Percent Word Problems
Percent word problems use percents to find real prices. For a discount, find the percent of the price and subtract it. For sales tax, a tip or a markup, find the percent and add it. For example, a $40 shirt that is 25% off costs 40 − 10 = $30, because 25% of 40 is 10.
Before this lesson: You should know how to find a percent of a number from percentages and how to use a multiplier from percent change.
Discounts, Tax, Tips and More
Most money problems with percents follow the same idea. Find the percent of the price, then decide if you add it or subtract it.
| Type | What it is | Add or subtract? | Multiplier for 20% |
|---|---|---|---|
| Discount | Money taken off the price in a sale | Subtract | 0.80 |
| Sales tax | Money added by the state or city | Add | 1.20 |
| Tip | Extra money you give for good service | Add | 1.20 |
| Markup | Money a store adds to what it paid | Add | 1.20 |
| Commission | Pay a salesperson earns from a sale | The percent itself is what they earn | 0.20 |
Two Ways to Solve Percent Word Problems
Method 1: Find the amount, then add or subtract
- Change the percent to a decimal.
- Multiply it by the price to find the discount, tax, tip or markup.
- Subtract it for a discount. Add it for tax, a tip or a markup.
Method 2: Use a multiplier
Multiply the price by one number. For a discount of p percent, multiply by 1 - p (as a decimal). For an increase, multiply by 1 + p.
\text{25\% off: } 40 \times 0.75 = 30 \qquad \text{8\% tax: } 65 \times 1.08 = 70.20Worked Examples
Example 1: A discount
A shirt costs $40. It is on sale for 25% off. What is the sale price?
Step 1. Find the discount: 0.25 \times 40 = 10.
Step 2. Subtract: 40 − 10 = 30.
Answer: The sale price is $30. With a multiplier: 40 \times 0.75 = 30.
Example 2: Sales tax
A pair of shoes costs $65. The sales tax is 8%. What is the total cost?
Step 1. Find the tax: 0.08 \times 65 = 5.20.
Step 2. Add: 65 + 5.20 = 70.20.
Answer: The total cost is $70.20.
Example 3: A tip
A meal costs $42.50. You leave a 20% tip. How much is the tip, and what is the total?
Step 1. Find the tip: 0.20 \times 42.50 = 8.50. A quick way is to find 10% (4.25) and double it.
Step 2. Add: 42.50 + 8.50 = 51.00.
Answer: The tip is $8.50, and the total is $51.00.
Example 4: A markup
A store buys a hat for $15 and marks it up 60%. What price does the store charge?
Step 1. A 60% markup means the price is 160% of the cost. As a decimal, that is 1.60.
Step 2. Multiply: 15 \times 1.60 = 24.
Answer: The store charges $24.
Example 5: Word problem with two steps
A jacket costs $80. It is 30% off, and then a 6% sales tax is added to the sale price. What do you pay?
Step 1. Find the sale price: 80 \times 0.70 = 56.
Step 2. Add the tax to the sale price: 56 \times 1.06 = 59.36.
Answer: You pay $59.36.
Common Mistakes
| Mistake | What it looks like | How to fix it |
|---|---|---|
| Subtracting the percent instead of the amount | 25% off $40 is 40 − 25 = $15 | Find 25% of 40 first. That is $10, so the price is $30. |
| Giving only the tax or tip | The total cost of the shoes is $5.20 | $5.20 is the tax. Add it to the price: $70.20. |
| Adding two discounts together | 25% off and then 20% off is 45% off | The second discount uses the new price. $100 → $75 → $60, which is 40% off. |
| Not rounding money to cents | $9.9 or $59.364 | Write money with two decimal places, rounded to the nearest cent: $9.90. |
Working Backward to the Original Price
Sometimes you know the sale price and need the original price. Divide the sale price by the multiplier.
If a jacket costs $45 after a 25% discount, you paid 75% of the original price. So the original price was 45 \div 0.75 = 60 dollars. You can also set this up as a proportion: \frac{45}{x} = \frac{75}{100}.
Money problems like these need careful decimal operations, so line up the decimal points and check your work.
Practice Problems
- A $35 game is 20% off. What is the sale price?
- A $60 coat is 15% off. What is the sale price?
- A $24 book has 7% sales tax. What is the total cost?
- A meal costs $55. What is an 18% tip?
- A store buys a lamp for $25 and marks it up 40%. What is the selling price?
- A salesperson earns 5% commission. How much does she earn on a $3,200 sale?
- A $50 backpack is 30% off, and then 8% tax is added. What is the total?
- A shirt costs $36 after a 10% discount. What was the original price?
- A $100 bike is 25% off, and then an extra 20% off the sale price. What is the final price?
- A dinner costs $64. You add a 15% tip and 6% tax, both on the $64. What is the total?
Show answers
- 35 \times 0.80 = 28, so $28.
- 60 \times 0.85 = 51, so $51.
- Tax: 0.07 \times 24 = 1.68. Total: 24 + 1.68 = $25.68.
- 0.18 \times 55 = 9.90, so the tip is $9.90.
- 25 \times 1.40 = 35, so $35.
- 0.05 \times 3200 = 160, so $160.
- Sale price: 50 \times 0.70 = 35. With tax: 35 \times 1.08 = 37.80, so $37.80.
- 36 is 90% of the original, so 36 \div 0.90 = 40. The original price was $40.
- 100 \times 0.75 = 75, then 75 \times 0.80 = 60. The final price is $60.
- Tip: 0.15 \times 64 = 9.60. Tax: 0.06 \times 64 = 3.84. Total: 64 + 9.60 + 3.84 = $77.44.
Percent Word Problems FAQ
Do you add sales tax before or after a discount?
Stores take the discount first, then add tax to the sale price. Since both steps multiply, you get the same total in either order.
How do you figure out a 20% tip fast?
Move the decimal point one place left to find 10%, then double it. For a $35 bill, 10% is $3.50, so a 20% tip is $7.00.
Is 30% off and then 20% off the same as 50% off?
No. The second discount is taken from the lower price. Multiply 0.70 \times 0.80 = 0.56, so you pay 56% of the price. That is 44% off, not 50%.
How do you find the original price after a discount?
Divide the sale price by the part you paid. If you paid $45 after 25% off, you paid 75%, so the original price was 45 ÷ 0.75 = $60.
Summary
- Find the percent of the price, then subtract for a discount or add for tax, tips and markups.
- A multiplier does it in one step: 0.75 for 25% off, 1.08 for 8% tax.
- For two changes, apply the second one to the new price.
- To find an original price, divide by the multiplier.
- Round money to the nearest cent.
Previous lesson: Percent Change
Next lesson: Simple Interest
Back to the Pre-Algebra (Math Basics) Index