The result of increasing the quantity x by 400% is 60. What is the value of x?

1. TRANSLATE the problem information

• Given information:
  • Starting with some quantity x
  • Increase x by 400%
  • The result is 60
• What this tells us: We need to express "x increased by 400%" mathematically

2. TRANSLATE the percentage increase

• "Increasing by 400%" means: original value + 400% of original value
• In math notation: \(\mathrm{x + \frac{400}{100}x = x + 4x}\)
• So our equation becomes: \(\mathrm{x + 4x = 60}\)

3. SIMPLIFY the equation

• Combine like terms: \(\mathrm{x + 4x = 5x}\)
• Our equation is now: \(\mathrm{5x = 60}\)
• Divide both sides by 5: \(\mathrm{x = 12}\)

Answer: A. 12

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students misinterpret "increasing by 400%" as "multiplying by 4"

They think: "If increasing x by 400% gives 60, then \(\mathrm{4x = 60}\)"
Solving: \(\mathrm{x = 60 \div 4 = 15}\)

This leads them to select Choice B (15)

Second Most Common Error:

Conceptual confusion about percentage increase: Students think "increased by 400%" means "becomes 400% of the original"

They set up: \(\mathrm{4x = 60}\) instead of \(\mathrm{x + 4x = 60}\)
This also gives \(\mathrm{x = 15}\), leading to Choice B (15)

The Bottom Line:

The key insight is understanding that "increasing BY a percentage" means adding that percentage to 100% of the original, not replacing the original with that percentage. You end up with more than you started with.