If the price of an item is $80 after a 20% discount, what was the original price?

To determine the original price of an item after a discount is applied, you can use the relationship between the discounted price, the discount rate, and the original price. In this scenario, if the price of an item is $80 after a 20% discount, this means that $80 represents 80% of the original price because the item has retained 80% of its value after the 20% discount has been taken off.

To find the original price, you can set up the equation:

Let the original price be denoted as ( P ). Since the item is sold at 80% of its original price after the discount, we can say:

[ 0.8P = 80 ]

To solve for ( P ), divide both sides of the equation by 0.8:

[ P = \frac{80}{0.8} ]

Calculating that, you find:

[ P = 100 ]

Thus, the original price before the discount was applied is $100. This reasoning clearly connects the discounted price to the original price using the percentage reduction.