document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1102005>Question 1102005</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The Music Store paid $14.95 for a DVD. Expenses are 21% of regular selling price and the required profit is 11% of regular selling price. During an inventory sale, the DVD was marked down 20%. <BR>\n" );
document.write( "(a) What was the regular selling price? <BR>\n" );
document.write( "(b) What was the sale price? <BR>\n" );
document.write( "(c) What was the operating profit or loss<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #717085 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=717085\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> cost of the DVD is 14.95<BR>\n" );
document.write( "operating expense is 21% of the regular selling price.<BR>\n" );
document.write( "required profit is 11% of the regular selling price.\r<BR>\n" );
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document.write( "total operating cost is cost of the DVD plus operating expense.<BR>\n" );
document.write( "this is equal to 14.95 + .21 * the regular selling price.\r<BR>\n" );
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document.write( "required profit is equal to regular selling price minus total operating cost\r<BR>\n" );
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document.write( "this translates to:\r<BR>\n" );
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document.write( ".11 * regular selling price = regular selling price minus .21 * regular selling price minus 14.95\r<BR>\n" );
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document.write( "add 14.95 to both sides of this equation and subtract .11 * regular selling price from both sides of this equation to get:\r<BR>\n" );
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document.write( "14.95 = regular selling price minus .21 * regular selling price minus .11 * regular selling price.\r<BR>\n" );
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document.write( "factor out regular selling price to get:\r<BR>\n" );
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document.write( "14.95 = regular selling price * (1 - .21 - .11)<BR>\n" );
document.write( "combine like terms to get:<BR>\n" );
document.write( "14.95 = regular selling price * .68\r<BR>\n" );
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document.write( "solve for regular selling price to get regular selling price = 14.95 / .68.\r<BR>\n" );
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document.write( "this results in regular selling price = 21.98529412\r<BR>\n" );
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document.write( "from the regular selling price, you can now calculate expense and required profit.\r<BR>\n" );
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document.write( "you get:\r<BR>\n" );
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document.write( "expense is equal to .21 * regular selling price = 4.616911765<BR>\n" );
document.write( "required profit is equal to .11 * regular selling price = 2.418382353\r<BR>\n" );
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document.write( "discount is equal to 20% of the regular selling price = 4.397058824.<BR>\n" );
document.write( "discounted selling price is equal to regular selling price minus discount = 17.58823529\r<BR>\n" );
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document.write( "your total cost is equal to the cost of the DVD plus the expense.<BR>\n" );
document.write( "this is equal to 14.95 + 4.616911765 = 19.56691176\r<BR>\n" );
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document.write( "everything seems to check out.\r<BR>\n" );
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document.write( "your total cost is equal to 19.56691176<BR>\n" );
document.write( "your regular selling price is 21.98529412<BR>\n" );
document.write( "your required regular profit is equal to regular selling price minus your total cost = 2.418382353 which is equal to .11 * your regular selling price.\r<BR>\n" );
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document.write( "your discounted sale price is equal to .8 * your regular selling price = 17.58823529\r<BR>\n" );
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document.write( "your profit based on the discounted sale price is equal to 17.58823529 - 19.56691176 = -1.978676471<BR>\n" );
document.write( "a negative profit is equal to a loss, therefore you have a loss of 1.978676471.\r<BR>\n" );
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document.write( "based on all of this, your solution is:\r<BR>\n" );
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document.write( "(a) the regular selling price was 21.98529412 = 21.99\r<BR>\n" );
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document.write( "(b) the sale price was 17.58823529 = 17.59\r<BR>\n" );
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document.write( "(c) the operating loss was 1.978676471 = 1.98\r<BR>\n" );
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