There are 48 members in the school's debate club. In a recent survey, club members were asked whether they plan...

1. TRANSLATE the problem information

• Given information:
  • Total debate club members: 48
  • Survey result: "3 out of every 8 members plan to participate"

• What this tells us: The participation rate is \(\frac{3}{8}\) of all members

2. INFER the solution approach

• This is a proportion problem: if 3 out of every 8 members participate, then we expect the same rate across all 48 members
• Strategy: Multiply the total membership by the participation rate
• Mathematical setup: \(48 \times \frac{3}{8}\)

3. SIMPLIFY the calculation

• \(48 \times \frac{3}{8} = (48 \times 3) \div 8\)
• \(= 144 \div 8\)
• \(= 18\)

Answer: B (18)

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students misinterpret "3 out of every 8" and think it means only 3 people total will participate, or they confuse the survey sample size with the participation rate.

Instead of recognizing that \(\frac{3}{8}\) is a rate to be applied to all 48 members, they might think the answer is simply 3, or they might try to work with 8 as if it's the total number surveyed rather than the denominator of a rate.

This may lead them to select Choice A (6) by thinking 3 people from the survey means 6 people total, or causes confusion and guessing.

Second Most Common Error:

Inadequate SIMPLIFY execution: Students set up the problem correctly as \(48 \times \frac{3}{8}\) but make arithmetic errors in the calculation.

Common mistakes include calculating \(48 \times 3 = 124\) instead of 144, or dividing incorrectly. Some students might also try to convert \(\frac{3}{8}\) to a decimal first and make rounding errors.

This may lead them to select Choice C (24) or Choice D (36) depending on their specific calculation error.

The Bottom Line:

This problem tests whether students can recognize survey data as a rate that applies proportionally to a larger population, then execute the arithmetic correctly. The key insight is seeing "3 out of 8" as a fraction that scales up to the full membership.