Calculating Original Price After Discount

Property To find the original price after a discount, use a proportion comparing the original percent (100%) to the new percent (100% discount %). $$ \frac{100}{100 \text{Discount \%}} = \frac{\text{Original Price}}{\text{Sale Price}} $$.

Examples A jacket bought at a 40% off sale cost 48 dollars. What was the original price? $$\frac{100}{60} = \frac{x}{48} \rightarrow 60x = 4800 \rightarrow x = 80$$. The original price was 80 dollars. A video game is on sale for 25% off and costs 45 dollars. Find its original price. $$\frac{100}{75} = \frac{x}{45} \rightarrow 75x = 4500 \rightarrow x = 60$$. The original price was 60 dollars.

Explanation When an item is discounted, its sale price is a new, smaller percentage of the original. The original is always 100%. If you get 30% off, you pay 70%. We use this simple logic to create a proportion that pits the original percent against the new percent to find the starting price, our mystery number!