What number is 40% greater than 115?

1. TRANSLATE the problem language into math

• Given information:
  • We need a number that is \(40\% \text{ greater than } 115\)
  • "40% greater than" means the original number plus 40% of that number

• What this tells us: We need to find \(115 + (40\% \text{ of } 115)\)

2. INFER an efficient approach

• We can solve this two ways:
  • Method 1: Find \(40\% \text{ of } 115\), then add to 115
  • Method 2: Recognize that "40% greater" means 140% of the original

• Method 2 is more efficient: \(40\% \text{ greater} = 100\% + 40\% = 140\% \text{ of original}\)

3. SIMPLIFY using the efficient method

• Convert percentage to decimal: \(140\% = 1.40\)
• Calculate: \(1.40 \times 115 = 161\)

Answer: 161

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Misinterpreting "\(40\% \text{ greater than } 115\)" as simply "\(40\% \text{ of } 115\)"

Students think they just need to find \(40\% \text{ of } 115\), calculating \(0.40 \times 115 = 46\), and stopping there. They don't realize that "greater than" means they need to add this to the original amount. This conceptual misunderstanding of percentage increase language is extremely common.

This leads to confusion when 46 doesn't appear as an answer choice, causing them to guess randomly.

Second Most Common Error:

Poor INFER reasoning: Adding 40 instead of 40% of 115

Some students see "40% greater" and incorrectly think this means "add 40 to the original number." They calculate \(115 + 40 = 155\). This stems from confusing percentage increase with simple addition.

This may lead them to select an incorrect answer if 155 appears as a choice, or causes confusion and guessing if it doesn't.

The Bottom Line:

The key challenge is correctly interpreting percentage increase language. "\(\mathrm{X}\% \text{ greater than } \mathrm{Y}\)" always means \(\mathrm{Y} + (\mathrm{X}\% \text{ of } \mathrm{Y})\), not just \(\mathrm{X}\% \text{ of } \mathrm{Y}\). Students who master this translation can solve these problems efficiently using the shortcut: \(\mathrm{X}\% \text{ greater} = (100 + \mathrm{X})\% \text{ of the original}\).