A moving company charges a flat fee of $50 plus an additional $20 per hour of labor. The total cost,...

1. TRANSLATE the question into mathematical terms

• Given information:
  • Cost function: \(\mathrm{C(h) = 50 + 20h}\)
  • Need to find: Total cost for 3 hours of labor
• What this tells us: We need to evaluate \(\mathrm{C(3)}\) by substituting \(\mathrm{h = 3}\) into the function

2. SIMPLIFY the function evaluation

• Substitute \(\mathrm{h = 3}\) into \(\mathrm{C(h) = 50 + 20h}\):
  • \(\mathrm{C(3) = 50 + 20(3)}\)
• Follow order of operations (multiply first, then add):
  • \(\mathrm{C(3) = 50 + 60}\)
  • \(\mathrm{C(3) = 110}\)

Answer: C. $110

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak SIMPLIFY execution: Not following order of operations correctly

Students might calculate from left to right instead of doing multiplication first:

• Incorrect: \(\mathrm{C(3) = 50 + 20(3) = 70(3) = 210}\)
• Or: \(\mathrm{(50 + 20) \times 3 = 70 \times 3 = 210}\)

This leads to confusion since 210 isn't among the answer choices, causing them to guess or recalculate incorrectly, potentially selecting Choice D ($150) as the closest large value.

Second Most Common Error:

Poor TRANSLATE reasoning: Misunderstanding what the question is asking

Students might think they need to find the hourly rate or manipulate the function algebraically rather than simply substituting the given value. This confusion about the task leads them to get stuck and randomly select an answer.

The Bottom Line:

This problem tests whether students can translate a straightforward question into function evaluation and execute basic arithmetic correctly. The key insight is recognizing that "find the cost for 3 hours" simply means "substitute 3 into the given function."