A manufacturing company uses a formula to calculate an employee's daily productivity score, S. The formula is S = 100...

1. TRANSLATE the problem information

• Given information:
  • Formula: \(\mathrm{S = 100 - 3d}\)
  • Employee produces 7 defective parts
  • Need to find productivity score S

• This tells us: \(\mathrm{d = 7}\) (number of defective parts)

2. SIMPLIFY by substituting and calculating

• Substitute \(\mathrm{d = 7}\) into the formula:
  \(\mathrm{S = 100 - 3(7)}\)

• Apply order of operations - multiply first:
  \(\mathrm{3 \times 7 = 21}\)

• Now subtract:
  \(\mathrm{S = 100 - 21 = 79}\)

Answer: B. 79 points

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak SIMPLIFY execution: Forgetting to multiply by 3 and instead calculating \(\mathrm{S = 100 - 7 = 93}\)

Students see the 7 defective parts and subtract directly from 100, missing that the formula requires multiplying the defective parts by 3 first.

This leads them to select Choice C (93 points)

Second Most Common Error:

Poor SIMPLIFY reasoning: Adding instead of subtracting, calculating \(\mathrm{S = 100 + 3(7) = 100 + 21 = 121}\)

Students correctly multiply \(\mathrm{3 \times 7 = 21}\), but then add this to 100 instead of subtracting, possibly misreading the minus sign in the formula.

This leads them to select Choice D (121 points)

Third Common Error:

Incomplete SIMPLIFY process: Only calculating the multiplication part, \(\mathrm{3 \times 7 = 21}\), and stopping there

Students correctly identify that \(\mathrm{3 \times 7 = 21}\) but fail to complete the subtraction step of the formula.

This leads them to select Choice A (21 points)

The Bottom Line:

Success on this problem requires careful attention to the complete formula structure and systematic application of order of operations - students often rush through and miss critical calculation steps.