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:
  • \(60\%\) of attendees chose afternoon slot
  • 180 more people chose afternoon than morning
  • Need to find morning attendees

2. INFER the complementary relationship

• If \(60\%\) chose afternoon, then \(40\%\) chose morning (percentages must add to \(100\%\))
• Let \(\mathrm{T}\) = total attendees
• \(\mathrm{Afternoon} = 0.60\mathrm{T}\), \(\mathrm{Morning} = 0.40\mathrm{T}\)

3. TRANSLATE the difference statement into an equation

• "180 more chose afternoon than morning" means:
• \(\mathrm{Afternoon} - \mathrm{Morning} = 180\)
• \(0.60\mathrm{T} - 0.40\mathrm{T} = 180\)

4. SIMPLIFY to solve for total attendees

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

5. SIMPLIFY to find morning attendees

• \(\mathrm{Morning} = 0.40\mathrm{T} = 0.40 \times 900 = 360\)

Answer: (C) 360

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students misinterpret "180 more chose afternoon" and think this means 180 people chose afternoon total, rather than understanding it's the difference between the two groups.

They might set up: \(\mathrm{Afternoon} = 180\), \(\mathrm{Morning} = ?\), leading to confusion about how to use the \(60\%\) information. This leads to confusion and guessing.

Second Most Common Error:

Incomplete SIMPLIFY execution: Students correctly find \(\mathrm{T} = 900\) but then calculate the afternoon attendees (\(0.60 \times 900 = 540\)) instead of the morning attendees that the question asks for.

This may lead them to select Choice (D) (540).

The Bottom Line:

This problem requires careful reading to distinguish between the total in each group versus the difference between groups, combined with understanding that percentage splits are complementary.