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How To Find Original Price

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Unveiling the Original Price: A Simple Guide to Reverse Calculations



Knowing the original price of an item before a discount or markup is applied can be crucial for making informed purchasing decisions or understanding historical pricing trends. Whether you're comparing deals, tracking inflation, or simply curious about the initial cost, this guide will equip you with the skills to find the original price, even when only the discounted price and percentage are known.

1. Understanding Percentage Discounts



Discounts are reductions in the original price, usually expressed as a percentage. For instance, a 20% discount means the selling price is 80% of the original price (100% - 20% = 80%). This understanding forms the basis for our calculations.

Example: A shirt is on sale for $20 after a 25% discount. This means the $20 represents 75% (100% - 25% = 75%) of the original price.


2. Calculating the Original Price from a Percentage Discount



This is the most common scenario. You know the sale price and the discount percentage. The calculation involves working backward from the sale price to find the full 100%. We can use two methods:

Method 1: Using a proportion

This method uses the ratio of the sale price to the percentage it represents.

Let's use the shirt example:

Sale price: $20
Discount percentage: 25%
Percentage remaining: 75% (100% - 25%)

We set up a proportion:

75/100 = $20/x (where 'x' is the original price)

Cross-multiply: 75x = 2000

Solve for x: x = 2000/75 = $26.67 (approximately)

Therefore, the original price of the shirt was approximately $26.67.


Method 2: Using a decimal multiplier

This method uses the decimal equivalent of the percentage remaining after the discount.

In our shirt example, 75% is equivalent to 0.75 (75/100).

The formula is: Original Price = Sale Price / Decimal Multiplier

Original Price = $20 / 0.75 = $26.67 (approximately)


3. Calculating the Original Price from a Percentage Markup



Markups are increases in price, often used by retailers to determine their selling price based on their cost price. Calculating the original price (cost price) from a marked-up price involves a similar process, but instead of subtracting the percentage, we will be dividing by the percentage increase plus 100%.

Example: A store sells a phone for $600 after a 50% markup.

The formula becomes: Original Price (Cost Price) = Selling Price / (1 + Markup Percentage as a decimal)

Original Price = $600 / (1 + 0.50) = $600 / 1.50 = $400

The original cost of the phone was $400.


4. Dealing with Sales Tax



If the sale price already includes sales tax, you need to account for that before calculating the original price. First, determine the sales tax rate and calculate the pre-tax price. Then use the methods outlined above with the pre-tax price to find the original price.

Example: A dress costs $77 after 7% sales tax. To find the pre-tax price, we can use the formula: Pre-tax price = Price including tax / (1 + tax rate as a decimal).

Pre-tax price = $77 / (1 + 0.07) = $77 / 1.07 = $71.96 (approximately)

Now you can use this pre-tax price ($71.96) and any discount percentage applied to calculate the original price as explained above.


Actionable Takeaways



Understand the difference between discounts and markups.
Master the proportional method or the decimal multiplier method for calculating the original price.
Remember to account for sales tax if it's included in the sale price.
Practice regularly to improve your calculation speed and accuracy.


Frequently Asked Questions (FAQs)



1. What if I only know the discount amount, not the percentage? You'll need to find the discount percentage first. Divide the discount amount by the sale price, then multiply by 100 to express it as a percentage.

2. Can I use these methods for multiple discounts? Not directly. For multiple discounts, you need to apply each discount sequentially. Calculate the price after the first discount, then apply the second discount to that new price, and so on.

3. What if the problem involves both a discount and a markup? Apply the discount first, then apply the markup to the resulting price or vice versa, depending on the order in which the changes occurred.

4. Are there online calculators to help with these calculations? Yes, many websites offer free online calculators for finding original prices. Simply search for "original price calculator".

5. What if the problem involves rounding errors? Slight discrepancies might arise due to rounding during calculations. These are usually negligible, but you should be aware of this possibility.

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How to Calculate an Original Amount Using Reverse Percentages Reverse percentages are commonly used to find the original price of an item after a percentage change (discount or tax). The method and process described on this page explains how to reverse a given percentage increase or decrease to find an original amount. Write the percentage change as a decimal multiplier.

Original Price Calculator 2 Apr 2024 · Enter the current sale price and the percent off of the original price to calculate the original price of a good. This calculate can also determine the sale price or percentage off given the original price and other variable.

How to find the original value before percentage off - BBC To find the original value of an amount before the percentage increase/decrease: Write the amount as a percentage of the original value. Find 1% of the original value. The original value is 100%,...

Reverse percentages - Percentages - Edexcel - GCSE Maths … To find the original price of the item, 100% has to be found. There are many ways to do this, but using a. is a method that will always work. 80% = 24. Divide both sides by 80 to get 1%: \ (1...

Original Price Calculator (Online Tool) - RetailBoss To calculate the original price given the sale price and discount percentage: Identify the sale price (P) and the discount percentage (d) as a decimal. Use the formula: Original Price = Sales Price / (1 – Discount Percentage) or P / (1 – d)

How to calculate the original price after a discount? Divide the discounted price by the percentage of the original price paid (expressed as a decimal). This will give you the original price. Example: Let's say you bought a laptop for $800 after a 10% discount. To find the original price, follow these steps: Percentage of original price paid: 100% - 10% = 90% (or 0.90 as a decimal)

Original Price Calculator [ Retail, Discount, Sale, Wholesale, Final ] 3 Dec 2024 · To find the original price, divide the sale price by 1−100PO , where PO is the percentage discount. The Original Price Calculator judges the initial price of an item before a discount was applied. This is useful for budgeting, understanding discounts, and making informed purchasing decisions.

How To Find The Original Price - Sciencing 7 Jan 2025 · To calculate the original price of a discounted or sale item, you need to know the sale price and the discount percentage. The calculations include a simple formula that divides the sale price by the result of 1 minus the discount in percentage form.

Reverse Percentages Calculator Online - Math Salamanders This calculator will help you to find the original number, when you have been given the percentage increase or decrease and the final number. Example: if a toy in a sale marked 20% off costs $210, what is the original price? Type 20 for the percentage. Select 'Percentage Decrease' because the items is 20% less in the sale.

Percentage change - BBC Bitesize The new price, £75, represents 125% of the original price. The original 100% plus the 25% increase in cost. To calculate the original value, the 100% cost, without a calculator, we first find a ...