An event offered two time slots, morning and afternoon. A city report states that 60% of attendees chose the afternoon...

1. TRANSLATE the problem information

• Given information:
  • 60% chose afternoon slot
  • Afternoon attendees exceed morning attendees by 180
• What this tells us:
  • Morning attendees = 40% (since \(60\% + 40\% = 100\%\))
  • We need the actual number who chose morning

2. INFER the approach

• Key insight: The difference between 60% and 40% is 20% of total attendees
• Strategy: Use the fact that this 20% difference equals 180 people
• Set up equation: \(0.60\mathrm{T} - 0.40\mathrm{T} = 180\), where T = total attendees

3. SIMPLIFY to find total attendees

• \(0.60\mathrm{T} - 0.40\mathrm{T} = 180\)
• \(0.20\mathrm{T} = 180\)
• \(\mathrm{T} = 180 \div 0.20 = 900\) (use calculator)

4. Calculate morning attendees

• Morning = 40% of total = \(0.40 \times 900 = 360\) (use calculator)

Answer: C (360)

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students misinterpret what the problem is asking for and confuse the difference (180) with the final answer.

They might think: "180 more chose afternoon, so 180 chose morning." This completely ignores the percentage information and leads them to select Choice A (180).

Second Most Common Error:

Poor INFER reasoning: Students correctly set up the percentage relationships but incorrectly calculate which group to find.

They find the total (900) and then calculate afternoon attendees: \(0.60 \times 900 = 540\), leading them to select Choice D (540) instead of recognizing they need the morning count.

The Bottom Line:

This problem requires connecting percentage relationships with absolute differences - students must recognize that the percentage gap corresponds to the numerical gap, then work backwards to find the specific group requested.