   SEARCH HOME Math Central Quandaries & Queries  Question from Roxane: I'm trying to figure out the formula for the following, I have a product that I want to receive a certain profit margin, but with this product I also have to pay a percentage of commission to someone. I need to know how to calculate my new selling price taking into account the markup percentage, but I don't want my gross margin to be lowered. I have calculated the markup percentage to get my new selling price with the commission, but it lowers my profit margin once I pay the commission and I don't want it to do that. Ho Roxane,

Suppose S is the selling price in dollars. Your cost is composed of two parts, the cost C before the commission and the commission D, both in dollars. I expect you calculate your profit margin M as a percent by

M = [[S - (C + D)]/S] × 100

Again I expect the commission D is a percentage of S, say E% then

D = E/100 × S

Hence

MS/100 = S - (C + E/100 × S)

Thus

S - MS/100 - ES/100 = C or
S(1 - M/100 - E/100) = C

Finally if M is the margin and E is the commission, both as percentages then the selling price S is

S = C/(1 - M/100 - E/100)

If I have misinterpreted what you mean by margin or commission let me know.

Penny     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.