# 6.3 Solve Sales Tax, Commission, and Discount Applications

The topics covered in this section are:

## 6.3.1 Solve Sales Tax Applications

Sales tax and commissions are applications of percent in our everyday lives. To solve these applications, we will follow the same strategy we used in the section on decimal operations. We show it again here for easy reference.

### HOW TO: Solve an application

1. Identify what you are asked to find and choose a variable to represent it.
2. Write a sentence that gives the information to find it.
3. Translate the sentence into an equation.
4. Solve the equation using good algebra techniques.
5. Check the answer in the problem and make sure it makes sense.
6. Write a complete sentence that answers the question.

Remember that whatever the application, once we write the sentence with the given information (Step 2), we can translate it to a percent equation and then solve it.

Do you pay a tax when you shop in your city or state? In many parts of the United States, sales tax is added to the purchase price of an item. See Figure 6.7. The sales

tax is determined by computing a percent of the purchase price.

To find the sales tax multiply the purchase price by the sales tax rate. Remember to convert the sales tax rate from a percent to a decimal number. Once the sales tax is calculated, it is added to the purchase price. The result is the total cost—this is what the customer pays.

### SALES TAX

The sales tax is a percent of the purchase price.

$\mathrm{Sales\ Tax} = \mathrm{Tax\ Rate} \cdot \mathrm{Purchase\ Price}$

$\mathrm{Total\ Cost} = \mathrm{Purchase\ Price} + \mathrm{Sales\ Tax}$

#### Example 1

Cathy bought a bicycle in Washington, where the sales tax rate was $6.5 \%$ of the purchase price. What was…

1. the sales tax and

Solution

#### Example 4

Rikki earned $\$87$commission when she sold a$ \$1,450$ stove. What rate of commission did she get?

Solution

## 6.3.3 Solve Discount Applications

Applications of discount are very common in retail settings Figure 6.8. When you buy an item on sale, the original price of the item has been reduced by some dollar amount. The discount rate, usually given as a percent, is used to determine the amount of the discount. To determine the amount of discount, we multiply the discount rate by the original price. We summarize the discount model in the box below. Figure 6.8 Applications of discounts are common in everyday life. (credit: Charleston’s TheDigitel, Flickr)

### DISCOUNT

An amount of discount is a percent off the original price.

$\mathrm{amount\ of\ discount} = \mathrm{discount\ rate} \cdot \mathrm{original\ price}$

$\mathrm{sale\ price} = \mathrm{original\ price} – \mathrm{discount}$

The sale price should always be less than the original price. In some cases, the amount of discount is a fixed dollar amount. Then we just find the sale price by subtracting the amount of discount from the original price.

#### Example 5

Jason bought a pair of sunglasses that were on sale for $\$ 10$off. The original price of the sunglasses was$ \$39$. What was the sale price of the sunglasses?

Solution

In Example 5, the amount of discount was a set amount, $\$10$. In Example 6 the discount is given as a percent of the original price. #### Example 6 Elise bought a dress that was discounted$35 \%$off of the original price of$ \$140$. What was Part 1. the amount of discount and Part 2. the sale price of the dress?

Solution

Part 1. Before beginning, you may find it helpful to organize the information in a list.

Original price $=$ \$140$

Discount rate $= 35 \%$

Amount of discount $=$?

Part 2.

Original price $= \$ 140$Amount of discount$= \$49$

Sale price $=$?

There may be times when you buy something on sale and want to know the discount rate. The next example will show this case.

#### Example 7

Jeannette bought a swimsuit at a sale price of $\$ 13.95$. The original price of the swimsuit was$ \$31$. Find the Part 1. amount of discount and Part 2. discount rate.

Solution

Part 1. Before beginning, you may find it helpful to organize the information in a list.

Original price $=$ \$31$

Amount of discount $=$?

Sale price $= \$ 13.95$Part 2. Before beginning, you may find it helpful to organize the information in a list. Original price$= \$31$

Solution