Apply percentages to discounts, taxes, tips, and interest. | Percentages | SAT Math

Core Idea

Discounts reduce a price (multiply by 1 − r), while taxes and tips increase it (multiply by 1 + r). The order matters when both apply, and the SAT expects you to know which base each percentage is taken from.

Understanding

A 25% discount on a $60 item:

$60 \times 0.75 = 45$

An 8% sales tax on that discounted price:

$45 \times 1.08 = 48.60$

Notice that tax is calculated after the discount. If you applied tax to the original $60 first and then discounted, you'd get a different (and wrong) answer. The SAT will test whether you apply each percentage to the correct intermediate value.

For tips, the convention is to tip on the pre-tax amount, though the problem will usually specify. Read carefully.

Simple interest follows $𝐼 = 𝑃 𝑟 𝑡$ , where $𝑃$ is principal, $𝑟$ is the annual rate as a decimal, and $𝑡$ is time in years. After $𝑡$ years the total amount is:

$𝐴 = 𝑃 (1 + 𝑟 𝑡)$

Compound interest uses:

$𝐴 = 𝑃 (1 + 𝑟 𝑛) 𝑛 𝑡$

where $𝑛$ is the number of compounding periods per year. The SAT usually gives you this formula — the skill is plugging in correctly and not confusing simple with compound.

Step by Step

Determine whether the percentage reduces (discount) or adds to (tax, tip) the amount.
Apply the discount first to get the sale price, then apply tax/tip to that result.
For interest problems, identify whether it's simple (I = Prt) or compound, and plug into the correct formula.
Check that each percentage is applied to the right base amount.

Misconceptions

Applying tax to the original price instead of the discounted price (or vice versa when the problem specifies a different order).
Thinking two successive 20% discounts equal a 40% discount — two 20% discounts actually give 36% total discount.
Confusing simple and compound interest formulas, especially forgetting to divide the rate by n in the compound formula.

Question

Worked Example

A laptop originally costs $800. It is on sale for 15% off, and then a 7% sales tax is applied to the sale price. What is the total cost?

Select an answer to see the explanation