How To Find The Original Price

Do you always strive to get the best deals on items you purchase? Knowing the original price of an item on sale can help you determine if that discount is worth considering. Some retailers mark prices upward and then take a discount off, so it looks like a great sale price, and learning how to do sales and sales tax calculations lets you find out just how good a deal you are getting.

To calculate the original price of a discounted or sale item, you need to know the sale price and the discount percentage. The calculations include a simple formula that divides the sale price by the result of 1 minus the discount in percentage form.

Use this formula to calculate the original or list price of an item.

\(\text{OP} = \frac{ \text{ Price}}{1 – \text{ Discount}}\)

OP represents the original price, Price is the sale price and Discount is the percentage of discount. First, calculate 1 – Discount, and then divide the sale price by this number. For example, if you have a sale price of $40 and a discount of 30 percent:

\(\begin{aligned}
\text{OP} &= \frac{40}{1 – 0.30} \
\,\
&= \frac{40}{0.7} \
\,\
&= 57.14 \text{ rounded to two decimals}
\end{aligned}\)

So, the original price of the sale item was $57.14.

You may want to calculate the original price of an item after (or with) sales tax so you know what the price will be when the sale is over, because you may not be able to make the purchase during the sale. In this instance, you have the sales price with tax and you want to find the original price with sales tax. You find the original price as above and add the sales tax to it.

Building on the previous example:

If the original price of the sale item is $57.14 and the tax rate is 8 percent, you would use this formula:

\(\begin{aligned}
\text{OP with sales tax} &= \text{OP} × (\text{ tax rate in decimal form} + 1)\)
\(&= \text{OP} × (1.08) \
&= 57.14 × 1.08 \
&= \$61.71
\end{aligned}\)

This is another method of finding the original price of an item in which you know the sale price and the percentage of the original price that is discounted. This calculation helps you to find the original price after a percentage decrease.

1. Subtract the
discount from 100 to get the percentage of the original price.
2. Multiply the
final price by 100.
3. Divide by the
percentage in Step One.

For example, if the sale price of an item is $200 and it was discounted by 30 percent, then:

\(100 – 30 = 70\)
\(200 × 100 = 20,000\)
\(20,000 ÷ 70 = 285.71\)

$285.71 was the original or list price of the item.

Convert percentages to decimal form by moving the decimal point two places to the left. Always round your answer to two digits following the period when you are finding values with money.