# Maths problem

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.

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.

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

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 - .15x = .85x = 4395,” and then solve for x.

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!

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.

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

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

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 :).

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.