document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=891549>Question 891549</A>: <I><SPAN STYLE=\"word-break: break-all;\"> there are 80 students in a class. Some take Mathematics, some Physics and others biology. All students take atleast one course and some two or three. 40 students take Mathematics and 31 biology. 7 students take mathematics and Physics only, 8 take Biology and physics only and 3 take mathematics and Biology only. 5 take all three courses how many take physics? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #539829 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=539829\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I get a Venn diagram ( hard to show it ) that gives me<BR>\n" );
document.write( "the following:<BR>\n" );
document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+P+ ALIGN=MIDDLE  ALT=\"+P+\"   DISABLED_style= \"max-width:90%; height:auto;\" > is ALL those who take physics<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+P+-+%28+7+%2B+5+%2B+8+%29+=+P+-20+ ALIGN=MIDDLE  ALT=\"+P+-+%28+7+%2B+5+%2B+8+%29+=+P+-20+\"   DISABLED_style= \"max-width:90%; height:auto;\" >  are those who ONLY take physics<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+M+=+40+ ALIGN=MIDDLE  ALT=\"+M+=+40+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = ALL those who take math<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+31+-+%28+3+%2B+5+%29+=+23+ ALIGN=MIDDLE  ALT=\"+31+-+%28+3+%2B+5+%29+=+23+\"   DISABLED_style= \"max-width:90%; height:auto;\" > are those who take biology but not math<BR>\n" );
document.write( "---------------------<BR>\n" );
document.write( "Now I can say:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+P+-+20+%2B+40+%2B+23+=+80+ ALIGN=MIDDLE  ALT=\"+P+-+20+%2B+40+%2B+23+=+80+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+P+%2B+43+=+80+ ALIGN=MIDDLE  ALT=\"+P+%2B+43+=+80+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+P+=+37+ ALIGN=MIDDLE  ALT=\"+P+=+37+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "37 students take physics<BR>\n" );
document.write( "check:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+37+-+%28+7+%2B+5+%2B+8+%29+=+17+ ALIGN=MIDDLE  ALT=\"+37+-+%28+7+%2B+5+%2B+8+%29+=+17+\"   DISABLED_style= \"max-width:90%; height:auto;\" > take ONLY physics<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+40+-+%28+3+%2B+5+%2B+7+%29+=+25+ ALIGN=MIDDLE  ALT=\"+40+-+%28+3+%2B+5+%2B+7+%29+=+25+\"   DISABLED_style= \"max-width:90%; height:auto;\" > take ONLY math<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+31+-+%28+3+%2B+5+%2B+8+%29+=+15+ ALIGN=MIDDLE  ALT=\"+31+-+%28+3+%2B+5+%2B+8+%29+=+15+\"   DISABLED_style= \"max-width:90%; height:auto;\" > take ONLY biology<BR>\n" );
document.write( "--------------------------<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+17+%2B+25+%2B+15+%2B+3+%2B+5+%2B+7+%2B+8+=+80+ ALIGN=MIDDLE  ALT=\"+17+%2B+25+%2B+15+%2B+3+%2B+5+%2B+7+%2B+8+=+80+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+42+%2B+18+%2B+20+=+80+ ALIGN=MIDDLE  ALT=\"+42+%2B+18+%2B+20+=+80+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+80+=+80+ ALIGN=MIDDLE  ALT=\"+80+=+80+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "OK<BR>\n" );
document.write( "Hope you can draw the 3 interlocking rings <BR>\n" );
document.write( "and put the numbers where they belong.<BR>\n" );
document.write( "Good luck<BR>\n" );
document.write( "  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );