document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1150818>Question 1150818</A>: <I><SPAN STYLE=\"word-break: break-all;\"> By selling a dress for $5500, a woman lost 30%. For how much should she have sold it to gain 30%  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #772312 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=772312\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> she sold the dress for 5500 and lost 30%.\r<BR>\n" );
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document.write( "let c equal the cost of the dress.<BR>\n" );
document.write( "let s equal the price she sold it at.<BR>\n" );
document.write( "let p equal the profit she sold it at.<BR>\n" );
document.write( "a negative profit is the same as a loss.\r<BR>\n" );
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document.write( "equation to use is:\r<BR>\n" );
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document.write( "p = (s - c) / c<BR>\n" );
document.write( "when p = -30%, then p = -.30<BR>\n" );
document.write( "you use the rate, not the percent.<BR>\n" );
document.write( "this becomes:<BR>\n" );
document.write( "-.30 = (5500 - c) / c<BR>\n" );
document.write( "multiply both sides of this equation by c to get:<BR>\n" );
document.write( "-.30 * c = 5500 - c<BR>\n" );
document.write( "add c to both sides of this equation to get:<BR>\n" );
document.write( "c - .30 * c = 5500<BR>\n" );
document.write( "combine like terms to get:<BR>\n" );
document.write( ".70 * c = 5500<BR>\n" );
document.write( "solve for c to get:<BR>\n" );
document.write( "c = 5500 / .7 = 7857.142857\r<BR>\n" );
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document.write( "to confirm, take 30% off 7857.142857 and you get 5500.<BR>\n" );
document.write( "5500 is what it sold at when 30% was lost.\r<BR>\n" );
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document.write( "to gain 30%, use the same equation.\r<BR>\n" );
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document.write( "p = (s - c) / c\r<BR>\n" );
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document.write( "when p = 30% and when c = 7857.142857, then the equation becomes:\r<BR>\n" );
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document.write( ".3 = (s - 7857.142857) / 7857.142857<BR>\n" );
document.write( "once again, you use the rate, not the percent.<BR>\n" );
document.write( "multiply both sides by 7857.142857 to get:<BR>\n" );
document.write( ".3 * 7857.142857 = s - 7857.142857<BR>\n" );
document.write( "add 7857.142857 to both sides of the equation to get:<BR>\n" );
document.write( ".3 * 7857.142857 + 7857.142857 = s<BR>\n" );
document.write( "solve for s to get:<BR>\n" );
document.write( "s = 10214.28571\r<BR>\n" );
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document.write( "to confirm, add 30% to 7857.142857 and you get 10214.28571<BR>\n" );
document.write( "this is what it sells at when 30% is gained.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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