Formula to calculate final profit I'm using SmugMug to host and sell my photography images, and I'm looking to set my prices. I can't seem to figure out a formula to simply calculate my final profit after all deductions.
Example:

The printing company charges $\$0.25$ for a $4\times 6$ image.
  I want to make a $\$5$ profit off of the images
  but the hosting site charges $15\%$ of my profit for their expenses.
If I charge $\$5.25$ for a print, my final profit will be $\$4.85$
  $((\$5.25 - \$0.25)-15\%)$ $=$ $\$4.85$ 
If I charge $\$5.40$ for a print, my final profit will be $\$5$ (which is what I want).
  $((\$5.40 - \$0.25)-15\%)$ $=$ $\$5.00$ 

What would the formula look like to set my prices in such a way that I will always make a $\$5$ profit off of an image?
 A: I'm going to assume that they deduct some percentage of your profit, rather than a fixed amount, since that's more intuitive.
Suppose you pay $x$ dollars for a print. The hosting site takes a fraction $p$ of your profit. You want to make $y$ dollars per sale. The price that you sell the image for is $z$ dollars.
We then have the following relationships. Your initial profit is given by $z - x$. The hosting site takes the fraction $p$ away from this profit, so you're left with the fraction $(1-p)$. This means the profit you're left with, after Smugmug's deduction is $(1-p)*(z-x)$. You want this to be equal to $d$, so $d = (1-p)(z-x)$. Since what we really care about here is $z$, the price that you sell for, we can rearrange, and get $z = \frac{d}{1-p} + x$.
Just to make it clear, let's substitute some numbers in, like the example you gave above. You want to make $\$5.00$, so $d = 5$. They take 15%, so $p = 0.15$. Finally, it costs you 25 cents for a print, so $x = 0.25$. If we substitute this in, we get $z = \frac{5}{0.85} + 0.25 = \$6.13$.
A: The formula looks like this.
If you charge C amount, the printing company will always take \$0.25 away. So gross profit is $P = C - 0.25$. You get a final profit of $P - 0.15 P = 0.85 P$, as 15% is taken away from you by the host.
So you want $0.85P = \$5.00$. Solving this yields $P = \$5.89$. And so you need to charge $\$6.14$.
Let's check. $6.14 - 0.25 = 5.89$. That's good. $0.85 \cdot 5.89 = 5.0065$. Great.
