document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=209326>Question 209326</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me with the following word problem, I can not do percentages at all and I can not figure out the answer.  Thank you so much! A chemist wants to mix a 5% alcohol solution with a 25% alcohol solution to obtain 8 liters of a 20% alcohol solution. How much (in liters) of the 25% solution should she use? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #158244 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=158244\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> What might help you is to always<BR>\n" );
document.write( "remember that percent means<BR>\n" );
document.write( "\"per one-hundred\", so whenever<BR>\n" );
document.write( "you see %, you must divide by<BR>\n" );
document.write( "100.<BR>\n" );
document.write( "------------------------------<BR>\n" );
document.write( "A good question to ask with this<BR>\n" );
document.write( "problem is: \"How much water and<BR>\n" );
document.write( "how much alcohol end up in the<BR>\n" );
document.write( "final solution?<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 the 5% solution added<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 the 25% solution added<BR>\n" );
document.write( "------------------------------<BR>\n" );
document.write( "The equation to solve in words is:<BR>\n" );
document.write( "(alcohol in 5% solution)+(alcohol in 25% soltion)/(alcohol + water in 20% solution) = 20%<BR>\n" );
document.write( "So, I can write:<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28.05a+%2B+.25b%29+%2F+8+=+.2 ALIGN=MIDDLE  ALT=\"%28.05a+%2B+.25b%29+%2F+8+=+.2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+%2B+b+=+8 ALIGN=MIDDLE  ALT=\"a+%2B+b+=+8\"   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=8 ALIGN=MIDDLE  ALT=\"8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=.05a+%2B+.25b++=+8%2A.2 ALIGN=MIDDLE  ALT=\".05a+%2B+.25b++=+8%2A.2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=.05a+%2B+.25b+=+1.6 ALIGN=MIDDLE  ALT=\".05a+%2B+.25b+=+1.6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Multiply both sides of (2) by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=.05 ALIGN=MIDDLE  ALT=\".05\"   DISABLED_style= \"max-width:90%; height:auto;\" > and subtract from (1)<BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=.05a+%2B+.05b+=+.05%2A8 ALIGN=MIDDLE  ALT=\".05a+%2B+.05b+=+.05%2A8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=.05a+%2B+.05b+=+.4 ALIGN=MIDDLE  ALT=\".05a+%2B+.05b+=+.4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "And, subtracting:<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=.05a+%2B+.25b+=+1.6 ALIGN=MIDDLE  ALT=\".05a+%2B+.25b+=+1.6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-.05a+-+.05b+=+-.4 ALIGN=MIDDLE  ALT=\"-.05a+-+.05b+=+-.4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=.2b+=+1.2 ALIGN=MIDDLE  ALT=\".2b+=+1.2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b+=+6 ALIGN=MIDDLE  ALT=\"b+=+6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "She should use 6 liters of the 25% solution<BR>\n" );
document.write( "check answer:<BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+%2B+b+=+8 ALIGN=MIDDLE  ALT=\"a+%2B+b+=+8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+%2B+6+=+8 ALIGN=MIDDLE  ALT=\"a+%2B+6+=+8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+2 ALIGN=MIDDLE  ALT=\"a+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Go back to (1)<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28.05a+%2B+.25b%29+%2F+8+=+.2 ALIGN=MIDDLE  ALT=\"%28.05a+%2B+.25b%29+%2F+8+=+.2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28.05%2A2+%2B+.25%2A6%29+%2F+8+=+.2 ALIGN=MIDDLE  ALT=\"%28.05%2A2+%2B+.25%2A6%29+%2F+8+=+.2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=.05%2A2+%2B+.25%2A6+=+1.6 ALIGN=MIDDLE  ALT=\".05%2A2+%2B+.25%2A6+=+1.6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=.1+%2B+1.5+=+1.6 ALIGN=MIDDLE  ALT=\".1+%2B+1.5+=+1.6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.6+=+1.6 ALIGN=MIDDLE  ALT=\"1.6+=+1.6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "It always helps if you can sum up the problem in<BR>\n" );
document.write( "an equation with words like I did (It helps me a lot)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );