# Maths problem **URL:** \ **Category:** Miscellaneous and Personal Stuff I Must Share\ **Created:** [January 19, 2006, 1:44pm UTC](https://boards.straightdope.com/t/maths-problem/340651 "2006-01-19T13:44:34Z")\ **Posts on this page:** 12\ **Page:** 1
**Author:** ![biddee](https://avatars.discourse-cdn.com/v4/letter/b/839c29/32.png) [@biddee](https://boards.straightdope.com/u/biddee)\ **Post date:** [January 19, 2006, 1:44pm UTC](https://boards.straightdope.com/t/maths-problem/340651/1 "2006-01-19T13:44:34Z")
Ok, for the life of me I can’t figure this out. I know that I suck at maths, but this is really bugging me, which is why I am throwing it out there for the geniuses here on the SDMB. We sell advertising in a magazine. A full page advert costs $4395. We received an order from an ad agency stating that their charge to their client is $5170.60. The agency fee is 15%. 15% of $4395 is $659.25. If you add that to $4395 then you get $5054.25. 15% of $5170.60 is $775.59 and when you subtract that from $5170.60 you get $4395.01. This way the agency gets 15% of the higher figure instead of the lower figure. What I can’t figure out is how they arrive at the higher figure in the first place. I know it’s probably really simple but would someone please explain it to me. ---
**Author:** ![audiobottle](https://avatars.discourse-cdn.com/v4/letter/a/bc8723/32.png) [@audiobottle](https://boards.straightdope.com/u/audiobottle)\ **Post date:** [January 19, 2006, 1:48pm UTC](https://boards.straightdope.com/t/maths-problem/340651/2 "2006-01-19T13:48:04Z")
I guess they said, “4395 is 85% of what?” And did 4395/0.85 = 5170.6. As for how they decided that was the correct way to do things, I have no idea. ---
**Author:** ![Mordib](https://avatars.discourse-cdn.com/v4/letter/m/c0e974/32.png) [@Mordib](https://boards.straightdope.com/u/Mordib)\ **Post date:** [January 19, 2006, 1:50pm UTC](https://boards.straightdope.com/t/maths-problem/340651/3 "2006-01-19T13:50:18Z")
well, if they are maing 15% on it then the cost to them needs to be 85% of the amount they charge so you take the original amount, divide it by 85 then multiply it by 100. Im sure theres a more acceptable way to show this but im willing to bet this is the method they use in the office 😛 ---
**Author:** ![Mordib](https://avatars.discourse-cdn.com/v4/letter/m/c0e974/32.png) [@Mordib](https://boards.straightdope.com/u/Mordib)\ **Post date:** [January 19, 2006, 1:51pm UTC](https://boards.straightdope.com/t/maths-problem/340651/4 "2006-01-19T13:51:28Z")
> [@Mordib](#): > > well, if they are maing 15% on it then the cost to them needs to be 85% of the amount they charge so you take the original amount, divide it by 85 then multiply it by 100. Im sure theres a more acceptable way to show this but im willing to bet this is the method they use in the office 😛 as audio bottle proved quite well, there was an easer way 😛 ---
**Author:** ![Spatial\_Rift\_47](https://avatars.discourse-cdn.com/v4/letter/s/a8b319/32.png) [@Spatial\_Rift\_47](https://boards.straightdope.com/u/Spatial_Rift_47)\ **Post date:** [January 19, 2006, 1:51pm UTC](https://boards.straightdope.com/t/maths-problem/340651/5 "2006-01-19T13:51:47Z")
It seems to me that they deliberately solved for whatever number would allow them to take 15% off the top and still have the cost of the ad left over. In other words, they said, “Okay, we need to charge $x such that x - .15_x = .85_x = 4395,” and then solve for x. ---
**Author:** ![biddee](https://avatars.discourse-cdn.com/v4/letter/b/839c29/32.png) [@biddee](https://boards.straightdope.com/u/biddee)\ **Post date:** [January 19, 2006, 1:57pm UTC](https://boards.straightdope.com/t/maths-problem/340651/6 "2006-01-19T13:57:34Z")
Thank you, thank you, thank you…I knew there was an easy way to do it, I just couldn’t figure it out…much much appreciated! ---
**Author:** ![Dead\_Cat](https://avatars.discourse-cdn.com/v4/letter/d/9fc29f/32.png) [@Dead\_Cat](https://boards.straightdope.com/u/Dead_Cat)\ **Post date:** [January 19, 2006, 3:03pm UTC](https://boards.straightdope.com/t/maths-problem/340651/7 "2006-01-19T15:03:41Z")
It’s just a way for the agency to ramp up their fees while still being able to claim it’s 15%. Seems pretty nasty to me. If I were the one paying them I wouldn’t be giving them a cent more than $5054.25. ---
**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:** [January 19, 2006, 4:08pm UTC](https://boards.straightdope.com/t/maths-problem/340651/8 "2006-01-19T16:08:26Z")
Unless **Dead Cat’s** posting is a whoosh, **audiobottle** has the correct solution. Let’s suppose this is a salary question and employee X makes $4,395 after 15% tax. What is the gross pay? Gross Pay = .15\* Gross Pay + Net Pay .85\*Gross Pay = $4,395 (Net Pay) Gross Pay = 4,395/.85 Gross Pay = 5,170.59 ---
**Author:** ![Al128](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/al128/32/16541_2.png) [@Al128](https://boards.straightdope.com/u/Al128)\ **Post date:** [January 19, 2006, 4:28pm UTC](https://boards.straightdope.com/t/maths-problem/340651/9 "2006-01-19T16:28:47Z")
basically your agency is charging you 15% for their services - and also 15% for receiving their fee 😃 technically there is a double-charge in there … go raise some hell 😛 ---
**Author:** ![Dead\_Cat](https://avatars.discourse-cdn.com/v4/letter/d/9fc29f/32.png) [@Dead\_Cat](https://boards.straightdope.com/u/Dead_Cat)\ **Post date:** [January 19, 2006, 7:17pm UTC](https://boards.straightdope.com/t/maths-problem/340651/10 "2006-01-19T19:17:52Z")
I wasn’t whooshing, but I may be being whooshed. I entirely agree with **Al128**. I also realise that **audiobottle** provided the OP with the answer they were looking for (it’s the OP that’s getting paid, not charged), I was just making a further comment to the effect that I thought what the agency is doing (nothing to do with the OP) is shitty business. It’s not like being taxed on salary, it’s a charge for a service. The service costs X, so the commission charged by the agency should be 0.15 \* X, not X/0.85 - X. IMHO :). ---
**Author:** ![Knowed\_Out](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/knowed_out/32/7380_2.png) [@Knowed\_Out](https://boards.straightdope.com/u/Knowed_Out)\ **Post date:** [January 19, 2006, 7:35pm UTC](https://boards.straightdope.com/t/maths-problem/340651/11 "2006-01-19T19:35:46Z")
When I used to work for a heavy equipment dealer, we marked up the price of parts 35%. That is, we divided the retailer price by .65 to get the customer price. When I questioned this, I was given the “This pays your salary” admonition. ---
**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:** [January 19, 2006, 8:54pm UTC](https://boards.straightdope.com/t/maths-problem/340651/12 "2006-01-19T20:54:18Z")
**Dead Cat** Sorry for saying you were whooshing. :smack: I wasn’t being critical of your calculations, it just \*seemed \*(to me) your posting was indignant in a humorous kind of way. > [@](#): > > I wouldn’t be giving them a cent more - harumph. (harumph mine). Yes, I say you are right - that company is sleazy and they are charging more than 15%. (I’ve got to make fewer postings from work).