Percent Word Problems

Percent word problems come in three main types, each asking you to find a different piece of information: **Type 1: Finding the Part** $$\text{Part} = \text{Percent} \times \text{Whole}$$ *"What is 25% of 80?"* **Type 2: Finding the Whole** $$\text{Whole} = \frac{\text{Part}}{\text{Percent}}$$ *"15 is 30% of what number?"* **Type 3: Finding the Percent** $$\text{Percent} = \frac{\text{Part}}{\text{Whole}} \times 100$$ *"What percent of 50 is 12?"* The key to solving percent problems is identifying which type you're dealing with, then applying the correct formula.

Finding the Part - Store Discount

A jacket costs 80 dollars. The store offers a 25% discount. How much money do you save?

Identify the problem type: We need to find 25% OF 80 dollars = Type 1: Finding the Part

Convert percent to decimal: $25\% = 25 \div 100 = 0.25$ = $0.25$

Multiply to find the part: $0.25 \times 80 = 20$ = $20$

Write the answer with units: The discount is 20 dollars = You save 20 dollars

Answer: You save 20 dollars on the jacket.

Finding the Whole - Test Score

Maria answered 36 questions correctly, which was 90% of the test. How many questions were on the test?

Identify the problem type: 36 IS 90% of what number? = Type 2: Finding the Whole

Set up the equation: $36 = 0.90 \times \text{Whole}$ = Part = Percent × Whole

Solve for the whole: $\text{Whole} = 36 \div 0.90 = 40$ = $40$ questions

Check the answer: $0.90 \times 40 = 36$ ✓ = Verified!

Answer: The test had 40 questions total.

Finding the Percent - Tip Calculation

A restaurant bill is 45 dollars. You leave a 9 dollar tip. What percent tip did you leave?

Identify the problem type: What PERCENT of 45 is 9? = Type 3: Finding the Percent

Set up the fraction: $\text{Percent} = \frac{\text{Part}}{\text{Whole}}$ = $\frac{9}{45}$

Divide and simplify: $9 \div 45 = 0.20$ = $0.20$

Convert to percent: $0.20 \times 100 = 20\%$ = $20\%$

Answer: You left a 20% tip.

Combined Problem - Final Price

A 120 dollar video game is on sale for 15% off, but there's also an 8% sales tax on the discounted price. What is the final price?

Find the discount amount: $0.15 \times 120 = 18$ dollars off = 18 dollars discount

Find the sale price: $120 - 18 = 102$ dollars = Sale price: 102 dollars

Calculate the tax: $0.08 \times 102 = 8.16$ dollars = Tax: 8.16 dollars

Add tax to sale price: $102 + 8.16 = 110.16$ dollars = Final price: 110.16 dollars

Answer: The final price is 110.16 dollars.

Percent problems appear constantly in everyday life: - **Shopping**: Calculating discounts ("30% off") and sales tax - **Dining**: Figuring out tips at restaurants (15%, 18%, 20%) - **Finance**: Understanding interest rates, loans, and investments - **School**: Converting test scores to percentages - **Health**: Reading nutrition labels ("25% of daily value") - **Sports**: Analyzing shooting percentages, win rates, and statistics Mastering these three problem types gives you a powerful toolkit for handling real-world math!

Mistake: Forgetting to convert percent to decimal before multiplying

Why: 25% means 25 per hundred, not 25. Using 25 instead of 0.25 gives an answer 100 times too large.

Correct: Always divide the percent by 100 first: $25\% = 0.25$, then multiply.

Mistake: Dividing when you should multiply (or vice versa)

Why: Confusing "finding the part" with "finding the whole" leads to inverse operations.

Correct: Ask yourself: Am I looking for a PIECE of something (multiply) or the TOTAL (divide)?

Mistake: Calculating percent increase/decrease incorrectly

Why: Applying the percent to the wrong number or forgetting to add/subtract from the original.

Correct: For increase: Original × (1 + percent). For decrease: Original × (1 - percent).

Mistake: Mixing up the part and the whole

Why: In "15 is what percent of 60?", students sometimes put 60 in the numerator.

Correct: The part (smaller value, 15) always goes in the numerator: $\frac{15}{60} = 25\%$.

Shopping and Discounts

Calculating sale prices requires finding the part (discount amount) and subtracting from the original.

A 50 dollar shirt is 30% off. The discount is $0.30 \times 50 = 15$ dollars, so you pay $50 - 15 = 35$ dollars.

Restaurant Tips

Tips are calculated as a percent of the bill before tax.

On a 60 dollar bill, a 20% tip is $0.20 \times 60 = 12$ dollars.

Test Scores and Grades

Converting scores to percentages helps compare performance across different tests.

If you got 42 out of 50 questions right, your percent is $\frac{42}{50} \times 100 = 84\%$.

Three types: Finding the Part (multiply), Finding the Whole (divide), Finding the Percent (divide then multiply by 100)

Always convert percent to decimal first by dividing by 100 (e.g., $25\% = 0.25$)

Part = Percent × Whole is the fundamental relationship

Identify key words: "of" usually means multiply, "is" means equals

Check your answer by plugging it back into the original problem

Q: How do I know which type of percent problem I'm solving?

A: Look at what's missing: If you know the percent AND the whole, find the part (multiply). If you know the part AND the percent, find the whole (divide). If you know the part AND the whole, find the percent (divide then × 100).

Q: Why do I divide by the percent to find the whole?

A: If Part = Percent × Whole, then Whole = Part ÷ Percent. Think of it like this: if 30 is 50% of something, that something must be bigger than 30. Dividing 30 by 0.50 gives 60.

Q: What's the difference between percent increase and percent of?

A: "20% of 100" is just 20. "20% increase on 100" means 100 + 20 = 120. Percent increase adds to the original; percent of is just multiplication.

Exit Presentation

Percent Word Problems

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Word Problems / Problem Types

Percent Word Problems

Master the three types of percent problems: finding the part, finding the whole, and finding the percent.

Intermediate25 min

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