document.write( "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 \n" ); document.write( "
Algebra.Com's Answer #486136 by KMST(5347)\"\" \"About 
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If your cost is \"C\" ,
\n" ); document.write( "and you want to multiply that cost by a factor \"F\" to get a selling price \"C%2AF\",
\n" ); document.write( "for a profit of 55% of the selling price,
\n" ); document.write( "the equation is \"F=1%2F%28%281-0.55%29%29\" ,
\n" ); document.write( "so \"F=1%2F0.45=200%2F9=1.81818181818\"\"...\"
\n" ); document.write( "For another percentage,
\n" ); document.write( "you would turn that percentage into a decimal,
\n" ); document.write( "and your factor would be \"F=1%2F%28%281-p%29%29\" ,
\n" ); document.write( "with \"p\"= your profit percentage (based on sales),
\n" ); document.write( "For example, if you were satisfied with a profit
\n" ); document.write( "amounting to 37.5% of sales,
\n" ); document.write( "you would use \"p=0.375\" , and
\n" ); document.write( "would calculate \"F=1%2F%28%281-0.375%29%29=1%2F0.625=1.6\" ,
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\n" ); document.write( "THE EXPLANATION:
\n" ); document.write( "If your cost is \"C\" ,
\n" ); document.write( "and you multiply that cost by a factor \"F\" to get the selling price, the selling price is \"C%2AF\" , and
\n" ); document.write( "the profit is \"C%2AF-C\".
\n" ); document.write( "If the profit is 55% of the selling price,
\n" ); document.write( "\"C%2AF-C=0.55%2AC%2AF\" ,
\n" ); document.write( "which can also be written as \"C%2A%28F-1%29=0.55%2AC%2AF\".
\n" ); document.write( "Because \"C\" is multiplying every term in the equation,
\n" ); document.write( "the value of C does not matter,
\n" ); document.write( "and the equation simplifies to
\n" ); document.write( "\"F-1=0.55%2AF\" --> \"F=0.55%2AF%2B1\" --> \"F-0.55%2AF=1\" --> \"F%2A%281-0.55%29=1\" --> \"F=1%2F%28%281-0.55%29%29\"
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