A technician charges a flat fee of $15 for a service call. In addition to the flat fee, the technician...

1. TRANSLATE the pricing information

• Given information:
  • Flat fee (fixed charge): \(\$15\)
  • Labor rate (variable charge): \(\$40\) per hour
  • Time worked: \(2.5\) hours
  • Find: Total charge

2. INFER the cost structure

• This is a linear cost model with two parts:
  • Fixed cost (flat fee) that doesn't change
  • Variable cost (labor) that depends on time worked
• Strategy: Calculate variable cost first, then add to fixed cost

3. Calculate the labor cost

• Labor cost = Rate × Time
• Labor cost = \(\$40/\mathrm{hour} \times 2.5\, \mathrm{hours} = \$100\)

4. SIMPLIFY to find total charge

• Total charge = Fixed cost + Variable cost
• Total charge = \(\$15 + \$100 = \$115\)

Answer: \(\$115\) (or 115)

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skills: Students misunderstand the cost structure and think they need to add the hourly rate directly to the flat fee, calculating \(\$15 + \$40 = \$55\), then getting confused about what to do with the \(2.5\) hours.

This leads to confusion and guessing since \(\$55\) doesn't seem like a complete answer.

Second Most Common Error:

Inadequate SIMPLIFY execution: Students correctly identify that they need to calculate \(\$40 \times 2.5 + \$15\), but make arithmetic errors. Common mistakes include calculating \(\$40 \times 2.5 = \$80\) (instead of \(\$100\)) or making addition errors in the final step.

This can lead them to incorrect answers like \(\$95\) instead of \(\$115\).

The Bottom Line:

This problem tests whether students can break down a real-world pricing model into its mathematical components and execute the calculations correctly. The key insight is recognizing that service pricing often combines fixed and variable costs.