The total cost C, in dollars, of renting a car for d days is given by \(\mathrm{C(d) = 25d +...

1. TRANSLATE the function notation

• Given information:
  • Function: \(\mathrm{C(d) = 25d + 45}\)
  • Need to find: \(\mathrm{C(3)}\)
• What \(\mathrm{C(3)}\) tells us: Replace every d in the function with 3

2. SIMPLIFY through substitution and calculation

• Substitute \(\mathrm{d = 3}\):
  \(\mathrm{C(3) = 25(3) + 45}\)
• Calculate step by step:
  • First: \(\mathrm{25 \times 3 = 75}\)
  • Then: \(\mathrm{75 + 45 = 120}\)

Answer: C (120)

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak SIMPLIFY execution: Students correctly substitute \(\mathrm{d = 3}\) but stop after calculating \(\mathrm{25(3) = 75}\)

They forget to add the constant term (+45) and think the answer is just 75.

This leads them to select Choice B (75).

Second Most Common Error:

Poor TRANSLATE reasoning: Students misunderstand function evaluation and think they should add the numbers in the function first, then multiply by the input value

They calculate \(\mathrm{(25 + 45) \times 3 = 70 \times 3 = 210}\) instead of \(\mathrm{25(3) + 45}\).

This leads them to select Choice D (210).

The Bottom Line:

Function evaluation problems seem straightforward, but students often rush through the arithmetic or misunderstand the order of operations, leading to systematic errors that produce tempting wrong answer choices.