How to Calculate the List Price of an Item on Sale

Step-by-Step Guide

1. 1

   Step 1: 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.
2. 2

   Step 2: 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.For example, 25% expressed as a decimal is .25. , Use the formula S=P−PD{\displaystyle S=P-PD}, where S{\displaystyle S} equals the sale price of the item, P{\displaystyle P} equals the original price of the item, and D{\displaystyle D} equals the discount percent of the item. , Make sure you substitute for the variable S{\displaystyle S}.
   
   For example, if the sales price is $51.75, your formula will look like this:
   51.75=P−PD{\displaystyle
   51.75=P-PD}. , Make sure you use the decimal form of the discount, and substitute for the variable D{\displaystyle D}.
   
   For example, if the item is 25% off, your formula will look like this:
   51.75=P−P(.25){\displaystyle
   51.75=P-P(.25)}. , To do this, pull out the variable P{\displaystyle P}.For example:51.75=P−P(.25){\displaystyle
   51.75=P-P(.25)}51.75=P(1−.25){\displaystyle
   51.75=P(1-.25)} , This will give you the percent of the item’s original price that the sales price represents.For example, 1−.25=.75{\displaystyle 1-.25=.75}.
   
   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:
   51.75=P(.75){\displaystyle
   51.75=P(.75)}. , This will give you the value of P{\displaystyle P}, the list price of the item.
   
   For example:51.75=P(.75){\displaystyle
   51.75=P(.75)}51.75.75=P(.75).75{\displaystyle {\frac {51.75}{.75}}={\frac {P(.75)}{.75}}}69=P{\displaystyle 69=P}So the original price of a sweater marked $51.75 after a 25% discount is $69.00.
3. 3

   Step 3: Set up an equation for finding the original price of a discounted item.

4. 4

   Step 4: Plug the sale price into the formula.

5. 5

   Step 5: Plug the discount percent into the formula.

6. 6

   Step 6: Use the distributive property to simplify the formula.

7. 7

   Step 7: Complete the calculation in parentheses.

8. 8

   Step 8: Divide each side of the equation by the percent of the original price.

Detailed Guide

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