# Percentage problem. **URL:** \ **Category:** Factual Questions\ **Created:** [October 9, 2005, 5:44pm UTC](https://boards.straightdope.com/t/percentage-problem/325423 "2005-10-09T17:44:19Z")\ **Posts on this page:** 5\ **Page:** 1
**Author:** ![FilmGeek](https://avatars.discourse-cdn.com/v4/letter/f/b19c9b/32.png) [@FilmGeek](https://boards.straightdope.com/u/FilmGeek)\ **Post date:** [October 9, 2005, 5:44pm UTC](https://boards.straightdope.com/t/percentage-problem/325423/1 "2005-10-09T17:44:19Z")
I often wake myself up in the morning by giving myself mental math problems while in the shower. Math is generally difficult for me, so this is a way for me to get my brain started in the morning. I tried this one today. If the item I want to buy is marked $100, and I know it was marked down 20%, what was the original price? Now, I know that if I want to find out what 20% of 100 is, I can do that in a number of ways (20% is easy, but other percentages are not, so I know the formula). I can’t seem to get what the original price would be, though. Through trial and error, I can see that it would be $125 (20% of 125 is 25, 125-25=100) but I know there is a mathematical way to figure this out without trial and error. Any help math dopers? ---
**Author:** ![TheLadyLion](https://avatars.discourse-cdn.com/v4/letter/t/d78d45/32.png) [@TheLadyLion](https://boards.straightdope.com/u/TheLadyLion)\ **Post date:** [October 9, 2005, 5:56pm UTC](https://boards.straightdope.com/t/percentage-problem/325423/2 "2005-10-09T17:56:42Z")
Algebra is your friend. Start with the known, $100 is 80% or 8/10 of the original price. 100 = x \* 8 / 10 multiply both sides by 10 1000 = x \* 8 divide both sides by 8 125 = x ---
**Author:** ![FilmGeek](https://avatars.discourse-cdn.com/v4/letter/f/b19c9b/32.png) [@FilmGeek](https://boards.straightdope.com/u/FilmGeek)\ **Post date:** [October 9, 2005, 6:02pm UTC](https://boards.straightdope.com/t/percentage-problem/325423/3 "2005-10-09T18:02:49Z")
I knew there was something wrong with focusing on 20%, but I couldn’t quite get it straight. Thanks… I’m going to assume you weren’t being snarky. ---
**Author:** ![Thudlow\_Boink](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/thudlow_boink/32/320_2.png) [@Thudlow\_Boink](https://boards.straightdope.com/u/Thudlow_Boink)\ **Post date:** [October 9, 2005, 6:03pm UTC](https://boards.straightdope.com/t/percentage-problem/325423/4 "2005-10-09T18:03:51Z")
What **TheLadyLion** said. Or, to spell it out in even more detail: Your question is: _ **What number** , minus 20% of **that number** , is $100?_ Let x stand for the number. Then your question translates into x – .20x = 100 Combine the x terms: 1x - 0.20x = (1 – 0.20)x = 0.80x, so .80x = 100 Then divide both sides by .80 to get x = 100 / .80 = 125 ---
**Author:** ![wolf\_meister](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/wolf_meister/32/15202_2.png) [@wolf\_meister](https://boards.straightdope.com/u/wolf_meister)\ **Post date:** [October 10, 2005, 3:49am UTC](https://boards.straightdope.com/t/percentage-problem/325423/5 "2005-10-10T03:49:22Z")
Heck, I couldn’t help but “plug” my own site on this one. Go here: [http://www.1728.com/percent2.htm](http://www.1728.com/percent2.htm) scroll down to Percent Decrease Calculator and it is an Example ‘C’ type problem. Needless to say, I came up with $125 also.