Skill: Calculate discounts, markups, taxes, and tips

A percentage change is found by multiplying the correct starting amount by a decimal.

• Discount: multiply by $1-r$
• Markup, tax, or tip: multiply by $1+r$

Here, $r$ is the percentage written as a decimal. For example, $25\% = 0.25$.

Example

A jacket costs 80$. It is on sale for$25%$off, and then an$8%$ sales tax is added. What is the final cost?

Step 1: Find the sale price.

A $25\%$ discount means you pay $100\%-25\%=75\%$ of the original price.

$$80(1-0.25)=80(0.75)=60$$

The sale price is 60$.

Step 2: Add the tax to the sale price.

The tax is based on the sale price, not the original price. An $8\%$ tax means multiplying by $1.08$.

$$60(1+0.08)=60(1.08)=64.80$$

Step 3: State the answer with money rounding.

The final cost is:

$$\boxed{\$64.80}$$

Always apply percentage changes to the amount that the problem identifies as the base. For changes in sequence, complete the first change before applying the next one.