# Determining the Final Price of an Item

(1) Assume that the original price of an item is eventually increased by 25%, and that a 25% discount is applied later. How does the final price compare to the original price?

(2) Assume that the original price of an item is eventually discounted by 25%, and that a 25% increase is applied later. How does the final price compare to the original price?

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#### Solution Preview

Here's the point of problems like these:

Many people think that if you increase the price of an item by 25%, and then you later decrease THAT price by 25%, the item will end up selling at the original price.

Also, many people think that if you decrease the price of an item by 25%, and then you later increase THAT price by 25%, the item will end up selling at the original price.

However, both of those are false.

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Let's look at the math of this.

Problem (1):

Let's denote the original price of an item by p (for "price").

Since 25% is equivalent (as a decimal) to 0.25,

the price after an increase of 25% will be

p + 0.25p = (1 + 0.25)p

[We've factored out the common factor of p in that step.]

Since 1 + 0.25 = 1.25, this can be written as

(1.25)p ...

#### Solution Summary

The Solution explains the math behind finding the final price for an item. A complete, detailed solution is provided, with an explanation of everything that's used in the solution.