How to Find the Price Before a Discount

When shopping, you often encounter discounted items, making it useful to understand the original price before any reductions. Knowing how to calculate this helps you assess the true value of a deal and manage your personal finances more effectively. This skill provides insight beyond the advertised markdown, empowering more informed purchasing decisions and revealing the initial cost of goods or services.

Understanding Discounts

A percentage discount signifies a reduction from an item’s initial cost, expressed as a portion of the whole. For instance, an item advertised as “20% off” means its price has been lowered by 20 percent of its original value. When a discount of X% is applied, you are essentially paying (100% – X%) of the original price. To use percentages in calculations, they must first be converted into their decimal equivalent. This conversion is straightforward: simply divide the percentage by 100, so 20% becomes 0.20, and 50% becomes 0.50.

The Original Price Formula

To determine an item’s original price before a discount, a specific formula is used. The core relationship is expressed as: Original Price = Discounted Price / (1 – Discount Percentage as a decimal). In this formula, “Original Price” represents the item’s cost before any reduction was applied. “Discounted Price” refers to the amount you pay after the discount. The “Discount Percentage as a decimal” is the discount rate converted from its percentage form.

The component (1 – Discount Percentage as a decimal) represents the portion of the original price that you are paying. For example, if an item is 25% off, you are paying 75% of its original price (1 – 0.25 = 0.75). Dividing the discounted price by this remaining percentage effectively reverses the discount.

Step-by-Step Calculation Examples

Consider an item purchased for $45 after a 25% discount. To find the original price, first convert the 25% discount to its decimal form, which is 0.25. Next, subtract this decimal from 1, resulting in 0.75 (1 – 0.25). Finally, divide the discounted price ($45) by 0.75, yielding an original price of $60 ($45 / 0.75 = $60).

Another example involves a product bought for $120 with a 40% discount. Converting 40% to a decimal gives 0.40. Subtracting this from 1 results in 0.60 (1 – 0.40). Dividing the discounted price of $120 by 0.60 provides an original price of $200 ($120 / 0.60 = $200).

For a third illustration, imagine an item priced at $75 after a 50% discount. The decimal equivalent of 50% is 0.50. Subtracting 0.50 from 1 gives 0.50 (1 – 0.50). Dividing the $75 discounted price by 0.50 reveals an original price of $150 ($75 / 0.50 = $150).