document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=68609>Question 68609</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am in a problem seminar class and have been asked to answer and prove the following:<BR>\n" );
document.write( "Two containers, A and B , contain different liquids called a and b correspondingly of equal volume. Suppose that one teaspoon of liquid a is poured into container B and then thoroughly mixed. Next suppose that one teaspoon of the uniform mixture in B is poured into container A. Which of the two containers (if any) is more contaminated?<BR>\n" );
document.write( "I have tried many different things and I always end up showing that the volumes will then be equal not what the contamination of each is. \r<BR>\n" );
document.write( "\n" );
document.write( "Can some one please HELP!!!!!!! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #48830 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=48830\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Suppose there are 100 teaspoons of a liquid and 100 teaspoons<BR>\n" );
document.write( "of b liquid to start with<BR>\n" );
document.write( "Going step by step, initially you have<BR>\n" );
document.write( "100a<BR>\n" );
document.write( "100b<BR>\n" );
document.write( "-----then move a teaspoon of a to b<BR>\n" );
document.write( "100a - 1*a<BR>\n" );
document.write( "100b + 1*a<BR>\n" );
document.write( "-----then move a teaspoon of b's mixture to a, dividing by 101 to<BR>\n" );
document.write( "get 1 teaspoon<BR>\n" );
document.write( "------------<BR>\n" );
document.write( "100a - 1*a + (100b + 1*a) / (100 + 1)<BR>\n" );
document.write( "100b + 1*a - (100b + 1*a) / (100 + 1)<BR>\n" );
document.write( "---------now simplify, note that 100b + a is a common factor in the 2nd one<BR>\n" );
document.write( "99a + (100/101)b + (1/101)a<BR>\n" );
document.write( "(100b + a)(1 - (1/101))<BR>\n" );
document.write( "-----------------<BR>\n" );
document.write( "(99 + (1/101))a + (100/101)b<BR>\n" );
document.write( "(100*(100/101))b + (100/101)a<BR>\n" );
document.write( "-----------------<BR>\n" );
document.write( "99.0099a + .990099b<BR>\n" );
document.write( "99.0099b + .990099a<BR>\n" );
document.write( "-----------------<BR>\n" );
document.write( "They seem to be equally contaminated with the other </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );