document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=581857>Question 581857</A>: <I><SPAN STYLE=\"word-break: break-all;\"> please help, this stuff makes no sense to me.<BR>\n" );
document.write( "How many liters each of a 12% acid solution and a 20% acid solution should be mixed in order to obtain 4 liters of a 15 % acid solution? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #371833 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=371833\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> In words:<BR>\n" );
document.write( "( liters of acid you end up with ) / ( liters of total solution you end up with ) = 15%<BR>\n" );
document.write( "A point of confusion might be that the acid is mixed with something to make<BR>\n" );
document.write( "a solution, but they don't tell you what that something is. It really doesn't matter.<BR>\n" );
document.write( "Just think of it as water. So 12% acid solution is 12% acid and 88% water.<BR>\n" );
document.write( "---------------<BR>\n" );
document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a+ ALIGN=MIDDLE  ALT=\"+a+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = liters of 12% solution needed<BR>\n" );
document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b+ ALIGN=MIDDLE  ALT=\"+b+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = liters of 20% solution needed<BR>\n" );
document.write( "given:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+.12a+ ALIGN=MIDDLE  ALT=\"+.12a+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = liters of acid in 12% solution<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+.2b+ ALIGN=MIDDLE  ALT=\"+.2b+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = liters of acid in 20% solution<BR>\n" );
document.write( "--------------------------------<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a+%2B+b+=+4+ ALIGN=MIDDLE  ALT=\"+a+%2B+b+=+4+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28+.12a+%2B+.2b+%29+%2F+4+=+.15+ ALIGN=MIDDLE  ALT=\"+%28+.12a+%2B+.2b+%29+%2F+4+=+.15+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "-------------------------<BR>\n" );
document.write( "This is 2 equations with 2 unknowns, so it's solvable<BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+.12a+%2B+.2b+=+.15%2A4+ ALIGN=MIDDLE  ALT=\"+.12a+%2B+.2b+=+.15%2A4+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+.12a+%2B+.2b+=+.6+ ALIGN=MIDDLE  ALT=\"+.12a+%2B+.2b+=+.6+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+12a+%2B+20b+=+60+ ALIGN=MIDDLE  ALT=\"+12a+%2B+20b+=+60+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3a+%2B+5b+=+15+ ALIGN=MIDDLE  ALT=\"+3a+%2B+5b+=+15+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Multiply both sides of (1) by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" > and<BR>\n" );
document.write( "subtract (1) from (2)<BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3a+%2B+5b+=+15+ ALIGN=MIDDLE  ALT=\"+3a+%2B+5b+=+15+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-3a+-+3b+=+-12+ ALIGN=MIDDLE  ALT=\"+-3a+-+3b+=+-12+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2b+=+3+ ALIGN=MIDDLE  ALT=\"+2b+=+3+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b+=+1.5+ ALIGN=MIDDLE  ALT=\"+b+=+1.5+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and, since<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a+%2B+b+=+4+ ALIGN=MIDDLE  ALT=\"+a+%2B+b+=+4+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a+%2B+1.5+=+4+ ALIGN=MIDDLE  ALT=\"+a+%2B+1.5+=+4+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a+=+2.5+ ALIGN=MIDDLE  ALT=\"+a+=+2.5+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-------------<BR>\n" );
document.write( "2.5 liters of 12% solution are needed<BR>\n" );
document.write( "1.5 liters of 20% solution are needed<BR>\n" );
document.write( "check answer:<BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28+.12%2A2.5+%2B+.2%2A1.5+%29+%2F+4+=+.15+ ALIGN=MIDDLE  ALT=\"+%28+.12%2A2.5+%2B+.2%2A1.5+%29+%2F+4+=+.15+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28+.3+%2B+.3+%29+%2F+4+=+.15+ ALIGN=MIDDLE  ALT=\"+%28+.3+%2B+.3+%29+%2F+4+=+.15+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+.6%2F4+=+.15+ ALIGN=MIDDLE  ALT=\"+.6%2F4+=+.15+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+.6+=+.15%2A4+ ALIGN=MIDDLE  ALT=\"+.6+=+.15%2A4+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+.6+=+.6+ ALIGN=MIDDLE  ALT=\"+.6+=+.6+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "OK </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );