# Finding price for desired margin

My algebra is rusty, I'm trying to rearrange an equation, the purpose of which is to calculate the price that would result in a desired margin. Here are my workings:

p = price
c = cost
m = margin
P = profit = p - c


$$m = 100\frac{P}{p}$$ $$m = 100\frac{p-c}{p}$$ $$\frac{m}{100} = \frac{p-c}{p}$$ $$p\frac{m}{100} = p-c$$

$$p = \frac{pm}{100} + c$$

I'm stuck at this point. I can't figure out how to factor out p from the RHS. Can someone show me how to continue?

• $p = c/(1-m/100)$ – Carlos Campos Jun 18 '18 at 12:53
• hint: $\frac{p-c}{p} = 1-\frac{c}{p}$ – David Diaz Jun 18 '18 at 13:10
• @DavidDiaz I tried that and I get to $$p = \frac{100c}{m-100}$$ which doesn't seem right – Kev Jun 18 '18 at 13:22
• Probably since you should have $$p = \frac{100 c}{100 - m}$$ – Stan Tendijck Jun 18 '18 at 13:29
• @StanTendijck Thank you! I can see where I went wrong. – Kev Jun 18 '18 at 13:35

$$m = 100\frac{p-c}{p}$$ $$m = 100(1 -\frac{c}{p})$$ $$m = 100 - \frac{100c}{p}$$ $$m-100 = -\frac{100c}{p}$$ $$\frac{1}{p} = -(\frac{m-100}{100c})$$ $$\frac{1}{p} = \frac{100-m}{100c}$$ $$p = \frac{100c}{100-m}$$