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You’ve probably bought an item on sale and wondered what the original, or list price, was. Or you may have gone shopping and saw that something was 25 percent off, and tried to figure out what price you would have to pay. Calculating the original price, sale price, or percent discount of an item involves basic algebra skills. It is helpful to know this process for your daily life, but you will likely also come across “percent off” questions in your school work as well.
Steps
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Assess what information you know. In order to calculate the list price, or the original price, of an item on sale, you need to know what the sale price is, and what the discount percent is.
- For example, you might know that a sweater is on sale for $51.75 after a 25% discount.
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Convert the discount percent to a decimal. Remember that percents are hundredths, so to convert, either divide the percent by 100, or simply place a decimal after the number and move it two places to the left. [1] X Research source
- For example, 25% expressed as a decimal is .25.
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Set up an equation for finding the original price of a discounted item. Use the formula , where equals the sale price of the item, equals the original price of the item, and equals the discount percent of the item. [2] X Research source
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Plug the sale price into the formula. Make sure you substitute for the variable .
- For example, if the sales price is $51.75, your formula will look like this: .
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Plug the discount percent into the formula. Make sure you use the decimal form of the discount, and substitute for the variable .
- For example, if the item is 25% off, your formula will look like this: .
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Use the distributive property to simplify the formula. To do this, pull out the variable . [3] X Research source
- For example:
- For example:
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Complete the calculation in parentheses. This will give you the percent of the item’s original price that the sales price represents. [4] X Research source
- For example, . So, if an item is 25% off, you would only pay 75% of the original price to purchase the item on sale. Your formula will look like this: .
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Divide each side of the equation by the percent of the original price. This will give you the value of , the list price of the item.
- For example:
So the original price of a sweater marked $51.75 after a 25% discount is $69.00.
- For example:
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-
Assess what information you know. In order to calculate the sale price of an item, you need to know what the original or list price is, and what the discount percent is.
- For example, you might know that a sweater is $69 and on sale for 25% off.
-
Convert the discount percent to a decimal. Remember that percents are hundredths, so to convert, either divide the percent by 100, or simply place a decimal after the number and move it two places to the left. [5] X Research source
- For example, 25% expressed as a decimal is .25.
-
Multiply the original price by the discount percent. [6] X Research source Make sure you use the decimal form of the percent. This will give you the discount, in dollars, off the original price.
- For example, . So, $17.25 is the discount off the original price.
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Subtract the discount amount from the original price of the item. This will give you the sale price. [7] X Research source
- For example, . So, the sale price of a $69 sweater that is 25% off is $51.75.
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-
Assess what information you know. In order to calculate the discount percent of an item, you need to know what the sale price is, and what the original or list price is.
- For example, you might know that a sweater’s original price is $69, and that it is on sale for $51.75.
-
Subtract the sale price from the original price. This will give you the markdown amount, the amount of dollars taken off the original price.
- For example, since , $17.25 was taken off the price of the sweater.
-
Set up a discount formula for your item. Use the formula , where equals the markdown, in dollars, of the item, equals the original price of the item, and equals the discount percent of the item. [8] X Research source
-
Plug the original price and the markdown into the formula. Be sure to substitute the original price for the variable , and the markdown for the variable .
- For example, if a sweater, originally $69, has a markdown of $17.25, your formula will look like this: .
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Divide each side of the equation by the original price. This will give you the percent of the discount as a decimal. To convert to a percent, move the decimal point two places to the right.
- For example:
So, a $69 sweater on sale for $51.75 is 25% off.
- For example:
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Community Q&A
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Question$37,000 put down on house, which was 20% of the original price. What is the total price of house?DonaganTop AnswererIt's five times the down-payment (because the down-payment is one-fifth of the original price).
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QuestionGiven sale price $10,200 at a discount of 10%, what is list price?DonaganTop AnswererAt a 10% discount, the sale price is 90% of the list price. So the list price is the sale price divided by 90%. 10,200 / 90% = 10,200 / 0.9 = 11,333.33.
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QuestionNet selling price is $10450, trade discount 20%, cash discount 5%, what is the list price?DonaganTop AnswererThe list price has been discounted a total of 25% to arrive at the selling price, meaning that the selling price is 75% of the list price. Therefore, 0.75 P = 10,450 (where P is the list price). Divide both sides of that equation by 0.75, so that P = 10,450 / 0.75, or $13,933.
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References
- ↑ https://www.mathsisfun.com/converting-percents-decimals.html
- ↑ https://sciencing.com/how-to-find-the-original-price-13712233.html
- ↑ https://sciencing.com/how-to-find-the-original-price-13712233.html
- ↑ http://www.purplemath.com/modules/percntof2.htm
- ↑ https://www.mathsisfun.com/converting-percents-decimals.html
- ↑ https://www.mathgoodies.com/lessons/percent/sale_price
- ↑ https://www.mathgoodies.com/lessons/percent/sale_price
- ↑ http://www.purplemath.com/modules/percntof2.htm
About This Article
Article Summary
X
Calculating the list price of an item on sale is fairly simple if you know what the discount is. First, convert the discount price to a decimal. For instance, if the item is 25 percent off, it would become .25. Then, subtract that decimal from 1. In this case, you would get .75. Finally divide the sale price by this new number. If the sale price is 51.75, you would divide this by .75 to get 69 dollars, the original list price. To learn how to calculate the sale price if you know the list price, read on!
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