document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=759061>Question 759061</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What amount of each mixture, one 95% alcohol and the other 15% alcohol, must be used to make 10 liters of a mixture which is 45% alcohol? What equation or equations will express this problem? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #461815 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39618)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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=461815\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> This extremely common two-part mixture problem can be handled with two equations: One is a rational equation using two unknown variables and another is a simple sum linear equation using the same two unknown variables.\r<BR>\n" );
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document.write( "ASSIGN VARIABLES TO ALL QUANTITIES<BR>\n" );
document.write( "H = concentration, such as percent, of the high concentration material<BR>\n" );
document.write( "L = concentration such as percent, of the low concentration material<BR>\n" );
document.write( "T = the target concentration desired for the mixture<BR>\n" );
document.write( "M =  amount of mixture at the target concentration<BR>\n" );
document.write( "u = amount of low concentration material to use (unknown)<BR>\n" );
document.write( "v = amount of high concentration material to use (unknown)\r<BR>\n" );
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document.write( "ACCOUNT FOR PURE COMPONENT<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u%2AL%2Bv%2AH ALIGN=MIDDLE  ALT=\"u%2AL%2Bv%2AH\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the amount of pure component<BR>\n" );
document.write( "The concentration is then in the quantity of mixture, M,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28uL%2BvH%29%2FM ALIGN=MIDDLE  ALT=\"%28uL%2BvH%29%2FM\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the resulting percent concentration for this example.\r<BR>\n" );
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document.write( "ACCOUNT FOR  MATERIAL AMOUNTS<BR>\n" );
document.write( "Simply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=M=u%2Bv ALIGN=MIDDLE  ALT=\"M=u%2Bv\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "EQUATIONS TO FORM THE SYSTEM<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28%28Lu%2BHv%29%2FM=T%29 ALIGN=MIDDLE  ALT=\"highlight%28%28Lu%2BHv%29%2FM=T%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28u%2Bv=M%29 ALIGN=MIDDLE  ALT=\"highlight%28u%2Bv=M%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Solve the system for u and v.<BR>\n" );
document.write( "Substitute the given known values to find the resulting values for u and v. </SPAN>\n" );
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