# Need a mathematical function for thisI **URL:** \ **Category:** Factual Questions\ **Created:** [October 23, 2007, 5:37pm UTC](https://boards.straightdope.com/t/need-a-mathematical-function-for-thisi/423726 "2007-10-23T17:37:09Z")\ **Posts on this page:** 8\ **Page:** 1
**Author:** ![Mindfield](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/mindfield/32/19759_2.png) [@Mindfield](https://boards.straightdope.com/u/Mindfield)\ **Post date:** [October 23, 2007, 5:37pm UTC](https://boards.straightdope.com/t/need-a-mathematical-function-for-thisi/423726/1 "2007-10-23T17:37:09Z")
I stink at math, so I’ll just get that out of the way right now. Now here’s the thing. There’s something we sell to someone who automatically deducts 5% off of the price we sell it to them at – part of the fact that it’s stuff being sold national distributor (us) to regional distributor (them) so they get an extra deal. The thing is there are some items which are net priced (meaning they are sold at actual cost rather than a percentage off of the retail cost) and we don’t want to lose money on those, so we want to up their charges by a percentage which reflects the percentage they will discount the items by. In other words, if we sell a net-priced item for $100, they will deduct $5 for their distributorship discount. We can’t up the price to $105 because 5% from $105 is still $99.75 – we lose a quarter. So what’s the equation to determine what value we need to add to a part to cover the 5% discount they will take off of it? ---
**Author:** ![Terminus\_Est](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/terminus_est/32/3087_2.png) [@Terminus\_Est](https://boards.straightdope.com/u/Terminus_Est)\ **Post date:** [October 23, 2007, 5:41pm UTC](https://boards.straightdope.com/t/need-a-mathematical-function-for-thisi/423726/2 "2007-10-23T17:41:18Z")
x - 0.05x = 100 where x is the amount you need to charge to get your desired amount of $100 You should be able take it from there. ---
**Author:** ![Joey\_P](https://avatars.discourse-cdn.com/v4/letter/j/919ad9/32.png) [@Joey\_P](https://boards.straightdope.com/u/Joey_P)\ **Post date:** [October 23, 2007, 5:44pm UTC](https://boards.straightdope.com/t/need-a-mathematical-function-for-thisi/423726/3 "2007-10-23T17:44:54Z")
If it’s 5%, take the original amount and divide it by .95 So $100/.95=$105.27 $105.27\*.95=$100 (well $100.01, but that’s a rounding error) ---
**Author:** ![MikeS](https://avatars.discourse-cdn.com/v4/letter/m/919ad9/32.png) [@MikeS](https://boards.straightdope.com/u/MikeS)\ **Post date:** [October 23, 2007, 5:45pm UTC](https://boards.straightdope.com/t/need-a-mathematical-function-for-thisi/423726/4 "2007-10-23T17:45:11Z")
If you want the item to be in the stores for x, and your distributor will put the item on the shelves for 95% of what you charge them (call that y), then x = 0.95 \* y, which means you should charge the distributor y = x / 0.95, or y = x \* 1.05263. ---
**Author:** ![jk1245](https://avatars.discourse-cdn.com/v4/letter/j/49beb7/32.png) [@jk1245](https://boards.straightdope.com/u/jk1245)\ **Post date:** [October 23, 2007, 5:46pm UTC](https://boards.straightdope.com/t/need-a-mathematical-function-for-thisi/423726/5 "2007-10-23T17:46:28Z")
Divide your needed price by .95. In your example, $100/.95 = $105.26 When they take 5% off, .05 \* 105.26 = $5.26, leaving you with $100. ---
**Author:** ![Blaster\_Master](https://avatars.discourse-cdn.com/v4/letter/b/cab0a1/32.png) [@Blaster\_Master](https://boards.straightdope.com/u/Blaster_Master)\ **Post date:** [October 23, 2007, 5:50pm UTC](https://boards.straightdope.com/t/need-a-mathematical-function-for-thisi/423726/6 "2007-10-23T17:50:50Z")
To expand on Terminus Est, who is correct, you can simplify and generalize the formula. **x = p/(1-d)** where **p** is the net price, and **d** is the discount. In this case, it would be **x = 100/(1-0.05) = 100/0.95 = 105.26** To double check, **105.26 x 0.05 = 5.26; 105.26 - 5.26 = 100** ---
**Author:** ![Mindfield](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/mindfield/32/19759_2.png) [@Mindfield](https://boards.straightdope.com/u/Mindfield)\ **Post date:** [October 23, 2007, 5:53pm UTC](https://boards.straightdope.com/t/need-a-mathematical-function-for-thisi/423726/7 "2007-10-23T17:53:50Z")
DOH! Subtract the amount they deduct from 100% and divide. This is one of those dense moments when I say “Why the hell didn’t I think of that?” I kept thinking you had to do some funky nested stuff to calculate the 5% discount first. Occam’s Razor. Thanks everyone! ---
**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 23, 2007, 8:10pm UTC](https://boards.straightdope.com/t/need-a-mathematical-function-for-thisi/423726/8 "2007-10-23T20:10:35Z")
[QUOTE=Mindfield] In other words, if we sell a net-priced item for $100, they will deduct $5 for their distributorship discount. We can’t up the price to $105 because 5% from $105 is still $99.75 – we lose a quarter. [/QUOTE] The fact that you realize this puts you way ahead of all too many math students I’ve known.