document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1062839>Question 1062839</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If discount is 10% then loss is 16% find loss% if discount becomes 25%? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #677847 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=677847\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "i think the answer will be 30% based on some other reasoning that i will detail later.\r<BR>\n" );
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document.write( "to see if this is correct, i'll use assumed numbers to see what comes out.\r<BR>\n" );
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document.write( "i'll assume the cost is 100.\r<BR>\n" );
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document.write( "if it was sold at a 16% loss, then the sale price had to be 84.\r<BR>\n" );
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document.write( "if it was sold at a 10% discount, then the retail price had to be 93 and 1/3.\r<BR>\n" );
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document.write( "this is equivalent to a retail price of 280/3.\r<BR>\n" );
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document.write( "now, if sale price is 75% of the retail price, then sale price is equal to .75 * 280/3 = 70\r<BR>\n" );
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document.write( "cost is still the same at 100.\r<BR>\n" );
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document.write( "loss is now 100 - 70 = 30\r<BR>\n" );
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document.write( "30/100 is equal to 30% of the cost.\r<BR>\n" );
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document.write( "this confirms the solution is correct.\r<BR>\n" );
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document.write( "this should be able to be done with variables instead of number.\r<BR>\n" );
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document.write( "let C = cost.<BR>\n" );
document.write( "let R = retail price<BR>\n" );
document.write( "let S = sale price\r<BR>\n" );
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document.write( "with a 10% discount, you get S = R - .10 * R = .9 * R.\r<BR>\n" );
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document.write( "with a 16% loss, you get S = C - .16 * C = .84 * C\r<BR>\n" );
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document.write( "we have S = .9 * R and we have S = .84 * C\r<BR>\n" );
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document.write( "this means that .9 * R = .84 * C\r<BR>\n" );
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document.write( "we can solve for C to get  C = .9 * r / .84\r<BR>\n" );
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document.write( "if we change the discount to 25%, then we get S = .75 * R\r<BR>\n" );
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document.write( "because of this change, S = .84 * C will becomes some other value times C which we don't know yet.\r<BR>\n" );
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document.write( "we'll make S = x * C\r<BR>\n" );
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document.write( "we will get:\r<BR>\n" );
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document.write( "S = .75 * R<BR>\n" );
document.write( "S = x * C\r<BR>\n" );
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document.write( "since they're both equal to S, we get .75 * R = x * C\r<BR>\n" );
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document.write( "we solve for C to get C = .75 * R / x\r<BR>\n" );
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document.write( "previously we had C = .9 * R / .84\r<BR>\n" );
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document.write( "since they're both equal to C, we get .75 * R / x = .9 * R / .84\r<BR>\n" );
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document.write( "we cross multiply to get .75 * R * .84 = .9 * R * x\r<BR>\n" );
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document.write( "we solve for x to get x = (.75 * R * .84) / (.9 * R) = .7\r<BR>\n" );
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document.write( "this means that S = .7 * C\r<BR>\n" );
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document.write( "since L = (C - S) / C, we get L = (C - .7 * C) / C which gets L = .3 * C / C which gets L = .3 = 30%.\r<BR>\n" );
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document.write( "this says that you sold at a 30% loss.\r<BR>\n" );
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document.write( "30% should be your answer.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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