# How to Find the Original Price of a Discounted Item Formula

**Imagine walking into your favorite store, and you spot an item that’s on sale for $75 after a 20% discount. But then, a thought crosses your mind: "What was the original price?"**This scenario is something that many of us experience, especially during sales seasons when discounts are everywhere. Knowing how to calculate the original price of a discounted item is not only useful for shoppers but can also help you be more financially savvy. But fear not, you don't need to be a math genius to figure this out.

In this article, we'll walk through how to find the original price of an item when you only know the discounted price and the percentage discount. We’ll also explore real-life examples, provide a simple formula, and break it down into easy-to-follow steps. We’ll even dive into some scenarios where understanding this can make a big difference in your financial decisions.

### The Basic Formula to Find the Original Price

The formula for finding the original price of an item based on its discounted price is quite simple:

**Original Price = Discounted Price ÷ (1 - Discount Rate)**

Let’s dissect this formula:

**Discounted Price**: This is the price of the item after the discount has been applied.**Discount Rate**: The percentage of the discount expressed as a decimal (e.g., 20% becomes 0.20).

To put it simply, if you know the discounted price of an item and the percentage discount, this formula will help you reverse-engineer the original price.

### Step-by-Step Breakdown of the Formula

Let's say you have an item that costs $75 after a 20% discount. Here's how you’d use the formula to find the original price.

#### Step 1: Convert the Discount Percentage to a Decimal

In this case, the discount is 20%. To convert this to a decimal, divide by 100:

20 ÷ 100 = 0.20

#### Step 2: Subtract the Discount Rate from 1

Now subtract the discount rate from 1 to get the proportion of the price that you paid:

1 - 0.20 = 0.80

#### Step 3: Divide the Discounted Price by the Result

Next, take the discounted price and divide it by the result from Step 2:

$75 ÷ 0.80 = $93.75

So, the original price of the item was $93.75 before the discount was applied.

### Why Does This Formula Work?

You might be wondering, “Why does dividing by 1 minus the discount rate give me the original price?” The answer lies in basic percentage math. When an item is discounted by a certain percentage, say 20%, it means you’re paying 80% of the original price. By dividing the discounted price by this percentage (0.80 in our example), you effectively “undo” the discount and get the original price.

### Real-Life Applications of Knowing the Original Price

Now that you know how to find the original price of a discounted item, let’s explore why this knowledge is useful in real-world situations:

#### 1. **Comparing Discounts**

Retailers often advertise “50% off!” or “Buy one, get one 50% off!” but without knowing the original price, it’s hard to determine if you’re really getting a deal. By calculating the original price, you can make an informed decision.

For example, if an item is 50% off and the sale price is $40, you can use the formula to find that the original price was $80. But what if another store sells a similar item for $60 with a 30% discount? Using the formula, you’ll find that the original price there was $85.71. This gives you better insight into which deal is actually more valuable.

#### 2. **Budgeting and Planning**

If you’re shopping with a strict budget, understanding the original price can help you plan your purchases. For example, if you know an item you want to buy will be on sale, you can calculate the original price and determine whether the sale fits your budget.

#### 3. **Price Adjustments**

Many stores offer price adjustments if an item you bought goes on sale shortly after your purchase. Knowing how to calculate the original price and compare it with the sale price can help you determine if it’s worth asking for a price adjustment.

### Common Scenarios and Challenges

Let’s delve into some scenarios where understanding the original price can be particularly helpful.

#### Scenario 1: Multiple Discounts

What happens if you have an item with multiple discounts? For instance, you might have a store offering a 10% discount, but on top of that, you have a coupon for an additional 15% off. How do you calculate the original price?

Here’s how to handle it:

- First, apply the 10% discount to the original price.
- Then apply the 15% discount on top of that new price.

If you know the final price after both discounts, you can work backward by applying the same steps in reverse.

#### Scenario 2: Tax Considerations

In some regions, you may also need to account for sales tax when calculating the original price. To find the pre-tax original price, you’d first remove the tax from the final price, and then use the formula above to find the original price before the discount.

#### Scenario 3: Clearance Sales and Irregular Discounts

Clearance sales sometimes offer a set amount off the original price (e.g., $20 off) instead of a percentage. In this case, you can modify the formula to include the set amount off. If you’re not given a clear percentage, knowing the original price can help you calculate how much you’re actually saving.

### Using Technology to Calculate the Original Price

You don’t always have to rely on manual calculations. Many tools, including mobile apps and online calculators, are designed to help you calculate the original price of discounted items.

#### Example Apps:

**Discount Calculator**: This app allows you to input the discounted price and discount rate, and it will instantly calculate the original price for you.**ShopSavvy**: This app not only helps you calculate discounts but also compares prices from multiple retailers to ensure you get the best deal.**RetailMeNot**: While primarily a coupon app, RetailMeNot also offers price comparison features that can be helpful in understanding original prices.

### A Table to Illustrate Various Scenarios

Discounted Price | Discount Rate | Original Price |
---|---|---|

$50 | 10% | $55.56 |

$75 | 20% | $93.75 |

$100 | 30% | $142.86 |

$120 | 25% | $160.00 |

### Conclusion: Always Know the True Value

Understanding how to calculate the original price of a discounted item gives you more power as a consumer. It allows you to make informed purchasing decisions, compare deals across stores, and stay within your budget. While sales and discounts are exciting, they can also be deceiving if you don’t know how much you’re really saving. So the next time you see a flashy sale sign, you’ll know exactly how to calculate the original price—and whether that sale is as good as it seems.

Mastering this simple formula ensures that you always know the true value of your purchases. Whether you're a savvy shopper or just trying to make sense of a discount, this formula is your key to unlocking the mysteries behind price tags.**

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