document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=589674>Question 589674</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Bottle A contains some water. Bottle B contains an equal amount of pure alcohol. First 1/3 of the water in A is poured into B. Stir Well. Then 1/3 of the mixture in B is poured into A. Stir Well. Again 1/3 of the mixture in A is poured into B. Stir Well. Finally the correct amount of mixture is poured from B into A so the both bottles contains the same amount of mixture. In what ratio is the pure alcohol divided between A and B now? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #374938 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=374938\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Call the amount of water in A at the start <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1+ ALIGN=MIDDLE  ALT=\"+1+\"   DISABLED_style= \"max-width:90%; height:auto;\" > unit<BR>\n" );
document.write( "Call the amount of alcohol in B at the start <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1+ ALIGN=MIDDLE  ALT=\"+1+\"   DISABLED_style= \"max-width:90%; height:auto;\" > unit<BR>\n" );
document.write( "----------<BR>\n" );
document.write( "After the 1st step, <BR>\n" );
document.write( "A has <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2%2F3+ ALIGN=MIDDLE  ALT=\"+2%2F3+\"   DISABLED_style= \"max-width:90%; height:auto;\" > units of water in it<BR>\n" );
document.write( "B has <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1%2F3+ ALIGN=MIDDLE  ALT=\"+1%2F3+\"   DISABLED_style= \"max-width:90%; height:auto;\" > units of water plus <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1+ ALIGN=MIDDLE  ALT=\"+1+\"   DISABLED_style= \"max-width:90%; height:auto;\" > unit of alcohol<BR>\n" );
document.write( "----------<BR>\n" );
document.write( "After the 2nd step,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%281%2F3%29+%2A+%281%2F3%29+=+1%2F9+ ALIGN=MIDDLE  ALT=\"+%281%2F3%29+%2A+%281%2F3%29+=+1%2F9+\"   DISABLED_style= \"max-width:90%; height:auto;\" > units of water from B is added to A, and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%281%2F3%29%2A1+=+1%2F3+ ALIGN=MIDDLE  ALT=\"+%281%2F3%29%2A1+=+1%2F3+\"   DISABLED_style= \"max-width:90%; height:auto;\" > units of alcohol from B is added to A<BR>\n" );
document.write( "Now A contains <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2%2F3+%2B+1%2F9+=+7%2F9+ ALIGN=MIDDLE  ALT=\"+2%2F3+%2B+1%2F9+=+7%2F9+\"   DISABLED_style= \"max-width:90%; height:auto;\" > units of water<BR>\n" );
document.write( "and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1%2F3+ ALIGN=MIDDLE  ALT=\"+1%2F3+\"   DISABLED_style= \"max-width:90%; height:auto;\" > units of alcohol<BR>\n" );
document.write( "Now B contains <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1%2F3+-+%281%2F3%29%2A%281%2F3%29+=+2%2F9+ ALIGN=MIDDLE  ALT=\"+1%2F3+-+%281%2F3%29%2A%281%2F3%29+=+2%2F9+\"   DISABLED_style= \"max-width:90%; height:auto;\" > units of water<BR>\n" );
document.write( "and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1+-+1%2F3+=+2%2F3+ ALIGN=MIDDLE  ALT=\"+1+-+1%2F3+=+2%2F3+\"   DISABLED_style= \"max-width:90%; height:auto;\" > units of alcohol<BR>\n" );
document.write( "---------<BR>\n" );
document.write( "Note that after each step the total units of both water and alcohol must = 1<BR>\n" );
document.write( "---------<BR>\n" );
document.write( "After the next step:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%281%2F3%29%2A%287%2F9%29+=+7%2F27+ ALIGN=MIDDLE  ALT=\"+%281%2F3%29%2A%287%2F9%29+=+7%2F27+\"   DISABLED_style= \"max-width:90%; height:auto;\" > units of water from A is added to B<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%281%2F3%29%2A%281%2F3%29+=+1%2F9+ ALIGN=MIDDLE  ALT=\"+%281%2F3%29%2A%281%2F3%29+=+1%2F9+\"   DISABLED_style= \"max-width:90%; height:auto;\" > units of alcohol from A is added to B<BR>\n" );
document.write( "Now A contains <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+7%2F9+-+7%2F27+=+14%2F27+ ALIGN=MIDDLE  ALT=\"+7%2F9+-+7%2F27+=+14%2F27+\"   DISABLED_style= \"max-width:90%; height:auto;\" > units of water<BR>\n" );
document.write( "and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1%2F3+-+1%2F9+=+2%2F9+ ALIGN=MIDDLE  ALT=\"+1%2F3+-+1%2F9+=+2%2F9+\"   DISABLED_style= \"max-width:90%; height:auto;\" > units of alcohol<BR>\n" );
