SOLUTION: Please can you give me the algebra equasion to apply to cost of goods to give me a gross profit percentage to sales of 55%. I am stuck somewhere with 1.8181 etc and dont know why.

Question 806982: Please can you give me the algebra equasion to apply to cost of goods to give me a gross profit percentage to sales of 55%. I am stuck somewhere with 1.8181 etc and dont know why. Very kind if you could assist. Thank you
Answer by KMST(5347) (Show Source): You can put this solution on YOUR website!
If your cost is ,
and you want to multiply that cost by a factor to get a selling price ,
for a profit of 55% of the selling price,
the equation is ,
so

For another percentage,
you would turn that percentage into a decimal,
and your factor would be ,
with = your profit percentage (based on sales),
For example, if you were satisfied with a profit
amounting to 37.5% of sales,
you would use , and
would calculate ,

THE EXPLANATION:
If your cost is ,
and you multiply that cost by a factor to get the selling price, the selling price is , and
the profit is .
If the profit is 55% of the selling price,
,
which can also be written as .
Because is multiplying every term in the equation,
the value of C does not matter,
and the equation simplifies to
--> --> --> -->
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