A machine in a factory produces 120 electronic components per hour. During a quality check, it is found that, on...

1. TRANSLATE the problem information

• Given information:
  • Production rate: 120 components per hour
  • Defective rate: \(\frac{1}{8}\) of all components produced
  • Operating time: 6 hours
  • Need to find: non-defective components produced

2. INFER the most efficient approach

• Key insight: We need non-defective components, but we're given the defective rate
• Two strategic options:
  • Calculate non-defective rate first, then multiply by total time
  • Calculate total production, then subtract defective components
• Let's use the second approach as it's more straightforward

3. Calculate total production

• Total components produced = rate × time
• Total = \(120\) components/hour × \(6\) hours = \(720\) components

4. SIMPLIFY to find defective components

• Defective components = \(\frac{1}{8}\) × total production
• Defective = \(\frac{1}{8} \times 720\)
  \(= 720 \div 8\)
  \(= 90\) components

5. Find non-defective components

• Non-defective = Total - Defective
• Non-defective = \(720 - 90\)
  \(= 630\) components

Answer: 630

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students misinterpret what the problem is asking for and calculate total production instead of non-defective components.

They correctly calculate \(120 \times 6 = 720\) but stop there, thinking this answers the question. They miss that the problem specifically asks for non-defective components, not total production. This leads them to select 720 as their final answer.

Second Most Common Error:

Inadequate SIMPLIFY execution: Students correctly understand they need to find non-defective components but make calculation errors with fractions.

A common mistake is calculating the defective components as \(720 \times 8 = 5,760\) instead of \(720 \div 8 = 90\), leading to impossible negative results. Or they might calculate \(\frac{7}{8}\) of 720 incorrectly, getting values like 315 (if they divide by 16 instead of multiply by \(\frac{7}{8}\)). This causes confusion and often leads to guessing.

The Bottom Line:

This problem tests both reading comprehension (understanding what "non-defective" means in context) and multi-step problem solving (total production → defective amount → non-defective amount). Success requires careful attention to what the question actually asks for, not just what's easiest to calculate first.