document.write( "Now B contains <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2%2F9+%2B+7%2F27+=+13%2F27+ ALIGN=MIDDLE  ALT=\"+2%2F9+%2B+7%2F27+=+13%2F27+\"   DISABLED_style= \"max-width:90%; height:auto;\" > units of water<BR>\n" );
document.write( "and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2%2F3+%2B+1%2F9+=+7%2F9+ ALIGN=MIDDLE  ALT=\"+2%2F3+%2B+1%2F9+=+7%2F9+\"   DISABLED_style= \"max-width:90%; height:auto;\" > units of alcohol<BR>\n" );
document.write( "---------<BR>\n" );
document.write( "check: water = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+14%2F27+%2B+13%2F27+=+1+ ALIGN=MIDDLE  ALT=\"+14%2F27+%2B+13%2F27+=+1+\"   DISABLED_style= \"max-width:90%; height:auto;\" > and<BR>\n" );
document.write( "alcohol = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2%2F9+%2B+7%2F9+=+1+ ALIGN=MIDDLE  ALT=\"+2%2F9+%2B+7%2F9+=+1+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "OK<BR>\n" );
document.write( "---------<BR>\n" );
document.write( "After the next step:<BR>\n" );
document.write( "Some fraction of the mixture in B is poured into A<BR>\n" );
document.write( "Let that fraction = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1%2Fx+ ALIGN=MIDDLE  ALT=\"+1%2Fx+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now B contains <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+13%2F27+-+13%2F%2827x%29+=+%2813%2F27%29%2A%28+1+-+1%2Fx+%29+ ALIGN=MIDDLE  ALT=\"+13%2F27+-+13%2F%2827x%29+=+%2813%2F27%29%2A%28+1+-+1%2Fx+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > units of water<BR>\n" );
document.write( "and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+7%2F9+-+7%2F%289x%29+=+%287%2F9%29%2A%28+1++-+1%2Fx%29+ ALIGN=MIDDLE  ALT=\"+7%2F9+-+7%2F%289x%29+=+%287%2F9%29%2A%28+1++-+1%2Fx%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > units of alcohol<BR>\n" );
document.write( "Now A contains <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+14%2F27+%2B+%281%2Fx%29%2A%2813%2F27%29++ ALIGN=MIDDLE  ALT=\"+14%2F27+%2B+%281%2Fx%29%2A%2813%2F27%29++\"   DISABLED_style= \"max-width:90%; height:auto;\" > units of water<BR>\n" );
document.write( "and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2%2F9+%2B+%281%2Fx%29%2A%287%2F9%29+ ALIGN=MIDDLE  ALT=\"+2%2F9+%2B+%281%2Fx%29%2A%287%2F9%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > units of alcohol<BR>\n" );
document.write( "----------<BR>\n" );
document.write( "The mixture in A now = the mixture in B, so<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%2813%2F27%29%2A%28+1+-+1%2Fx+%29+%2B+%287%2F9%29%2A%28+1+-+1%2Fx+%29+=+14%2F27+%2B+%281%2Fx%29%2A%2813%2F27%29+%2B+2%2F9+%2B+%281%2Fx%29%2A%287%2F9%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+13%2F27+-+13%2F%2827x%29+%2B+7%2F9+-+7%2F%289x%29+=+14%2F27+%2B+13%2F%2827x%29+%2B+2%2F9+%2B+7%2F%289x%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+13%2F%2827x%29+-+21%2F%2827x%29+-+13%2F%2827x%29+-+21%2F%2827x%29+=+14%2F27+%2B+6%2F27+-+13%2F27+-+21%2F27+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-42%2F%2827x%29+=+-14%2F27+ ALIGN=MIDDLE  ALT=\"+-42%2F%2827x%29+=+-14%2F27+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+21%2F%2827x%29+=+7%2F27+ ALIGN=MIDDLE  ALT=\"+21%2F%2827x%29+=+7%2F27+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+21%2Fx+=+7+ ALIGN=MIDDLE  ALT=\"+21%2Fx+=+7+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+3+ ALIGN=MIDDLE  ALT=\"+x+=+3+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "----------<BR>\n" );
document.write( "The units of alcohol in A is now<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2%2F9+%2B+%281%2F3%29%2A%287%2F9%29+=+6%2F27+%2B+7%2F27+ ALIGN=MIDDLE  ALT=\"+2%2F9+%2B+%281%2F3%29%2A%287%2F9%29+=+6%2F27+%2B+7%2F27+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+6+%2F27+%2B+7%2F27+=+13%2F27+ ALIGN=MIDDLE  ALT=\"+6+%2F27+%2B+7%2F27+=+13%2F27+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The units of alcohol in B is now<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%287%2F9%29%2A%28+1+-+1%2F3+%29+=+%287%2F9%29%2A%282%2F3%29+ ALIGN=MIDDLE  ALT=\"+%287%2F9%29%2A%28+1+-+1%2F3+%29+=+%287%2F9%29%2A%282%2F3%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%287%2F9%29%2A%282%2F3%29+=+14%2F27+ ALIGN=MIDDLE  ALT=\"+%287%2F9%29%2A%282%2F3%29+=+14%2F27+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The ratio of alcohol is<BR>\n" );
document.write( "A/B = 13/14<BR>\n" );
document.write( "----------<BR>\n" );
document.write( "Unless I goofed somewhere<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );