A fitness center charges a monthly membership fee plus an additional cost for personal training sessions. The total monthly cost...

1. TRANSLATE the problem information

• Given information:
  • Cost function: \(\mathrm{C(s) = 12s + 85}\)
  • Number of sessions used: \(\mathrm{s = 8}\)
• We need to find the total monthly cost when \(\mathrm{s = 8}\)

2. INFER the solution approach

• To find the cost for 8 sessions, we need to substitute \(\mathrm{s = 8}\) into our function
• This means we'll evaluate \(\mathrm{C(8)}\) using the given formula

3. SIMPLIFY through substitution and calculation

\(\mathrm{C(8) = 12(8) + 85}\)

\(\mathrm{C(8) = 96 + 85}\)

\(\mathrm{C(8) = 181}\)

Answer: D. $181

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students may not understand what "uses 8 personal training sessions" means in terms of the function. They might think they need to somehow add 8 to the entire function or manipulate the equation differently rather than simply substituting \(\mathrm{s = 8}\).

This leads to confusion and guessing rather than systematic solution.

Second Most Common Error:

Poor SIMPLIFY execution: Students correctly identify that they need to substitute \(\mathrm{s = 8}\), but make arithmetic errors. The most common mistakes are:

• Calculating \(\mathrm{12 \times 8}\) incorrectly (getting 84 instead of 96)
• Adding \(\mathrm{96 + 85}\) incorrectly

These calculation errors may lead them to select Choice A ($96) if they forget to add the 85, or other incorrect choices based on their arithmetic mistakes.

The Bottom Line:

This problem tests whether students understand function notation and can perform accurate substitution. The key insight is recognizing that evaluating a function simply means "plugging in" the given value and calculating the result.