   SEARCH HOME Math Central Quandaries & Queries  Question from Anni: I need to find selling price to put us at 24% margin. 15% commission is based on selling price and is included in our cost. I'm trying to do it excel and keep getting a circular reference. Total cost= cost + commission (15% of selling price) Selling price=total cost + 24% margin Hi Anni,

Suppose the cost is $C$ dollars, the total cost is $TC$ dollars and the selling price is $SP$ dollars. Since the total cost= cost + commission (15% of selling price) we have

$TC = C + 0.15 \times SP \mbox{ dollars.}$

Since the selling price is the total cost plus a 24% margin we also have that

$SP = TC + 0.24 \times TC = 1.24 \times TC \mbox{ dollars.}$

Substituting this expression for $SP$ into the first equation yields

$TC = C + 0.15\times 1.24 \times TC = C + 0.186 \times TC \mbox{ dollars.}$

Hence

$TC - 0.186 \times TC = 0.814 \times TC = C \mbox{ dollars.}$

or

$TC = \frac{C}{0.814} \mbox{ dollars.}$

Since $SP = 1.24 \times TC \mbox{ dollars.}$ we finally get

$SP = \frac{1.24}{0.814} \times C = 1.52 \times C \mbox{ dollars.}$     