Calculating Original Price from Discount Percentage

When shopping, understanding how to calculate the original price from a discounted price can save you a lot of money. In this guide, we'll explore the methods and formulas used to determine the original price before a discount was applied. By mastering this skill, you can better evaluate sales and make informed purchasing decisions.

1. Understanding the Discount Formula

The basic formula to calculate the original price from a discount percentage is:

$\text{Original Price}=\frac{\text{Discounted Price}}{1-\left(\frac{\text{Discount Percentage}}{100}\right)}$Original Price=1−(100Discount Percentage​)Discounted Price​

2. Breaking Down the Formula

• Discounted Price: This is the price after the discount has been applied.
• Discount Percentage: This is the percentage by which the original price was reduced.

3. Example Calculation

Suppose you are buying a jacket that costs $80 after a 20% discount. To find out the original price before the discount:

1. Convert the discount percentage into decimal form: $20\%=0.20$20%=0.20
2. Subtract this from 1 to find the proportion of the original price that you paid: $1-0.20=0.80$1−0.20=0.80
3. Divide the discounted price by this proportion: $\frac{80}{0.80}=100$0.8080​=100

So, the original price of the jacket was $100.

4. Using Algebra to Understand the Calculation

Let’s use algebra to derive the same result:

• Let $P$P be the original price.
• The discount percentage is $D$D, and the discounted price is $P_{discounted}$Pdiscounted​.

The relationship is:

$P_{discounted}=P\times (1-\frac{D}{100})$Pdiscounted​=P×(1−100D​)

To find $P$P:

$P=\frac{P_{discounted}}{1-\frac{D}{100}}$P=1−100D​Pdiscounted​​

This confirms our earlier formula.

5. Real-World Application

Knowing how to calculate the original price is useful for comparing discounts across different stores. For instance, if Store A offers a 25% discount and Store B offers a 15% discount, but you don’t know the original prices, calculating them can help you determine which offer is better.

6. Using a Discount Calculator

For convenience, many online discount calculators can perform this calculation automatically. You simply input the discounted price and the discount percentage, and the calculator does the rest.

7. Practical Tips

• Always check if the discount is applied to the entire purchase or just specific items.
• Be aware of additional costs such as taxes and shipping fees that might affect the final price.

8. Conclusion

Calculating the original price from a discount percentage is a valuable skill that helps in making informed buying decisions. With the right formula and a bit of practice, you can easily determine how much you’re saving and whether a sale is worth it.