Have you ever encountered a problem that involves reverse percentages? It can be quite confusing, especially if you’re not a math whiz. But don’t worry, we’ve got you covered. In this article, we’ll explain what reverse percentages are, how to solve them, and provide some examples to help you understand the concept better.
What Are Reverse Percentages?
Before we dive into the nitty-gritty of solving reverse percentages, let’s first define what they are. In a regular percentage problem, you’re given a percentage and you have to find the amount or value it represents. For example, if a shirt costs $50 and it’s on sale for 20% off, you need to find out how much the shirt costs after the discount. However, in a reverse percentage problem, you’re given the discounted price and the percentage off, and you need to find out the original price before the discount.
How to Solve Reverse Percentages
Now that we know what reverse percentages are, let’s move on to solving them. There are two main methods to solve reverse percentage problems:
Method 1: Multiplying by the Reciprocal
This method involves finding the original price by multiplying the discounted price by the reciprocal of the percentage off. Here’s the formula:
Let’s use the previous example to illustrate this method:
The discounted price is $40, and the percentage off is 20%. To find the original price, we’ll use the formula:
Therefore, the original price of the shirt is $50.
Method 2: Using Proportions
This method involves setting up a proportion with the discounted price and the original price. Here’s the formula:
Let’s use the same example to illustrate this method:
The discounted price is $40, and the percentage off is 20%. To find the original price, we’ll use the formula:
Therefore, the original price of the shirt is $50.
Examples of Reverse Percentage Problems
Let’s look at some examples of reverse percentage problems to help you understand the concept better.
Example 1:
A phone is on sale for 15% off. If the discounted price is $340, what was the original price?
To solve this problem, we’ll use method 1:
Therefore, the original price of the phone was $400.
Example 2:
A watch is on sale for $60, which is 25% off the original price. What was the original price?
To solve this problem, we’ll use method 2:
Therefore, the original price of the watch was $80.
Conclusion
Reverse percentage problems can be challenging, but with the right methods and practice, you can solve them with ease. Remember to always double-check your answers and use a calculator if necessary. We hope this guide has been helpful and informative. Happy calculating!
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