document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1198758>Question 1198758</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The members of a College staff club were asked to indicate the brand of beer they drink. 5 members drank stars and Trophy beers, 7 members drank star and club beers, 6 members drank starbeer only, 11 drank Trophy beer only while 5 drank club only. Three members drank all the three brands. assuming that each member drank at least one brand of beer, Find<BR>\n" );
document.write( "i, the number of members that drank star beer<BR>\n" );
document.write( "ii, the number of members that drank Trophy beer<BR>\n" );
document.write( "iii, the number of members that drank club beer<BR>\n" );
document.write( "iv, the total number of members in the club </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #832395 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=832395\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Here's the venn diagram with 8 distinct regions<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/display-illustration.mpl?tutor=math_tutor2020&illustration_name=Screenshot_159bb.png\"><BR>\n" );
document.write( "The region labels are:<BR>\n" );
document.write( "S = people who drank star beer only<BR>\n" );
document.write( "T = people who drank trophy beer only<BR>\n" );
document.write( "C = people who drank club beer only<BR>\n" );
document.write( "ST = people who drank star and trophy, but not club<BR>\n" );
document.write( "TC = people who drank trophy and club, but not star<BR>\n" );
document.write( "SC = people who drank star and club, but not trophy<BR>\n" );
document.write( "STC = people who drank all three brands<BR>\n" );
document.write( "N = people who drank none of the three brands mentioned\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Given Facts:<BR>\n" );
document.write( "<TABLE  border = \"1\" cellpadding = \"5\">\n" );
document.write( "<tr><TD >Number</TD><TD >Fact</TD></tr><tr><TD >1</TD><TD >5 members drank stars and Trophy beers</TD></tr><tr><TD >2</TD><TD >7 members drank star and club beers</TD></tr><tr><TD >3</TD><TD >6 members drank starbeer only</TD></tr><tr><TD >4</TD><TD >11 drank Trophy beer only</TD></tr><tr><TD >5</TD><TD >5 drank club only</TD></tr><tr><TD >6</TD><TD >3 members drank all the three brands</TD></tr><tr><TD >7</TD><TD >Each member drank at least one brand of beer</TD></tr>\n" );
document.write( "</TABLE><BR>\n" );
document.write( "Fact 6 indicates the value \"3\" goes in region STC.<BR>\n" );
document.write( "Facts 1 and 6 will lead to 5-3 = 2 members who drank stars and trophy, but not club beer. Write \"2\" in region ST<BR>\n" );
document.write( "Facts 2 and 6 will lead to 7-3 = 4 members who drank star and club, but not trophy beer. Write \"4\" in region SC\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Fact 3 indicates we'll write \"6\" in region S.<BR>\n" );
document.write( "Fact 4 indicates we'll write \"11\" in region T.<BR>\n" );
document.write( "Fact 5 indicates we'll write \"5\" in region C.<BR>\n" );
document.write( "Fact 7 means we have \"0\" in region N, because each person drank at least one type.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "This is what we have so far<BR>\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/display-illustration.mpl?tutor=math_tutor2020&illustration_name=Screenshot_160.png\"><BR>\n" );
document.write( "Your teacher doesn't give enough info to determine what value goes in region TC.<BR>\n" );
document.write( "I would ask your teacher for clarification about this.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "------------------------------------------------------\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "i, the number of members that drank star beer\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "We add up the values inside the circle labeled \"Star\"<BR>\n" );
document.write( "6+2+4+3 = 15\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Answer: 15 people drank star beer\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "------------------------------------------------------\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "ii, the number of members that drank Trophy beer\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Like I mentioned earlier, we don't know what value goes in region TC. <BR>\n" );
document.write( "We unfortunately do not have enough information to determine how many people drank trophy beer. <BR>\n" );
document.write( "Similar situations apply to the remaining questions as well.<BR>\n" );
document.write( "</font> </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );