Robert rented a truck to transport materials he purchased from a hardware store. He was charged an initial fee of...

1. TRANSLATE the problem information

• Given information:
  • Initial rental fee: \(\$20.00\) (fixed cost)
  • Additional charge: \(\$0.70\) per mile driven (variable rate)
  • Miles driven: 38 miles

• What this tells us: We have a linear cost model where total cost = fixed cost + (rate × quantity)

2. TRANSLATE into mathematical equation

• Set up the cost equation: \(\mathrm{Total\ cost} = \$20.00 + \$0.70 \times (\mathrm{miles\ driven})\)
• Substitute the known value: \(\mathrm{Total\ cost} = \$20.00 + \$0.70 \times 38\)

3. SIMPLIFY through calculation

• Calculate the variable cost: \(\$0.70 \times 38 = \$26.60\) (use calculator)
• Add the fixed and variable costs: \(\$20.00 + \$26.60 = \$46.60\)

Answer: A. \(\$46.60\)

Why Students Usually Falter on This Problem

Most Common Error Path:

Calculation errors in SIMPLIFY: Students make arithmetic mistakes when multiplying \(\$0.70 \times 38\), getting values like \(\$32.60\) instead of \(\$26.60\).

When they add this incorrect variable cost to the \(\$20.00\) initial fee, they get a total that doesn't match any answer choice. This leads to confusion and guessing among the available options.

Second Most Common Error:

Incomplete TRANSLATE reasoning: Students correctly identify the \(\$0.70\) per mile rate and 38 miles, but forget to include the initial \(\$20.00\) fee in their calculation.

They calculate only the variable portion: \(\$0.70 \times 38 = \$26.60\), and might think this is the final answer. Since \(\$26.60\) isn't among the choices, this causes them to get stuck and randomly select an answer.

The Bottom Line:

This problem tests whether students can properly set up and execute a linear cost calculation. The key is remembering that rental problems typically have both fixed costs (initial fees) and variable costs (per-unit charges).