document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=756515>Question 756515</A>: <I><SPAN STYLE=\"word-break: break-all;\"> cost of articles is in ratio 3:2, on the first there is 40% loss and on the second there is 30% gain. What is the overall percentage of gain or loss? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #460239 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=460239\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> i calculate a 12% loss.<BR>\n" );
document.write( "an easier way to figure it out is as follows:<BR>\n" );
document.write( "since the cost is in a ratio of 3:2, then use any value for the cost that comes out to be in a 3:2 ratio.<BR>\n" );
document.write( "assume the cost of the first product is 300 dollars and assume the cost of the second product is 200 dollars.<BR>\n" );
document.write( "the sum of the costs for the first product and second product is currently set at 500 (300 + 200).<BR>\n" );
document.write( "the first product takes a 40% loss and the second product takes a 30% gain.<BR>\n" );
document.write( "300 - 300*.4 + 200 + 200*.3 = 300 - 120 + 200 + 60 which equals 440.<BR>\n" );
document.write( "you went from 500 to 440 dollars.<BR>\n" );
document.write( "that's a loss of 60 dollars which is equal to 12% of the original cost.\r<BR>\n" );
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document.write( "the harder way is to do it with variables rather than assuming some numbers.<BR>\n" );
document.write( "you do the same thing only now you need more understanding of algebra.<BR>\n" );
document.write( "let a represent the cost of the first product and let b represent the cost of the second product.\r<BR>\n" );
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document.write( "since the cost of the products are in the ratio of 3:2, then we can solve for a in terms of b or versa.\r<BR>\n" );
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document.write( "the ratio formula is 3/2 = a/b<BR>\n" );
document.write( "that reads as:<BR>\n" );
document.write( "3 is to 2 as a is to b.<BR>\n" );
document.write( "we can cross multiply to get:<BR>\n" );
document.write( "2a = 3b<BR>\n" );
document.write( "divide both sides of this equation by 2 to get:<BR>\n" );
document.write( "a = 3b/2\r<BR>\n" );
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document.write( "the sum of the costs of the products today is:<BR>\n" );
document.write( "a + b which we can then translate to 3b/2 + b because a is equal to 3b/2 which means it can be replaced by 3b/2 in the equation.\r<BR>\n" );
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document.write( "3b/2 + b is the same as 3b/2 + 2b/2 which becomes 5b/2<BR>\n" );
document.write( "5b/2 represents the cost of the 2 products today which is also the same as a + b<BR>\n" );
document.write( "we get a + b = 5b/2 because we replaced a with its equivalent of 3b/2.\r<BR>\n" );
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document.write( "now to the revised cost.<BR>\n" );
document.write( "a is reduced by 40% and b is increased by 30%.<BR>\n" );
document.write( "a - .4a becomes .6a<BR>\n" );
document.write( "b + .3b becomes 1.3b<BR>\n" );
document.write( "the revised costs become:<BR>\n" );
document.write( ".6a + 1.3b\r<BR>\n" );
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document.write( "since a is equal to 3b/2, we can replace a in the equation with 3b/2 to get:<BR>\n" );
document.write( "the revised costs become:<BR>\n" );
document.write( ".6(3b/2) + 1.3b<BR>\n" );
document.write( "simplify this to get:<BR>\n" );
document.write( ".9b + 1.3b which makes the revised costs equal to 2.2b.\r<BR>\n" );
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document.write( "the original costs are 5b/2 which translates to 2.5b<BR>\n" );
document.write( "the revised costs are 2.2b.<BR>\n" );
document.write( "the ratio of the revised cost to the original cost is equal to 2.2b / 2.5b which is equal to .88\r<BR>\n" );
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document.write( "this means the revised costs are equal to 88% of the original cost which means we took a loss of 12% because 88% - 100% is equal to -12%.\r<BR>\n" );
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document.write( "you can solve it by replacing the variables with assumed numbers since any number would do because all they have to be is in the correct ratio.\r<BR>\n" );
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document.write( "you cal also solve it directly by dealing with variables rather than numbers.<BR>\n" );
document.write( "dealing with variables is a little more complex but the same logic is applied to both and both will arrive at the same answer if you did it correctly.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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