document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1193384>Question 1193384</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi<BR>\n" );
document.write( "there were 2222 participants in halls A B and C. During the first interval,3/5 in A went to B .During the second interval, 2/3 of B went over to C. During the last interval,half of C left. In the end there were twice as many participants in C as in B and twice as many participants in B as in A.<BR>\n" );
document.write( "How many were in B at first.<BR>\n" );
document.write( "Thanks </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #825390 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=825390\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "Let the beginning numbers in the halls be A, B, and C.<br><BR>\n" );
document.write( "In the first interval, 3/5 of A move to B (2/5 stay in A)<br><BR>\n" );
document.write( "# in A: (2/5)A<BR>\n" );
document.write( "# in B: B+(3/5)A<BR>\n" );
document.write( "# in C: still C<br><BR>\n" );
document.write( "In the second interval, 2/3 of those in B moved to C (1/3 remained in B)<br><BR>\n" );
document.write( "# in A: (2/5)A<BR>\n" );
document.write( "# in B: (1/3)(B+(3/5)A) = (1/3)B+(1/5)A<BR>\n" );
document.write( "# in C: C+(2/3)(B+(3/5)A) = C+(2/3)B+(2/5)A<br><BR>\n" );
document.write( "In the third interval, half of those in C left (half remained)<br><BR>\n" );
document.write( "# in A: (2/5)A<BR>\n" );
document.write( "# in B: (1/3)B+(1/5)A<BR>\n" );
document.write( "# in C: (1/2)C+(1/3)B+(1/5)A<br><BR>\n" );
document.write( "In the end, the number in B was twice the number in A:<br><BR>\n" );
document.write( "(1/3)B+(1/5)A=2((2/5)A)<BR>\n" );
document.write( "(1/3)B=(3/5)A<BR>\n" );
document.write( "B=(9/5)A<br><BR>\n" );
document.write( "And in the end, the number in C was twice the number in B:<br><BR>\n" );
document.write( "(1/2)C+(1/3)B+(1/5)A=2((1/3)B+(1/5)A)<BR>\n" );
document.write( "(1/2)C=(1/3)B+(1/5)A=(1/3)((9/5)A)+(1/5)A=(3/5)A+(1/5)A=(4/5)A<BR>\n" );
document.write( "C=(8/5)A<br><BR>\n" );
document.write( "The total number of students was 2200:<br><BR>\n" );
document.write( "A+B+C=2200<BR>\n" );
document.write( "A+(9/5)A+(8/5)A=2200<BR>\n" );
document.write( "(22/5)A=2200<BR>\n" );
document.write( "A=500<br><BR>\n" );
document.write( "B=(9/5)A=900<BR>\n" );
document.write( "C=(8/5)A=800<br><BR>\n" );
document.write( "ANSWER: The number in B at the start was 900<br><BR>\n" );
document.write( "CHECK:<BR>\n" );
document.write( "start (A,B,C) = (500,900,800)<BR>\n" );
document.write( "after first interval: (200,1200,800)<BR>\n" );
document.write( "after second interval: (200,400,1600)<BR>\n" );
document.write( "after third interval: (100,400,800)<br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );