# 5.14: Find Discount Prices Given Sales

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

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**Practice**Prices Involving Discounts

Have you ever purchased a book from a bookstore? Take a look at this dilemma.

A local bookstore has a 30% off everything sale. The sales tax is 5%. What is the total price on a book whose cover price is $15.99?

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Use this Concept to learn how to solve this problem. You will see it again at the end of the Concept.
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### Guidance

Fortunately for the consumer, price changes aren’t always increases. In order to reduce inventories or motivate buyers, stores often have sales in which they discount prices by a percent. Instead of a percent increase, this is a percent decrease. We can calculate these
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sale prices.
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Let's take a look at how to solve these problems.

At the end of the summer, a clothing store puts all swimwear on sale. They offer a discount of 60%. If the regular price is $29.99 on a bikini, what is the sale price?

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Amount of discount:
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Subtract discount from original price:
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The sale price is only $12.00.
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Not so fast. We almost forgot to pay the tax. If the sales tax is 6.25%, we must now add the tax to the sale price.
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Amount of tax:
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Add tax to the sale price:
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The sale price with tax is $12.75.
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Here is another situation.

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Notice that with a discount you subtract the amount and with sales tax you add the cost.
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Absolutely! A lot of this math you are probably able to figure out in your head. However, it is a good idea to understand the steps and how the pricing is figured out!
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Calculating a price with tax is the same as increasing by a percent.
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What if you know the total price including the tax and want to know the original price of a product?
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A store clerk charges you $78.75 for a DVD player. The tax in your area is 5%. So how much was the original price of the DVD player?

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We can find this out by using an equation.
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In order to get the total cost, the cash register computes the 5% tax and adds the tax to the original price like we did three sections ago. In other words:

Now let’s use variables and convert the percent to decimal.

In this equation, we and are like terms so they can be combined.

In this case, if we are given , we can solve for . Or if we are given , we can solve for . In our example, we paid a total cost of $78.75. Substitute in the equation and solve for .

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The original price was $75.00.
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Here is another one.

You are charged $29.10 for an item with 7% tax included. What was the original price of the item?

First, let's write an equation and solve it.

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The original price of the item was $27.20.
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Find each new price given a discount of 30%.

#### Example A

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Solution:
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#### Example B

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Solution:
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#### Example C

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Solution:
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Now let's go back to the dilemma from the beginning of the Concept.

Let's go through each step of the solution.

Amount of discount:

Subtract discount from original price:

The sale price is $11.19.

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Don’t forget the sales tax!
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Amount of tax:

Add tax to the sale price:

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The sale price with tax is $11.75.
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### Vocabulary

- Wholesale price
- the price that a merchant pays when they purchase a product from a manufacturer.

- Markup
- the amount that the merchant charges retail to the customer. The difference between wholesale and retail is the markup and also the profit.

- Sales Tax
- a percentage charged on purchases, and that goes to the government.

- Discounts
- when merchants have a sale a percent of the decrease is calculated to sell the product at a lower price.

### Guided Practice

Here is one for you to try on your own.

You purchase some plants for your gardens. Two trees have a price of $55.00 each. Six tulips cost $2.50 each. The tax on your purchase is 5.75% but there is an early-bird special of 10% off your entire purchase to those who show up before 10am. What is the total cost?

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Solution
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Add up all of the products:
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Total price of products:
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125.00

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Calculate the tax of 5.75%:
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Add the tax to the price:
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Calculate the 10% discount:
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Subtract the discount from the price:
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The grand total is $118.97.
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### Video Review

### Practice

Directions: Your food bill at a restaurant is $85.77, calculate your total cost after the tip. Be sure to round when necessary.

- service 10%
- decent service 15%
- great service 20%
- outstanding service 25%
- poor service 5%

Directions: What was the original price given total cost and tax rate? Be sure to round when necessary.

- total cost: $1475.68 tax rate: 7%
- total cost: $63.80 tax rate: 4.5%
- total cost: $55.90 tax rate: 4%
- total cost: $80.20 tax rate: 2.5%
- total cost: $120.00 tax rate: 5%
- total cost: $99.50 tax rate: 2%
- total cost: $155.30 tax rate: 3%
- total cost: $250.75 tax rate: 3.5%

Directions: Solve each problem. There are several steps to solving each problem. Be sure to round when necessary.

- You take a taxi ride in a foreign country where they add 20% to your total for late night travel. The driver expects an additional 15% tip. How much do you owe for the taxi ride if the meter shows $45?
- You take your mother out for lobster for Mother’s Day. The lobster platters are $24.95 each but include the drink and dessert buffet. Your waitress is a mother, too, so you leave her a 20% tip. However, you did bring a coupon for 25% off. What is your total cost for 2 people?

### Image Attributions

## Description

## Learning Objectives

Here you'll find discount prices given sales.