Question:Sarah signed up for a gym membership with a 12-month contract requiring a $180 cancellation fee if terminated early. However,...

1. TRANSLATE the problem information

• Given information:
  • Initial cancellation fee: \(\$180\)
  • Fee decreases by \(\$8.50\) for each full month completed
  • Sarah completed exactly 7 months
  • Need to find: Final cancellation fee

2. INFER the solution approach

• Key insight: We need to find how much the fee has decreased, then subtract that from the original amount
• Strategy: Calculate total reduction first (months × reduction per month), then subtract from initial fee

3. SIMPLIFY by calculating the total reduction

• Total reduction = \(\$8.50 \times 7\) months = \(\$59.50\)

4. SIMPLIFY by finding the final cancellation fee

• Final fee = Initial fee - Total reduction
• Final fee = \(\$180 - \$59.50 = \$120.50\)

Answer: A (\(\$120.50\))

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE reasoning: Students misunderstand "each full month completed" and calculate using 6 months instead of 7 months.

They might think "after 7 months" means only 6 complete months have passed, leading to:

Total reduction = \(\$8.50 \times 6 = \$51.00\)

Final fee = \(\$180 - \$51.00 = \$129.00\)

This may lead them to select Choice D (\(\$129.00\))

Second Most Common Error:

Poor SIMPLIFY execution: Students make arithmetic errors when calculating either the multiplication or the final subtraction.

Common calculation mistakes include:

• Incorrectly computing \(\$8.50 \times 7\)
• Making subtraction errors with \(\$180 - \$59.50\)
• Mixing up the order of operations

This leads to confusion and selection of incorrect answer choices.

The Bottom Line:

This problem tests whether students can systematically break down a linear decrease scenario. The key is recognizing that "exactly 7 months completed" means the full reduction applies to all 7 months, then executing the arithmetic carefully.