document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=990480>Question 990480</A>: <I><SPAN STYLE=\"word-break: break-all;\"> a chemist has two soltions of H. One has a 40% concentration and the other has a 25% concentration. How many liters of each solution must be mixed to obtain 135 liters of a 37% solution? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #610488 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52832)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=610488\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "1. Never heard or saw this term &nbsp;\"soltion of H\".\r<BR>\n" );
document.write( "\n" );
document.write( "I understand that you wanted to write &nbsp;\"solutions\" &nbsp;instead of \"soltions\", &nbsp;but again I never heard or saw the term &nbsp;\"solution of H\". &nbsp;I suspect that such thing do not exist. \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "2. OK, &nbsp;actually, &nbsp;it doesn't matter. &nbsp;We will talk about, &nbsp;let say, &nbsp;an abstract solution. \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Then you have the system of two linear equations in two unknowns &nbsp;<B>x</B> &nbsp;and &nbsp;<B>y</B> &nbsp;that are two unknowns volumes of the solutions in units of volume, &nbsp;let say, &nbsp;in liters\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28x+%2B+y+=+135%2C%0D%0A0.4%2Ax+%2B+0.25%2Ay+=+0.37%2A%28x%2By%29%29 ALIGN=MIDDLE  ALT=\"system%28x+%2B+y+=+135%2C%0D%0A0.4%2Ax+%2B+0.25%2Ay+=+0.37%2A%28x%2By%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >,\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "or \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28x+%2B+y+=+135%2C%0D%0A0.4%2Ax+%2B+0.25%2Ay+=+0.37%2A135%29 ALIGN=MIDDLE  ALT=\"system%28x+%2B+y+=+135%2C%0D%0A0.4%2Ax+%2B+0.25%2Ay+=+0.37%2A135%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >,\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "or\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28x+%2B+y+=+135%2C%0D%0A0.4%2Ax+%2B+0.25%2Ay+=+49.95%29 ALIGN=MIDDLE  ALT=\"system%28x+%2B+y+=+135%2C%0D%0A0.4%2Ax+%2B+0.25%2Ay+=+49.95%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The first equation is the conservation law for the volume of liquid.<BR>\n" );
document.write( "The second equation is the conservation law for the volume of solute.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "This is how to construct &nbsp;(to make, &nbsp;to write) &nbsp;the system of equations. &nbsp;It is the most important part in solving problems on mixtures and on solutions. \r<BR>\n" );
document.write( "\n" );
document.write( "The rest is just techniques &nbsp;(which is important, though).\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Try to solve the system yourself. &nbsp;You may use the substitution method\r<BR>\n" );
document.write( "\n" );
document.write( "(express &nbsp; y = 135 -x &nbsp;from the first equation,<BR>\n" );
document.write( "substitute it into the second equation,<BR>\n" );
document.write( "you will get the single equation for the unknown &nbsp;<B>x</B>,<BR>\n" );
document.write( "then solve this equation<BR>\n" );
document.write( "and back substitute the found value of &nbsp;<B>x</B>&nbsp; into the first equation of the original system to get the solution for &nbsp;<B>y</B>).\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Good luck!\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );