math

So what's the problem.

eBay, purveyor of buying and selling the stuff from your Grandma's house, or from China. Has a IMHO terrible fee structure which works like this.

You sell the item you want (S), then it gets taxed (T). That taxed sale then has two additional fees applied to it, one for transaction (E), another for international (I). Finally a static fee is needed for the listing itself (F). Oh and all of this is taxed.

This results in the following Formula to calculate how much you will actually make from a sale (P).

S - ST - ([ES*(1+T)])T - ([IS*(1+T)])T - F(1+T) = P

This is stupid, and I shouldn't be taxed on my tax, but whatever. I just need to math my way out of this. It took all evening but I was able to take the formula above and isolate S

P+F+F(1*T)

------------------------------------------- = S

1-T-E-E*(2T+T^2 )-I-I(2*T+T^2 )

The result of this is a sale prince which accounts for eBay's fees

I've attached a screenshot to my excel sheet to prove that it works. I'm going to bed.