If 15% of a number is 60, what is the number?945240400

1. TRANSLATE the problem information

• Given information:
  • 15% of some unknown number equals 60
  • We need to find that unknown number

• In mathematical terms: If x is our unknown number, then \(0.15\mathrm{x} = 60\)

2. INFER the solution strategy

• To find x when \(0.15\mathrm{x} = 60\), we need to isolate x
• We can do this by dividing both sides by 0.15
• Alternative thinking: "If 0.15 times something equals 60, then that something equals 60 divided by 0.15"

3. SIMPLIFY the calculation

• \(\mathrm{x} = 60 \div 0.15\)
• To make this easier, convert to multiplication: \(\mathrm{x} = 60 \times (1/0.15) = 60 \times (100/15)\)
• Simplify the fraction: \(100/15 = 20/3\)
• Calculate: \(\mathrm{x} = 60 \times (20/3)\)
  \(= 60 \times 20 \div 3\)
  \(= 1200 \div 3\)
  \(= 400\) (use calculator)

Answer: D. 400

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak INFER skill: Students confuse the direction of the operation and think "15% of 60" instead of recognizing they need to find what number has 15% equal to 60.

They incorrectly calculate: \(0.15 \times 60 = 9\)

This leads them to select Choice A (9)

Second Most Common Error:

Poor SIMPLIFY execution: Students correctly set up \(0.15\mathrm{x} = 60\) but make calculation errors when dividing by the decimal 0.15.

Common mistakes include treating \(60 \div 0.15\) as \(60 \div 15 = 4\), or getting confused with decimal placement during division.

This leads to confusion and guessing among the remaining choices.

The Bottom Line:

This problem tests whether students can correctly interpret "percentage of" language and work backwards from a percentage result to find the original number. The key insight is recognizing that if 15% gives you 60, you need to scale up to find what 100% would be.