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How to Determine Discounts and Sale Prices

How to Determine Discounts and Sale Prices

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It’s great when stores have sales, but figuring out the discounted price can sometimes be tricky. Have no fear—help is here! In this guide, you will learn how to find the sale price and the percent of discount by using some simple math.

Finding Discount Price

If you need to find the discount (sale) price after discount, you can calculate it using two methods.

Method 1:

Step 1: Subtract the percent of discount from 100%:

100 percent − Percent of discount = Decreased percent

Step 2: Multiply the result by the original price to find the discount price:

(Original price) · (Decreased percent) = Discount (sale) price

Method 2:

Step 1: Multiply the original price by the percent of discount in decimal form to obtain the decrease in amount:

(Original price) · (p%) = Decrease in amount (saved money)

Step 2: Subtract the decrease in amount from the original price to find the sale price:

Sale price = (Original price) − (Original price) · (p%)

Obviously, using either method provides the same answer.

Sample Problem 1

The Howard University bookstore gives 15% discounts to students. What does a student actually pay for a book costing $24?

Let’s use the first method to solve this problem.

Step 1: Let x indicate the sale price.

Step 2: Find the decreased percent by subtracting the percent of discount from 100%:

100% − 15% = 85%

Step 3: Let’s change the decreased percent to decimal form:

85% = 0.85

Step 4: Find the sale price x by multiplying the original price by the decreased percent:

x = ($24)(0.85) = $20.40

Solution: The sale price of the book is $20.40.

Sample Problem 2

Mindy bought a color TV for 20% off the original price. What did she pay for the TV if the original price was $650?

Let’s solve this problem using method 2.

Step 1: Let x indicate the discount price. Change the discount percent to the decimal form:

20% = 0.20

Step 2: Multiply the original price by the percent of discount in decimal form to obtain the decrease in the amount:

(Original price) · (p%) = Decrease in the amount (saved money)

$650 · 0.20 = $130

We found that Mindy saved $130.

Step 3: Subtract the savings from the original price to find the sale price:

(Original price) − (Saved amount) · (p%) = Sale price

$650 − $130 = $520

Solution: The sale price for the TV was $520.

Finding the Percent of Discount

If you need to figure out the percent of discount, use the following formula:

Sometimes you’re given the discount amount (saved money); sometimes you need to find it by subtracting the sale price from the original price.

Sample Problem 3

At an office supply store, customers are given a discount if they buy more than $100 worth of goods. If a customer is given a discount of $19.32 on a total order of $552, what is the percent of discount?

Step 1: Let the discount percent be p. We know the discount amount, which is $19.32, and we know the original price, so we can use the formula right away:

Step 2: We found the discount percent in its decimal form. Let’s change it to a percent:

0.035 = 3.5%

Solution: The discount percent was 3.5%.

Sample Problem 4

A $120 dress is on sale for $96. What is the discount percentage?

Step 1: Let p indicate the discount percent that we need to find. Next, let’s find the discount amount (saved money) by subtracting the sale price from the original price:

$120 − $96 = $24

We found that the discount amount is $24.

Step 2: We know the original price and the discount amount, so we can use the formula to find the discount percent:

Step 3: We found the discount percent in its decimal form. Let’s change it to a percent:

0.2 = 20%

Solution: The discount percentage is 20%.

Double Discount Sales

At the end of the season, many retail stores apply an additional discount to already discounted items. For example, a 60% discount is followed by a 30% discount. But an item marked at 90% off is not the same as one that was marked down 60% and then another 330%. Take a look at these two problems to see what we mean.

Sample Problem 5

A retail store put a cashmere pullover on 90% sale. If the original price was $200, what is the sale price?

Step 1: Let x indicate the sale price. Find the decreased percent by subtracting 90% from 100%:

100% − 90% = 10%

Step 2: Convert the decreased percent into its decimal form:

10% = 0.10

Step 3: Find the sale price by multiplying the original price by the decreased percent in the decimal form:

x = $200(0.10) = $20

Solution: The sale price is $20.

We found that the cost of the item with a straight 90% discount is $20.

Sample Problem 6

A retail store put a cashmere pullover on 60% sale. At the end of the season, the store gives an additional 30% discount. What is the sale price of the pullover at the end of the season if the original price was $200?

Step 1: Let x indicate the sale price after the 60% discount. First, find the decreased percent:

100% − 60% = 40%

Step 2: Change the decreased percent to its decimal form:

40% = 0.40

Step 3: Find the sale price by multiplying the original price by the decreased percent in the decimal form:

x = $200(0.40) = $80

We found that the sale price after the first 60% discount is $80. This amount becomes our new original price, which represents a new 100%.

Step 4: Let y indicate the new sale price. Find the decreased percent after the second discount by subtracting the additional discount percent (30%) from 100%:

100% − 30% = 70%

Step 5: Change the decreased percent into its decimal form:

70% = 0.70

Step 6: Find the sale price y by multiplying the new original price ($80) by the decreased percent in decimal form:

y = $80(0.70) = $56

Solution: The sale price is $56.

This price is quite different from the $20 price with a straight 90% discount.

Now that you know how to figure out sales and discount prices, bargain hunting will be that much easier. Happy shopping!

From The Complete Idiot’s Guide to Algebra Word Problems by Izolda Fotiyeva, Ph.D.