140 is p% greater than 10. What is the value of p?

1. TRANSLATE the problem statement

• Given information:
  • 140 is p% greater than 10
  • Need to find the value of p

• What "p% greater than" means: If something is p% greater than a base value, it equals the base value plus p% of that base value.

2. TRANSLATE this into a mathematical equation

• "140 is p% greater than 10" becomes:
  \(140 = 10 + (\mathrm{p\%\ of\ 10})\)
  \(140 = 10 + (\mathrm{p}/100) \times 10\)
  \(140 = 10 + 0.1\mathrm{p}\)

3. SIMPLIFY to solve for p

• Subtract 10 from both sides:
  \(140 - 10 = 0.1\mathrm{p}\)
  \(130 = 0.1\mathrm{p}\)

• Divide both sides by 0.1:
  \(\mathrm{p} = 130 \div 0.1 = 1,300\)

Answer: B. 1,300

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students confuse "p% greater than" with "p% of"

Instead of setting up \(140 = 10 + (\mathrm{p}/100) \times 10\), they might write \(140 = (\mathrm{p}/100) \times 10\). Solving this gives them \(140 = 0.1\mathrm{p}\), so \(\mathrm{p} = 1,400\).

This may lead them to select Choice A (1,400).

Second Most Common Error:

Incomplete SIMPLIFY execution: Students correctly set up the equation and get to \(130 = 0.1\mathrm{p}\), but then think \(\mathrm{p} = 130\)

They forget the final division step (dividing by 0.1) and stop at the intermediate result.

This may lead them to select Choice D (130).

The Bottom Line:

The key challenge is distinguishing between "p% of a number" and "p% greater than a number." The word "greater" signals addition—you take the original amount plus the percentage increase.