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?
Here are the full workings to convert the margin equation to the price equation, for anyone interested. Thanks to @DavidDiaz and @StanTendijck for pointing me in the right direction.
$$m = 100\frac{p-c}{p}$$ $$m = 100(1 -\frac{c}{p})$$ $$m = 100 - \frac{100c}{p}$$ $$m-100 = -\frac{100c}{p}$$ $$\frac{1}{p} = -(\frac{m-100}{100c})$$ $$\frac{1}{p} = \frac{100-m}{100c}$$ $$p = \frac{100c}{100-m}$$