Percentage Word Problems
Real-world problems with step-by-step solutions. Click "Show Solution" when you're ready.
How to Solve Any Percentage Word Problem
Every percentage problem fits one of three patterns:
| Pattern | Key Phrase | Formula |
|---|---|---|
| Find the part | "What is X% of Y?" | Answer = Y × X/100 |
| Find the percent | "X is what % of Y?" | Answer = (X ÷ Y) × 100 |
| Find the whole | "X is Y% of what?" | Answer = X ÷ (Y/100) |
Tricky Percentage Concepts
Successive percentages don't add: 10% off then 10% off ≠ 20% off. The second discount applies to the already-reduced price.
Percentage increase then decrease doesn't cancel: +10% then −10% = −1%. The base changes between operations.
"Of" vs "off": "10% of $80" = $8 (the amount). "10% off $80" = $72 (the result). Students confuse these constantly.
Study Tips
Draw a bar model: Visualize the whole as a bar, shade the percentage. This helps with "find the whole" problems.
Estimate first: Before calculating, estimate. "10% of $80 is about $8, so 15% is about $12." If your exact answer is wildly different, you made an error.
Check with the reverse: After solving, plug your answer back in. If 10% off $80 = $72, verify: $72 is $8 less than $80, and $8/$80 = 10%. ✓