document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=282751>Question 282751</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Greetings! I need help on this problem which, albeit it looks terribly simple in a first glance, I'm finding difficulty in getting the right solution. the answer to this problem is supposed to be $200. Here goes:<BR>\n" );
document.write( "A dealer bought a phonograph for $160. For how many dollars must he mark it so that after deducting 10% of the marked price, he may sell it at a profit of 12-1/2% of the cost?<BR>\n" );
document.write( "Thanks very much for the help guys! :) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #205275 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=205275\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> C = Cost of Phonograph = $200.<BR>\n" );
document.write( "M = Marked Up Price of Phonograph = (1+x) * C.<BR>\n" );
document.write( "D = Discounted Selling Price of Phonograph = 1.125 * C.<BR>\n" );
document.write( "D = Discounted Selling Price of Phonograph =  .9 * M.\r<BR>\n" );
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document.write( "Note that M - .1 * M = .9 * M.\r<BR>\n" );
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document.write( "You have 2 equations that need to be solved simultaneously.\r<BR>\n" );
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document.write( "They are:\r<BR>\n" );
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document.write( "D = 1.125 * C and D = .9 * M.\r<BR>\n" );
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document.write( "Since M = (1+x) * C, Then the equations become:\r<BR>\n" );
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document.write( "D = 1.125 * C and D = .9 * (1+x) * C.\r<BR>\n" );
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document.write( "Since both expressions equal to D, then both expressions are equal to each other and you get:\r<BR>\n" );
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document.write( "1.125 * C = .9 * (1+x) * C\r<BR>\n" );
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document.write( "Divide C from both sides of this equation to get\r<BR>\n" );
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document.write( "1.125 = .9 * (1+x)\r<BR>\n" );
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document.write( "Divide both sides of this equation by .9 and you get:\r<BR>\n" );
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document.write( "1.25 = 1 + x\r<BR>\n" );
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document.write( "Subtract 1 from both sides of this equation and you get\r<BR>\n" );
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document.write( ".25 = x\r<BR>\n" );
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document.write( "That's your answer.\r<BR>\n" );
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document.write( "The Price needs to be marked up 25% in order to sell it at a discount of 10% and still make a profit of 12.5%\r<BR>\n" );
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document.write( "In numbers, this is what happens:\r<BR>\n" );
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document.write( "The cost is $200.<BR>\n" );
document.write( "the marked price is 1.25 * 200 = $250.<BR>\n" );
document.write( "The discounted price is $250 - .1 * $250 = $250 - $25 = $225.<BR>\n" );
document.write( "The profit is $225 - $200 = $25.<BR>\n" );
document.write( "The profit margin is $25/$200 = .125 = 12.5%.<BR>\n" );
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