify they need \(12.5\%\) of 800 but make calculation errors, particularly with the decimal conversion.

Common mistake: \(12.5\% = 0.0125\) instead of \(0.125\), leading to \(0.0125 \times 800 = 10\) reserved, so \(800 - 10 = 790\) distributed. Since 790 isn't an option, this leads to confusion and guessing.

The Bottom Line:

This problem tests whether students can properly interpret "the rest" in percentage contexts and execute multi-step calculations. The key insight is recognizing that finding a percentage of the total is just the first step - you still need to determine what that represents in the context.