A recreation center charges $18 per hour to rent a badminton court and $26 per hour to rent a tennis...

1. TRANSLATE the problem information

• Given information:
  • Badminton court rental: $18 per hour
  • Tennis court rental: $26 per hour
  • \(\mathrm{b}\) = hours of badminton court rental
  • \(\mathrm{c}\) = hours of tennis court rental
  • Total cost inequality: \(18\mathrm{b} + 26\mathrm{c} \leq 200\)

• What this tells us: We need to understand what each term in the expression means

2. INFER the meaning of each term

• Look at the structure: coefficient × variable
• \(18\mathrm{b}\) means: ($18 per hour) × (\(\mathrm{b}\) hours) = total cost for badminton
• \(26\mathrm{c}\) means: ($26 per hour) × (\(\mathrm{c}\) hours) = total cost for tennis

3. TRANSLATE back to answer choices

• \(26\mathrm{c}\) = total amount charged for tennis court rentals
• This matches choice (C) exactly

Answer: C

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students confuse the rate per hour with the total cost, focusing only on the coefficient 26 instead of the entire term \(26\mathrm{c}\).

They might think \(26\mathrm{c}\) represents just the hourly rate ($26) and select Choice A. They miss that the question asks about the term \(26\mathrm{c}\), not just the number 26.

Second Most Common Error:

Poor attention to variable meaning: Students mix up which variable represents which activity, thinking \(\mathrm{c}\) might represent badminton hours instead of tennis hours.

This confusion about what \(\mathrm{c}\) represents could lead them to select Choice B (badminton costs), thinking \(26\mathrm{c}\) somehow relates to badminton rental costs.

The Bottom Line:

This problem tests whether students can correctly interpret algebraic expressions in real-world contexts. The key is recognizing that coefficient × variable gives total cost, not just the rate.