Percent Applications
Solve problems involving discount, sales tax, tip, commission, and markup using the percent equation and proportion methods. Build fluency with multi-step real-world financial scenarios.
A lesson of Pre-Algebra, in Ratios, Rates & Proportional Reasoning, about 10 minutes.
By the end of this lesson, you will be able to solve real-world percent problems including tips, tax, discount, and commission.
The Three Types of Percent Problems
| Find | Formula |
|---|---|
| Percent of a number (part) | $\text{part} = \text{percent} \times \text{whole}$ |
| What percent | $\text{percent} = \text{part} \div \text{whole}$ |
| The whole | $\text{whole} = \text{part} \div \text{percent}$ |
Sales Tax
Tax amount = tax rate × original price
Total price = original price + tax amount (or: original price × (1 + tax rate))
Example: A $45 item is taxed at 8%.
Tax = $0.08 \times 45 = $3.60$
Total = $45 + 3.60 = $48.60$
Tip
Tip = tip rate × original bill
Example: A $32 restaurant bill with a 20% tip.
Tip = $0.20 \times 32 = $6.40$
Total = $32 + 6.40 = $38.40$
Discount and Sale Price
Discount amount = discount rate × original price
Sale price = original price − discount amount (or: original price × (1 − discount rate))
Example: A $120 jacket is 25% off.
Discount = $0.25 \times 120 = $30$
Sale price = $120 - 30 = $90$ (or: $0.75 \times 120 = $90$)
Commission
Commission = commission rate × total sales
Example: A salesperson earns 6% commission on $8,500 in sales.
Commission = $0.06 \times 8500 = $510$
Summary
Tax/tip: add a percent of the original. Discount: subtract a percent.
Shortcut: multiply by $(1 + r)$ for increases; $(1 - r)$ for decreases (where $r$ is the rate as a decimal).
Commission: earning a percent of total sales.