The result of decreasing the quantity x by 25% is 60. What is the value of x?45758085

1. TRANSLATE the problem information

• Given information:
  • The quantity x is decreased by 25%
  • The result of this decrease is 60
  • We need to find the original value x

2. INFER the mathematical relationship

• When we decrease something by 25%, we keep 75% of the original amount
• This means: 75% of x equals 60
• In decimal form: \(0.75\mathrm{x} = 60\)

3. SIMPLIFY to solve for x

• Divide both sides by 0.75:

\(\mathrm{x} = 60 \div 0.75\) (use calculator)

\(\mathrm{x} = 80\)

Answer: C (80)

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students misinterpret "decreasing by 25%" as simply subtracting 25 from the original number.

They set up the equation as: \(\mathrm{x} - 25 = 60\), which gives \(\mathrm{x} = 85\).

This leads them to select Choice D (85).

Second Most Common Error:

Poor INFER reasoning: Students confuse percentage decrease with percentage of the original, thinking the result should be 25% of x instead of 75% of x.

They set up: \(0.25\mathrm{x} = 60\), which gives \(\mathrm{x} = 240\) (not among the choices).

This causes confusion and leads to guessing among the available options.

The Bottom Line:

The key insight is understanding that "decreasing by 25%" means you keep 75% of the original, not that you subtract the number 25. This requires translating percentage language correctly into mathematical operations.