document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=865059>Question 865059</A>: <I><SPAN STYLE=\"word-break: break-all;\"> You need a 15% solution. You are going to mix 10 liters of a 27% solution with an amount of a 10% solution. How much of the 10% solution should you use? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #521480 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=521480\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let's say this solution is a mixture of water and alcohol. \r<BR>\n" );
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document.write( "We have \"10 liters of a 27% solution\", so we have 10*0.27 = 2.7 liters of pure alcohol. \r<BR>\n" );
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document.write( "Let x be the amount of the 10% solution we have. This amount will be in liters. So for this portion, we have 0.10x liters of pure alcohol.\r<BR>\n" );
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document.write( "Combine the two pure amounts: 2.7 + 0.10x<BR>\n" );
document.write( "That's as far as you can go for that bit. We have a total of 2.7 + 0.10x liters of pure alcohol.\r<BR>\n" );
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document.write( "This is out of a total of 10+x liters of solution (10 from the first bit, x from the second)\r<BR>\n" );
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document.write( "This ratio is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282.7+%2B+0.10x%29%2F%2810%2Bx%29 ALIGN=MIDDLE  ALT=\"%282.7+%2B+0.10x%29%2F%2810%2Bx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and this represents the fraction of pure alcohol over the total amount of solution. We want this fraction to be equal to 0.15 (15%) since we want a 15% solution at the end. So set it equal to 0.15 and solve for x\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282.7+%2B+0.10x%29%2F%2810%2Bx%29=0.15 ALIGN=MIDDLE  ALT=\"%282.7+%2B+0.10x%29%2F%2810%2Bx%29=0.15\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2.7+%2B+0.10x=0.15%2810%2Bx%29 ALIGN=MIDDLE  ALT=\"2.7+%2B+0.10x=0.15%2810%2Bx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2.7+%2B+0.10x=0.15%2810%29%2B0.15%28x%29 ALIGN=MIDDLE  ALT=\"2.7+%2B+0.10x=0.15%2810%29%2B0.15%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2.7+%2B+0.10x=1.5%2B0.15x ALIGN=MIDDLE  ALT=\"2.7+%2B+0.10x=1.5%2B0.15x\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2.7+%2B+0.10x-0.15x=1.5 ALIGN=MIDDLE  ALT=\"2.7+%2B+0.10x-0.15x=1.5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.10x-0.15x=1.5-2.7 ALIGN=MIDDLE  ALT=\"0.10x-0.15x=1.5-2.7\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=24 ALIGN=MIDDLE  ALT=\"x=24\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Remember that we made x equal to the amount of 10% solution we'll mix in. So because the initial problem is asking for that, we can stop here.\r<BR>\n" );
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document.write( "So we must mix in <font size=4 color=\"red\">24 liters</font> of the 10% alcohol solution with 10 liters of the 27% alcohol solution to get a final solution of 15% alcohol.\r<BR>\n" );
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document.write( "Final Answer:  <font size=4 color=\"red\">24 liters</font><BR>\n" );
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