document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=708706>Question 708706</A>: <I><SPAN STYLE=\"word-break: break-all;\"> a scientist wants to  make a solution that is 30% acid using one solution that is 50 % acid and another solution that is 20% acid.How many liters of each solution does the scientist need to  make 75 liters of the mixture? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #436219 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39617)</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=436219\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=v ALIGN=MIDDLE  ALT=\"v\"   DISABLED_style= \"max-width:90%; height:auto;\" >= known resulting volume, 75 liters<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%5B1%5D ALIGN=MIDDLE  ALT=\"p%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > = low concentration material, 20%<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%5B2%5D ALIGN=MIDDLE  ALT=\"p%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > = high concentration material, 50%<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%5Bt%5D ALIGN=MIDDLE  ALT=\"p%5Bt%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > = the target concentration of mixture, 30%<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > = how much low concentration material to use<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" > = how much high concentration material to use\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "INITIAL SYSTEM<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28xp%5B1%5D%2Byp%5B2%5D%29%2Fv=p%5Bt%5D ALIGN=MIDDLE  ALT=\"%28xp%5B1%5D%2Byp%5B2%5D%29%2Fv=p%5Bt%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2By=v ALIGN=MIDDLE  ALT=\"x%2By=v\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Work with and possibly do other simplifications to the percent-concentration equation, <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28xp%5B1%5D%2Byp%5B2%5D%29=vp%5Bt%5D ALIGN=MIDDLE  ALT=\"%28xp%5B1%5D%2Byp%5B2%5D%29=vp%5Bt%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Use the volume sum equation to solve for either variable and substitute into the percentage equation and find the single variable there.  As general example, solve for y:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "x+y=v, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=v-x ALIGN=MIDDLE  ALT=\"y=v-x\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  Substitute.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28xp%5B1%5D%2B%28v-x%29p%5B2%5D%29=vp%5Bt%5D ALIGN=MIDDLE  ALT=\"%28xp%5B1%5D%2B%28v-x%29p%5B2%5D%29=vp%5Bt%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and solve for x<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=xp%5B1%5D%2Bvp%5B2%5D-xp%5B2%5D=vp%5Bt%5D ALIGN=MIDDLE  ALT=\"xp%5B1%5D%2Bvp%5B2%5D-xp%5B2%5D=vp%5Bt%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=xp%5B1%5D-xp%5B2%5D=-vp%5B2%5D%2Bvp%5Bt%5D ALIGN=MIDDLE  ALT=\"xp%5B1%5D-xp%5B2%5D=-vp%5B2%5D%2Bvp%5Bt%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%28p%5B1%5D-p%5B2%5D%29=-vp%5B2%5D%2Bvp%5Bt%5D ALIGN=MIDDLE  ALT=\"x%28p%5B1%5D-p%5B2%5D%29=-vp%5B2%5D%2Bvp%5Bt%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%28p%5B2%5D-p%5B1%5D%29=vp%5B2%5D-vp%5Bt%5D ALIGN=MIDDLE  ALT=\"x%28p%5B2%5D-p%5B1%5D%29=vp%5B2%5D-vp%5Bt%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Equivalent to multiplying both sides by -1<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=v%28v%5B2%5D-p%5Bt%5D%29%2F%28p%5B2%5D-p%5B1%5D%29 ALIGN=MIDDLE  ALT=\"x=v%28v%5B2%5D-p%5Bt%5D%29%2F%28p%5B2%5D-p%5B1%5D%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "And that would be the symbolic form for x, the lower concentration material. Just substitute the given values.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );