Question:A community theater has 220 seats in its auditorium.For a matinee performance, 40% of the seats are reserved for students.How...

1. TRANSLATE the problem information

• Given information:
  • Total seats: 220
  • Student reserved seats: 40% of total
• What this tells us: We need to find 40% of 220

2. TRANSLATE "40%" into mathematical form

• 40% means 40 out of 100, which equals \(\frac{40}{100} = 0.40\)
• So "40% of 220" becomes \(0.40 \times 220\)

3. SIMPLIFY the calculation

• \(0.40 \times 220 = 88\) seats

Answer: B. 88

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students multiply by 40 instead of 0.40

They think "40% of 220" means \(40 \times 220\), forgetting that percent means "per hundred." This calculation gives them 8,800, but seeing no such large answer choice, they might divide by 10 and select Choice (D) (880).

Second Most Common Error:

Conceptual confusion about percentages: Students mix up common percentages

They might calculate 50% instead of 40% (perhaps seeing "40%" but thinking of the more familiar "50%"), getting 110. This leads them to select Choice (C) (110).

Third Common Error:

Incomplete TRANSLATE reasoning: Students calculate 20% instead of 40%

They might halve the percentage accidentally or calculate 10% (which is 22) and double it instead of quadrupling it, getting 44. This leads them to select Choice (A) (44).

The Bottom Line:

The key challenge is accurately converting the percentage to its decimal equivalent and remembering that "percent of" always means multiplication, not addition or other operations.