Penny wants a new television. She sees that the one she wants is on sale at two different stores. The original price is $399. First, Pick is having a 25% off sale on all TVs. Halmarket is selling the same TV for $299. Which store has the better deal?

In this concept, you will learn how to find prices involving discounts.

### Finding Prices Involving Discounts

A **discount** is the difference between the original price and the reduced price. It is described as a number of dollars or as a percent.

Find the reduced price in two steps:

First, find the dollar amount of the discount. Multiply the original price by the discount.

Next, subtract the dollar value of the discount from the original price. The total is the reduced price of the item.

Let’s look at an example.

Tracy went shopping for a new pair of sneakers. She found a blue pair that was $58. The sign said that they were 15% off the original price. How much is the discount? How much did Tracy end up paying for the sneakers?

First, find the discount amount. Find 15% of $58. 15% is also 0.15. Multiply the original price by the discount.

Next, subtract the discount from the original price.

The discount was $8.70. Tracy paid $49.30 for the sneakers.

You can also find the reduced price by multiplying the original price by the percent of the price you will pay. The percent you are paying is 100% minus the discount %.

Let’s look at Tracy’s sneakers again.

The sneakers are 15% off. Use mental math to calculate the percent Tracy will be paying. Think, “100 minus 15 is 85.”

Next, multiply the original price by the percent she will be paying. 85% is also 0.85.

This also gives the reduced price of the sneakers, $49.30.

### Examples

#### Example 1

Earlier, you were given a problem about Penny and the TVs.

Pick has it on sale for 25% off and Halmarket has it on sale for $299. Originally the price was $399. To compare the prices, Penny needs to find the sale price of the TV at First Pick.

First, find the discount amount. Find 25% of $399. 25% is also 0.25. Multiply the original price by the discount.

Next, subtract the discount from the original price.

The TV at First Pick is on sale for $299.25. Compare $299.25 to the price of the TV at Hal market, $299.

The TV is cheaper at Hal market, but only by $0.25.

#### Example 2

Find the discount and the reduced price.

Kara bought a new dress. The original price of the dress was $65.50. There was a 15% discount on the dress.

What was the amount of the discount? How much did Kara pay for the dress?

First, find the discount amount. Find 15% of $65.50. 15% is also 0.15. Multiply the original price by the discount.

(Note: Dollars are only measured to the second decimal digit. Round 9.825 to the nearest hundredths place.)

Next, subtract the discount from the original price.

The discount was $9.83. Kara spent $55.67 on the dress.

#### Example 3

If a $50.00 shirt is 25% off, how much would you pay for the shirt?

First, find the discount amount. Find 25% of $50. 25% is also 0.25. Multiply the original price by the discount.

Next, subtract the discount from the original price.

You would pay $37.50.

#### Example 4

If a video game that usually costs $45.50 is 30% off, how much would you pay for the game?

First, use mental math to find the percentage you would end up paying for the video game. Think, “If the discount is 30%, I would pay 70% of the price.” 70% is also 0.7.

Then, multiply the original price by percent you would pay.

You would pay $31.85.

#### Example 5

If a backpack was reduced to $30 and the original price was $40, what percent was the discount?

First, use the given information to find the reduced amount. The reduced amount is the difference between the original price and the sale price.

Next, write an equation to find the discount percent. Remember, the original price multiplied by the discount percent is the reduced amount. Use

to represent the unknown discount percent.

Then, solve for

to find the discount percent.

Finally, convert the decimal to a percent.

The backpack was discounted 25%.

### Review

Find the reduced price.

- Original price: $19.95, discount 15%
- Original price: $20.00, discount 50%
- Original price: $35.50, discount 10%
- Original price: $50.00, discount 30%
- Original price: $100.00, discount 20%
- Original price: $75.00, discount 30%
- Original price: $29.95, discount 20%
- Original price: $18.00, discount 10%
- Original price: $47.50, discount 10%
- Original price: $75.00, discount 30%
- Original price: $125.00, discount 20%
- Original price: $225.50, discount 10%
- Original price: $456.00, discount 25%
- Original price: $530.00, discount 30%
- Original price: $750.00, discount 12%

### Review (Answers)

To see the Review answers, open this PDF file and look for section 8.18.