Question 806982
If your cost is {{{C}}} ,
and you want to multiply that cost by a factor {{{F}}} to get a selling price  {{{C*F}}},
for a profit of 55% of the selling price,
the equation is {{{F=1/((1-0.55))}}} ,
so {{{F=1/0.45=200/9=1.81818181818}}}{{{...}}}
For another percentage,
you would turn that percentage into a decimal,
and your factor would be {{{F=1/((1-p))}}} ,
with {{{p}}}= your profit percentage (based on sales),
For example, if you were satisfied with a profit
amounting to 37.5% of sales,
you would use {{{p=0.375}}} , and
would calculate {{{F=1/((1-0.375))=1/0.625=1.6}}} ,
 
THE EXPLANATION:
If your cost is {{{C}}} ,
and you multiply that cost by a factor {{{F}}} to get the selling price,  the selling price is {{{C*F}}} , and
the profit is {{{C*F-C}}}.
If the profit is 55% of the selling price,
{{{C*F-C=0.55*C*F}}} ,
which can also be written as {{{C*(F-1)=0.55*C*F}}}.
Because {{{C}}} is multiplying every term in the equation,
the value of C does not matter,
and the equation simplifies to
{{{F-1=0.55*F}}} --> {{{F=0.55*F+1}}} --> {{{F-0.55*F=1}}} --> {{{F*(1-0.55)=1}}} --> {{{F=1/((1-0.55))}}}