The result of decreasing a number by 40% is 36. What is the original number?45506090

1. TRANSLATE the problem information

• Given information:
  • Original number decreased by 40% equals 36
  • Need to find the original number

2. INFER the mathematical relationship

• Key insight: "Decreasing by 40%" means we keep 60% of the original
• If x is the original number, then 60% of x equals 36
• This gives us: \(\mathrm{0.60x = 36}\)

3. SIMPLIFY to solve for the original number

• Divide both sides by 0.60: \(\mathrm{x = 36 \div 0.60}\)
• Calculate: \(\mathrm{x = 60}\) (use calculator)

4. Verify the answer

• Check: \(\mathrm{60 - (0.40 \times 60) = 60 - 24 = 36}\) ✓

Answer: C (60)

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak INFER skill: Students incorrectly think "decreasing by 40%" means multiplying by 0.40 instead of 0.60.

They set up: \(\mathrm{0.40x = 36}\), leading to \(\mathrm{x = 36 \div 0.40 = 90}\)

This may lead them to select Choice D (90)

Second Most Common Error:

Poor TRANSLATE reasoning: Students misinterpret the problem direction and think they need to decrease 36 by 40%.

They calculate: \(\mathrm{36 - (0.40 \times 36) = 36 - 14.4 = 21.6}\), then look for the closest answer choice.

This leads to confusion and guessing among the given choices.

The Bottom Line:

The key challenge is understanding that "decreased by 40%" leaves you with 60% of the original, not 40%. Students must recognize that percentage decrease problems require working with the complement percentage.