How do you apply a 20% discount?

Unmasking the Original Price: Reverse Engineering a 20% Discount

We’ve all been there. A tantalizing sale sign promises 20% off, and a tempting item is marked at a seemingly low price. But have you ever wondered what the original price really was? Understanding how discounts work, and more importantly, how to reverse them, can empower you to be a savvier shopper.

This article focuses on a common scenario: calculating the original price after a 20% discount has already been applied. Let’s say you found a fantastic item on sale for $80, after a 20% discount. How do we determine the pre-discount price?

The key is understanding that the sale price represents 80% (100% – 20%) of the original price. Therefore, the sale price is a fraction (0.8) of the original price. To find the original price, we simply need to reverse this calculation.

Instead of multiplying the original price by 0.8 to get the sale price, we divide the sale price by 0.8.

Here’s the formula:

Original Price = Sale Price / (1 – Discount Rate)

In our example:

Original Price = $80 / (1 – 0.20) = $80 / 0.8 = $100

Therefore, the original price of the item was $100.

Let’s break it down further:

• Discount Rate: Express the discount percentage as a decimal (20% = 0.20).
• 1 – Discount Rate: This represents the percentage of the original price that remains after the discount (100% – 20% = 80%, or 0.8).
• Sale Price: The price you see after the discount has been applied.

This formula isn’t limited to 20% discounts. You can adapt it for any percentage discount by simply replacing “0.20” with the appropriate decimal representation of your discount. For example, a 15% discount would use 0.15, and so on.

By understanding this simple yet powerful calculation, you can easily determine the original price of any discounted item and make more informed purchasing decisions. No more wondering – just knowing! So next time you encounter a sale, grab your calculator and uncover the true value.