# Math

### Math

When 25 percent off and 50 percent off not 75 percent off, the company has masterfully manipulated the laws of mathematics in an effort to make the sale look more appealing and to keep as much money as possible for themselves. The important word to look for when figuring out these types of word problems is that word additional. By throwing in that word, retailers change the base that they are calculating from. Instead of calculating the extra 25 percent based off based on the original price, they can calculate it based on the new price or in some cases from the amount of discount already given. This means it is extra important to understand how these things are calculated, especially when the original discount is less than 50 percent.

To illustrate the difference, think of a product that cost \$4 to start. If it is then 50 percent off, it would be \$2. An additional 25 percent off would be 50 cents, so you would pay \$1.50 for the item. If it had actually been 75 percent off, as the signs are intended to mislead, it would have cost \$1. On higher ticket items, the difference grows exponentially. But to illustrate the issue even more clearly, consider what happens when advertisers throw in extra words like “additional savings.”

That means the seller had now taken the additional amount based on what you have already saved. When you start with an item that is 50 percent off, the word savings doesn’t mean much. But it can.  Take for example, a \$6 item that is initially marked down 33 percent. It is now a \$4 item. But then the retailer says they will mark it down for an additional 50 percent savings. That means you get it for \$2, right? Wrong. The additional savings is calculated using the amount taken off the price, in this case \$2. So an additional savings of 50 percent is \$1. Take one away from four and you end up paying \$3.

Further complicating this is that stores also sometimes use the phrase save an additional fo percent of already discounted price.  In that case, the formerly \$6 item really would be \$2, making the total percentage discount, from the original price to be 66 percent. Not the 83 percent it might initially appear to be.  These trick of math are one way retail stores stay ahead of consumers.