Question:The result of decreasing the quantity y by 75% is 15. What is the value of y?25456075

1. TRANSLATE the problem information

• Given information:
  • Original quantity: \(\mathrm{y}\)
  • After decreasing \(\mathrm{y}\) by 75%, the result is 15
  • Need to find: the value of \(\mathrm{y}\)

• What 'decreasing by 75%' means: We subtract 75% of \(\mathrm{y}\) from \(\mathrm{y}\), leaving us with 25% of \(\mathrm{y}\)

2. TRANSLATE the mathematical relationship

• If we decrease \(\mathrm{y}\) by 75%, we remove \(0.75\mathrm{y}\) from \(\mathrm{y}\)
• What remains: \(\mathrm{y} - 0.75\mathrm{y} = 0.25\mathrm{y}\)
• This remaining amount equals 15: \(0.25\mathrm{y} = 15\)

3. SIMPLIFY to solve for y

• We have: \(0.25\mathrm{y} = 15\)
• To isolate \(\mathrm{y}\), divide both sides by 0.25:
  \(\mathrm{y} = 15 \div 0.25\)
• Since \(0.25 = \frac{1}{4}\), dividing by 0.25 is the same as multiplying by 4:
  \(\mathrm{y} = 15 \times 4 = 60\)

4. Verify the answer

• Check: If \(\mathrm{y} = 60\), then 75% of 60 = \(0.75 \times 60 = 45\)
• Decreasing 60 by 45: \(60 - 45 = 15\) ✓ This matches the problem statement

Answer: C (60)

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students misinterpret 'decreasing by 75%' and think it means subtracting the number 75 (instead of 75% of \(\mathrm{y}\)) or confuse what percentage remains.

Some students might think the problem means '\(\mathrm{y} - 75 = 15\)' and solve to get \(\mathrm{y} = 90\), or they might incorrectly believe that 75% of the original quantity remains (instead of 25% remaining). These translation errors lead to setting up completely wrong equations from the start.

This leads to confusion and guessing among the answer choices.

The Bottom Line:

The key challenge is correctly translating percentage language into mathematical relationships. Students must understand that 'decreasing by 75%' means removing three-quarters of something, leaving one-quarter behind.