Question:If 18% of a number is 72, what is the number?90200288400

1. TRANSLATE the problem information

• Given information:
  • 18% of some unknown number equals 72
  • Need to find that unknown number

• What this tells us: We need to set up an equation where 18% (as a decimal) multiplies our unknown number to give 72.

2. TRANSLATE into mathematical form

• Let \(\mathrm{x}\) = the unknown number
• '18% of x is 72' becomes: \(\mathrm{0.18 \times x = 72}\)
• Remember: \(\mathrm{18\% = \frac{18}{100} = 0.18}\)

3. SIMPLIFY to solve the equation

• We have: \(\mathrm{0.18x = 72}\)
• Divide both sides by 0.18: \(\mathrm{x = 72 \div 0.18}\)
• Calculate: \(\mathrm{x = 400}\) (use calculator)

4. Verify the answer

• Check: 18% of 400 = \(\mathrm{0.18 \times 400 = 72}\) ✓

Answer: D (400)

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students often struggle with converting percentage language into proper mathematical equations. They might set up the equation as \(\mathrm{18x = 72}\) (forgetting to convert 18% to 0.18) or as \(\mathrm{x \div 18 = 72}\) (confusing the relationship).

When they use \(\mathrm{18x = 72}\), they get \(\mathrm{x = 72 \div 18 = 4}\), which isn't among the choices, leading to confusion and guessing.

Second Most Common Error:

Conceptual confusion about percentages: Students sometimes reverse the relationship, asking themselves '72 is 18% of what?' but then thinking about it as 'what percent of 72 is 18?' This conceptual mix-up can cause them to perform incorrect calculations.

This leads to abandoning systematic solution and guessing among the answer choices.

The Bottom Line:

The key challenge is accurately translating percentage language into mathematical equations. Students must remember that '18% of a number' means multiplying that number by 0.18, not by 18.