# 6.17: Prices Involving Discounts

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

**Practice**Prices Involving Discounts

One afternoon while Taylor is working in the candy store, a couple decided to purchase some chocolates. They spent a lot of time looking through all of the boxes, but finally decided on a large assorted box of some very lovely dark chocolates.

“That is a good choice,” Taylor said. “That box is also on sale for 15% off.”

“Terrific,” said the man.

Taylor took the chocolates and went to the cash register. As she went to put in the pricing, she noticed that there wasn’t anything happening on the screen. She walked to the kitchen in the back where her Mom was working.

“Mom, the register won’t work,” Taylor said.

“Well I am in the middle of making taffy. You’ll have to do the math in your head,” her Mom responded.

Taylor walked back in and picked up a piece of paper and a pencil.

The original price of the chocolates was $26.50.

There is a 15% discount.

**Given the discount, what was the new price for the chocolates?**

**Use what you will learn in this Concept to help Taylor figure this out.**

### Guidance

In this Concept, you will learn how to use percents in everyday life.

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 we buy that item when it is on sale, we can find the amount of the discount if we know the rate of discount that the store is offering. On some items that we buy, we pay a sales tax that is a percent of the price. When we eat out in a restaurant, we leave a tip that is a percent of the amount of the meal.

**Let’s begin by thinking about markups and discounts.**

**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 can be expressed as an amount of money or as a percent of the original price of the item.

**Why would someone use a markup?**

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

**Why would someone use a discount?**

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

**To figure out a discount or a markup, we need to know the percent of change. What is a percent of change?**

**The** *percent of change***is the percent that the price is changing by.** If the markup is 10%, then that is the percent of change. If the discount is 10%, then that is the percent of change.

**We can use the following formula:**

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

*Write this formula in your notebook and then continue with the lesson.*

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*}\text{Amount of change} & = \text{percent of change} \times \text{original amount}\\ & = 35 \% \times \$ 149\\ & = 0.35 \times \$ 149\\ & = \$ 52.15\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 selling price is $201.15**

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*}\text{Amount of change} & = \text{percent of change} \times \text{original amount}\\ & = 20 \% \times \$ 189\\ & = 0.20 \times \$ 189\\ & = \$ 37.80 \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 sale price is $151.20.**

Find the markup or discount of each price.

#### Example A

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

**Solution: \begin{align*}$174.90\end{align*}**

#### Example B

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

**Solution: \begin{align*}$170.05\end{align*}**

#### Example C

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

**Solution:\begin{align*}$10.50\end{align*}**

Here is the original problem once again.

One afternoon while Taylor is working in the candy store, a couple decided to purchase some chocolates. They spent a lot of time looking through all of the boxes, but finally decided on a large assorted box of some very lovely dark chocolates.

“That is a good choice,” Taylor said. “That box is also on sale for 15% off.”

“Terrific,” said the man.

Taylor took the chocolates and went to the cash register. As she went to put in the pricing, she noticed that there wasn’t anything happening on the screen. She walked to the kitchen in the back where her Mom was working.

“Mom, the register won’t work,” Taylor said.

“Well I am in the middle of making taffy. You’ll have to do the math in your head,” her Mom responded.

Taylor walked back in and picked up a piece of paper and a pencil.

The original price of the chocolates was $26.50.

There is a 15% discount.

First, figure out the discount.

\begin{align*}26.50 \times .15 = 3.975\end{align*}

Round up to 3.98

Next, subtract this discount from the original price.

\begin{align*}26.50 - 3.98 = \$ 22.52\end{align*}

**This is the cost of the chocolates.**

### Vocabulary

Here are the vocabulary words in this Concept.

- Markup
- the amount that a store marks up an item that has been purchased at a wholesale cost.It is how stores make money on the items that they sell. It is a percent added to the wholesale cost.

- Discount
- a percentage off of a selling price. It is an amount that is subtracted from the original price.

- Percent of Change
- the percentage amount that a price is being reduced or increased by.

### Guided Practice

Here is one for you to try on your own.

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?

**Answer**

First find the amount of markup.

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

The markup is $20.

Now find the 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 discount.

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

The discount is $19.80.

Now 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.**

### Video Review

Here is a video for review.

- This is a James Sousa video on discounts and markups.

### Practice

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

1. $19.00

2. $12.00

3. $18.00

4. $25.00

5. $13.50

6. $9.95

7. $45.00

8. $90.00

9. $85.00

10. $17.00

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

11. $55.00

12. $35.50

13. $18.00

14. $8.75

15. $25.00

16. $40.00

17. $35.00

18. $12.50

19. $38.90

20. $16.75

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### Image Attributions

Here you'll learn to find prices involving markups and discounts.