How to Calculate Percentage Discount

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  • 0:04 Calculating a…
  • 1:21 Answer Format &…
  • 2:31 Examples
  • 4:05 A Different Unknown
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Lesson Transcript
Maria Airth

Maria has a Doctorate of Education and over 20 years of experience teaching psychology and math related courses at the university level.

Expert Contributor
Matthew Bergstresser

Matthew has a Master of Arts degree in Physics Education. He has taught high school chemistry and physics for 14 years.

This lesson reviews the steps for calculating percent discount. The lesson includes scenarios such as unknown sales price, unknown discount rate and unknown original price.

Calculating a Percentage Discount

Joe wants to buy a mystery box that costs $125. The box is on sale for 20% off. How much does the box cost after the discount?


Step 1:

Remember the formula for finding the discount price of an item. Where S = sale price, r = discount percentage rate and p = original price, the discount formula is:

  • S = p - rp

Step 2:

Convert the percentage rate into a decimal - remove the percent sign and move the decimal two places to the left. If there's no decimal, assume one just to the right of the ones place. Here, as you can see, 20% = 0.20.

Step 3:

Insert values (including decimal value of rate) into the discount formula:

  • S = 125 - 0.2(125)

Remember that when two variables are next to each other, it means that you multiply them.

Step 4:

Solve the equation for S:

  • S = 125 - 25 = 100

Step 5:

Format the answer with the currency notation, or in this case, dollars, leaving us with $100.

Answer Format & Alternative Method

Let's first take a look at the answer format. Discount calculations imply dealing with monetary units, thus the answer should always be given in proper currency notation. The type of currency to use should match what's given in the original problem. Here we used dollars, but currency could be in any form. For this example, the correct answer is $100. Additionally, it's appropriate to answer a word problem with a full sentence. Thus, the best answer to this word problem is: ''The mystery box costs $100 after the discount has been applied.''

Now let's take a look at the alternative method. In the original formula, we find out the amount of the discount and remove it from what we would normally pay. There's another way to calculate the discount cost: we could figure out the percentage of the cost that's going to be paid first, and then just multiply that rate by the total cost.

In the example, there's a 20% discount, which means that Joe will have to pay for 80% of the original cost (100% - 20% = 80%). The sales price is 80% of the original price, so:

  • S = 0.8(125) = 100


Example 1

Mary has learned that the $450 purse she'd been wanting is finally on sale at a 45% discount. How much will the purse cost now?

Step 1: Use the formula S = p - rp

Step 2: Convert rate from percent to decimal: 45% = 0.45

Step 3: Plug values into formula: S = 450 - 0.45(450)

Step 4: Solving: S = 450 - 0.45(450) = 450 - 202.5 = 247.5

Step 5: Add the currency unit, which gives us $247.50. Stated in full, the answer is: ''The purse will cost $247.50 with the discount.''

Example 2

This time using the second method:

Using the alternative method, how much does a $5.50 toy cost with a 10% discount?

Step 1: If 10% is discounted, that leaves 90% to pay.

Step 2: Convert to decimal: 90% = 0.9

Step 3: Plug the variables into the formula: S = 0.9(5.50)

Step 4: Solving, we get: 4.95

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Additional Activities


Percentages are essentially fractions that have been multiplied by 100. Percentages are useful when expressing discounts. It is helpful to know how to calculate percentage discounts when shopping. Let's look at some practice problems dealing with percentages. You may use a calculator to complete the problems. Show your work.


  1. A designer shirt is on sale for 30% off its normal price of $20. What is the amount saved and sale price of the shirt?
  2. A chair is on sale for $45. Normally it is $75 dollars. What is the percentage discount?
  3. A box of chocolate chip cookies is on sale for $3.25. The percentage discount was 15%. What was the original price of the box of cookies?



The sale price is $14.


This is a 40% discount.


This value was rounded from $3.7375. We know the original price was the $3.25 hence the 1 in the 1.15 and we have to add in the 15/100 hence the .15 in 1.15. This gives us the original cost of around $3.74. We only round to two decimal places because the lowest coin value is one cent, or $0.01.

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