document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=244989>Question 244989</A>: <I><SPAN STYLE=\"word-break: break-all;\"> One antifreeze solution is 10% alcohol. Another antifreeze solution is 18% alcohol. How many liters of each antifreeze solution should be combined to create 20 liters of antifreeze solution that is 15% alcohol?   </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #179106 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=179106\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> x = liters of first solution.<BR>\n" );
document.write( "y = liters of second solution.\r<BR>\n" );
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document.write( "formula for amount of alcohol required in the new solution is:\r<BR>\n" );
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document.write( ".10 * x + .18 *y = .15 * 20\r<BR>\n" );
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document.write( "formula for total amount of solution required is:\r<BR>\n" );
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document.write( "x + y = 20\r<BR>\n" );
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document.write( "you have 2 equations that have to be solved simultaneously.\r<BR>\n" );
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document.write( "since x + y = 20, this means that y = 20-x\r<BR>\n" );
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document.write( "substitute in the other equation and solve for x.\r<BR>\n" );
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document.write( ".10 * x + .18 *y = .15 * 20 becomes:\r<BR>\n" );
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document.write( ".10 * x + .18 * (20-x) = .15 * 20\r<BR>\n" );
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document.write( "simplify to get:\r<BR>\n" );
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document.write( ".10 * x + .18 * 20 - .18 * x = .15 * 20\r<BR>\n" );
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document.write( "simplify further to get:\r<BR>\n" );
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document.write( ".10 * x + 3.6 - .18 * x = 3\r<BR>\n" );
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document.write( "combine like terms to get:\r<BR>\n" );
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document.write( "-.08 * x + 3.6 = 3\r<BR>\n" );
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document.write( "subtract 3.6 from both sides of the equation to get:\r<BR>\n" );
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document.write( "-.08 * x = -.6\r<BR>\n" );
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document.write( "divide both sides of this equation by -.08 to get\r<BR>\n" );
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document.write( "x = -.6 / -.08 = 7.5\r<BR>\n" );
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document.write( "if x = 7.5, then y = 20-7.5 = 12.5\r<BR>\n" );
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document.write( "we have x = 7.5 litres and y = 12.5 liters\r<BR>\n" );
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document.write( "substitute in original solution equation to get:\r<BR>\n" );
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document.write( ".10 * x + .18 *y = .15 * 20 becomes:\r<BR>\n" );
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document.write( ".10 * 7.5 + .18 * 12.5 = .15 * 20\r<BR>\n" );
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document.write( "simplify to get:\r<BR>\n" );
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document.write( ".75 + 2.25 = 3 which is true so the answer is confirmed to be good.\r<BR>\n" );
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document.write( ".1 * 7.5 liters of solution 1 + .18 * 12.5 liters of solution 2 = .15 * 20 liters.\r<BR>\n" );
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document.write( "you need 7.5 liters of solution 1 and 12.5 liters of solution 2 to make a total of 20 liters.\r<BR>\n" );
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document.write( "The percent alcohol will be .1 * 7.5 + .18 * 12.5 = 3 liters of alcohol.\r<BR>\n" );
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document.write( "3 liters / 20 liters = 15% of the new solution.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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