# 6.17: Prices Involving Discounts

**At Grade**Created by: CK-12

**Practice**Prices Involving Discounts

In 2002, a Cook County home had an assessed value of $100,000. By 2008, the assessed value of the home had been marked 160% by Cook County assessors. What was the assessed value of the home in 2008?

In this concept, you will learn how to use percents in everyday life for situations involving discounts and markups.

### Finding Prices Involving Discounts

A store owner buys an item at a wholesale cost and marks it up by adding a percent of the price to the price he paid for it. If you buy that item when it is on sale, you can find the amount of the discount if you know the rate of discount the store is offering.

A **markup** is an increase in the price of an item. A **discount** is a decrease in the price of an item. Both of these changes can be expressed as an amount of money or as a percent of the original price of the item.

A markup is often how stores or businesses make a profit. They buy merchandise at one price and sell it for another price. The difference in the price they bought it for and the price they sell it for is the profit margin.

Stores discount items all the time. Often, they are still making a profit, but they discount an item by a specific percentage to try to sell more of that item.

To figure out a discount or a markup, you need to know the percent of change.

The **percent of change** is the percent the price is changing by. If the markup is 10%, then that is the percent of change (an increase). If the discount is 10%, then that is the percent of change (a decrease).

You can use the following formula to solve markup and discount problems:

\begin{align*}\text{Percent of change} \times \text{original amount} = \text{amount of the change}\end{align*}

Let’s look at an example.

A camera store buys a camera for $149 and marks up the price by 35%. What price does the camera sell for?

First, find the amount of the markup.

\begin{align*}\begin{array}{rcl}
\text{Amount of change} &=& \text{percent of change} \times \text{original amount}\\
&=& 35\% \times \$149
\end{array}\end{align*}

Next, convert the percent to a decimal and multiply.

\begin{align*}\begin{array}{rcl}
&=& 0.35 \times \$149\\
&=& \$52.15
\end{array}\end{align*}

The markup is $52.15.

Now find the selling price by adding the markup to the wholesale price.

\begin{align*}$149 + $52.15 = $201.15\end{align*}

The answer is the selling price is $201.15.

Let’s look at another example.

A camera that normally sells for $189 is on sale at a 20% discount. What is the sale price?

First, find the amount of the discount.

\begin{align*}\begin{array}{rcl}
\text{Amount of change} &=& \text{percent of change} \times \text{original amount}\\
&=& 20\% \times $189
\end{array}\end{align*}

Next, convert the percent to a decimal and multiply.

\begin{align*}\begin{array}{rcl}
&=& 0.20 \times $189\\
&=& $37.80
\end{array}\end{align*}

The discount is $37.80.

Now find the sale price by subtracting the discount from the original price.

\begin{align*}$189 - $37.80 = $151.20\end{align*}

The answer is the sale price is $151.20.

### Examples

#### Example 1

Earlier, you were given a problem about the Cook County home assessment.

The assessors valued the home at $100,000 in 2002. By 2008, Cook County assessors had marked up the assessed value of the home by 160%. What was the assessed value of the home in 2008?

First, find the amount of the markup.

\begin{align*}\begin{array}{rcl}
\text{Amount of change} &=& \text{percent of change} \times \text{original amount}\\
&=& 160\% \times $100,000
\end{array}\end{align*}

Next, convert the percent to a decimal and multiply.

\begin{align*}\begin{array}{rcl}
&=& 1.60 \times $100,000\\
&=& $160,000
\end{array}\end{align*}

The markup is $160,000.

Now find the new assessed value by adding the markup to the original assessed value.

\begin{align*}$100,000 + $160,000 = $260,000\end{align*}

The answer is the assessed value of the home in 2008 was $260,000.

#### Example 2

A pair of shoes with a wholesale price of $40 was marked up 50%. During a sale, the shoes were discounted 33%.

What was the sale price?

First, find the amount of markup.

\begin{align*}\begin{array}{rcl}
\text{Amount of change} &=& \text{percent of change} \times \text{original amount}\\
&=& 50\% \times $40\\
&=& 0.50 \times $40\\
&=& $20
\end{array}\end{align*}

The markup is $20.

Next, find the regular selling price by adding the markup to the wholesale price.

The selling price is \begin{align*}$40 + $20 = $60\end{align*}

Now find the amount of the discount.

\begin{align*}\begin{array}{rcl}
\text{Amount of change} &=& \text{percent of change} \times \text{original amount}\\
&=& 33\% \times $60\\
&=& 0.33 \times $60\\
&=& $19.80
\end{array}\end{align*}

The discount is $19.80.

Finally, find the sale price by subtracting the discount from the selling price.

\begin{align*}$60 - $19.80 = $40.20\end{align*}

The sale price is $40.20.

#### Example 3

A camera store buys a camera for $159.00 and marks it up 10%. What is the new price of the camera?

First, find the amount of the markup.

\begin{align*}\begin{array}{rcl}
\text{Amount of change} &=& \text{percent of change} \times \text{original amount}\\
&=& 10\% \times $159\\
\end{array}\end{align*}

Next, convert the percent to a decimal and multiply.

\begin{align*}\begin{array}{rcl}
&=& 0.10 \times $159\\
&=& $15.90
\end{array}\end{align*}

The markup is $15.90.

Now find the selling price by adding the markup to the wholesale price.

\begin{align*}$159 + $15.90 = $174.90\end{align*}

The answer is the new price is $174.90.

#### Example 4

A chair that costs $199.00 is on sale for 15% off. What is the sale price of the chair?

First, find the amount of the discount.

\begin{align*}\begin{array}{rcl}
\text{Amount of change} &=& \text{percent of change} \times \text{original amount}\\
&=& 15\% \times $199
\end{array}\end{align*}

Next, convert the percent to a decimal and multiply.

\begin{align*}\begin{array}{rcl}
&=& 0.15 \times $199\\
&=& $29.85
\end{array}\end{align*}

The discount is $29.85.

Now find the sale price by subtracting the discount from the original price.

\begin{align*}$199 - $29.85 = $169.15\end{align*}

The answer is the sale price is $169.15.

#### Example 5

A shirt that costs $15.00 is on sale for 30% off. What is the sale price of the shirt?

First, find the amount of the discount.

\begin{align*}\begin{array}{rcl}
\text{Amount of change} &=& \text{percent of change} \times \text{original amount}\\
&=& 30\% \times $15
\end{array}\end{align*}

Next, convert the percent to a decimal and multiply.

\begin{align*}\begin{array}{rcl}
&=& 0.30 \times $15\\
&=& $4.50
\end{array}\end{align*}

The discount is $4.50.

Now find the sale price by subtracting the discount from the original price.

\begin{align*}$15 - $4.50 = $10.50\end{align*}

The answer is the sale price is $10.50.

### Review

Here is a list of wholesale prices. Figure out each sale price if the markup is 20%.

- $19.00
- $12.00
- $18.00
- $25.00
- $13.50
- $9.95
- $45.00
- $90.00
- $85.00
- $17.00

Each item is discounted 15%. Figure out each new sale price; the original prices are listed below.

- $55.00
- $35.50
- $18.00
- $8.75
- $25.00

### Review (Answers)

To see the Review answers, open this PDF file and look for section 6.17.

### Resources

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In this concept, you will learn how to use percents in everyday life for situations involving discounts and markups.

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