Determining the Original Price Before a Discount

Often, when items are on sale, customers might wonder about the original price before a discount was applied. This article will guide you through the process of calculating the original price using a practical example. We'll provide step-by-step instructions and explain the math behind it.

Understanding the Problem

A common question in retail involves the calculation of the original price when a discount has been applied. For example, if an item has a sale price of $35 after a 20% discount, what was its original selling price?

The Formula and Explanation

To find the original price before the discount, we can use the formula for calculating the original price based on the sale price and the discount percentage. The formula is:

Original Price (P) Sale Price / (1 - Discount Rate)

This can be mathematically expressed as:

Original Price (P) Sale Price / (1 - (Discount Rate / 100))

Step-by-Step Calculation

Identify the sale price and the discount rate. In our example, the sale price is $35, and the discount rate is 20%, or 0.20 in decimal form. Substitute these values into the formula:

P Sale Price / (1 - Discount Rate)

P 35 / (1 - 0.20)

P 35 / 0.80

P 43.75

Therefore, the original selling price of the coat was $43.75.

Alternative Methods

There are several other ways to solve this problem, and each has its own unique approach. Let’s explore a couple of these alternative methods:

Method 2: Using Basic Algebra

Let the original price be P. The sale price after 20% discount is given by:

Sale Price 0.80 * P

Given that the sale price is $35, we can set up the equation:

0.80 * P 35

Now, solve for P:

P 35 / 0.80

P 43.75

Method 3: Percentage Calculation

Recognize that a 20% discount means the customer pays 80% of the original price. Let the original price be 100, then after a 20% discount, the price is 80. Set up a proportion:

80 / 100 35 / X

Solve for X by cross-multiplying:

X (35 * 100) / 80

X 43.75

Case-Checking

As a final check, consider the scenario where the 40 after the coat was on sale or if the retail price was 40 and another 20% discount was applied. In such cases, the original price would be calculated differently. However, based on the given information, the original price remains $43.75.

Practical Application and Retail Math

Understanding how to calculate the original price is crucial for both buyers and sellers. In practical retail scenarios, knowing this can help in setting prices, determining discounts, and more. Additionally, considering retail tax, such as the 10.25% tax in Chicago, can further refine the calculations to provide accurate final prices to customers.

In conclusion, the original selling price of the coat, based on the given sale price and discount, is $43.75. This method can be applied to any similar problem involving original and sale prices, making it a valuable skill in understanding and managing retail pricing effectively.