Question:The function \(\mathrm{g(t)=5t+12}\). For what value of t does \(\mathrm{g(t)=47}\)?

1. TRANSLATE the problem information

• Given information:
  • Function: \(\mathrm{g(t) = 5t + 12}\)
  • Need to find: the value of t where \(\mathrm{g(t) = 47}\)

• What this tells us: We need to set the function expression equal to 47 and solve for t

2. TRANSLATE the question into an equation

• The question "For what value of t does g(t) = 47?" means we substitute the function expression for g(t):
  \(\mathrm{5t + 12 = 47}\)

3. SIMPLIFY by solving the linear equation

• Subtract 12 from both sides to isolate the term with t:
  \(\mathrm{5t = 47 - 12}\)
  \(\mathrm{5t = 35}\)

• Divide both sides by 5 to solve for t:
  \(\mathrm{t = 35 ÷ 5 = 7}\)

Answer: A. 7

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak SIMPLIFY execution: Students correctly set up \(\mathrm{5t + 12 = 47}\) but make arithmetic mistakes in the solving process. Common errors include:

• Calculating \(\mathrm{47 - 12 = 33}\) instead of 35
• Forgetting to perform the final division step

When they calculate 47 - 12 incorrectly as 33, then divide by 5, they get \(\mathrm{t = 6.6}\), leading them to select Choice B (6) as the closest answer.

Second Most Common Error:

Incomplete SIMPLIFY process: Students correctly calculate \(\mathrm{5t = 35}\) but stop there, forgetting to divide by 5 to fully isolate t.

This causes them to think the answer is 35, leading them to select Choice C (35).

The Bottom Line:

This problem tests whether students can systematically work through a linear equation without rushing. The key is maintaining accuracy through each arithmetic step and completing the full solution process.