A number n is increased 6%. If the result is 318, what is the value of n?

1. TRANSLATE the problem information

• Given information:
  • A number n is increased by 6%
  • The result after the increase is 318
  • Need to find the original number n

• What this tells us: We need to set up an equation where the original number times the increase factor equals 318.

2. TRANSLATE the percent increase

• Increasing by 6% means multiplying by \((1 + 0.06) = 1.06\)
• This gives us the equation: \(\mathrm{n} \times 1.06 = 318\)

3. SIMPLIFY to solve for n

• Divide both sides by 1.06:
  \(\mathrm{n} = 318 ÷ 1.06\) (use calculator)
  \(\mathrm{n} = 300\)

4. Verify the answer

• Check: \(300 \times 1.06 = 318\) ✓

Answer: C. 300

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students misunderstand what "increased by 6%" means and set up the wrong equation.

Common incorrect interpretations:

• \(\mathrm{n} + 6 = 318\) (adding 6 instead of 6%)
• \(\mathrm{n} + 0.06 = 318\) (adding the decimal form directly)
• \(\mathrm{n} \times 0.06 = 318\) (multiplying by just the percentage, not the increase factor)

These fundamental translation errors lead to wrong values and cause students to select incorrect answer choices or get confused and guess.

Second Most Common Error:

Conceptual confusion about working backwards: Students work from 318 in the wrong direction.

Instead of finding what number increased by 6% gives 318, they:

• Decrease 318 by 6%: \(318 \times 0.94 ≈ 299\), leading them to select Choice B (299)
• Increase 318 by 6%: \(318 \times 1.06 ≈ 337\), leading them to select Choice D (337)

The Bottom Line:

Success requires correctly translating "increased by 6%" into multiplication by 1.06, then setting up and solving the resulting equation. The most critical skill is recognizing that percent increase means multiplying by (1 + percentage in decimal form).