A manufacturer reduces the weight of a gadget by 7% during a redesign. If the new weight is k times...

1. TRANSLATE the problem information

• Given information:
  • Original weight gets reduced by 7%
  • New weight = k × original weight
  • Need to find k

2. TRANSLATE percentage reduction to algebra

• Let original weight = W
• 7% reduction means: New weight = \(\mathrm{W - 0.07W = 0.93W}\)

3. INFER the key relationship

• The problem states "new weight is k times the original weight"
• This means: \(\mathrm{New\ weight = k \times Original\ weight}\)
• Therefore: \(\mathrm{0.93W = k \times W}\)

4. SIMPLIFY to solve for k

• From \(\mathrm{0.93W = k \times W}\)
• Divide both sides by W: \(\mathrm{k = 0.93}\)

Answer: C (0.93)

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students confuse the 7% reduction with the final answer

Many students see "7% reduction" and immediately think \(\mathrm{k = 0.07}\), failing to realize that 0.07 represents how much was removed, not what remains. They don't convert the reduction to the final percentage of the original weight.

This may lead them to select Choice A (0.07)

Second Most Common Error:

Poor TRANSLATE reasoning: Students add instead of subtract the percentage

Some students mistakenly think a "7% reduction" means the new weight is 107% of the original (1.07 times), confusing reduction with increase.

This may lead them to select Choice D (1.07)

The Bottom Line:

The key challenge is correctly interpreting what "reduced by 7%" means mathematically - it's the complement \(\mathrm{(100\% - 7\% = 93\%)}\) that matters, not the reduction amount itself.