document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=975876>Question 975876</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me with this ..\r<BR>\n" );
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document.write( "In a a group of 60 students ..<BR>\n" );
document.write( "34 are members of Music Club <BR>\n" );
document.write( "30 are members of Art Club<BR>\n" );
document.write( "32 are members of Math Club<BR>\n" );
document.write( "25 are members of Art and Music Club<BR>\n" );
document.write( "14 are members of Math and Music Club<BR>\n" );
document.write( "11 are members of art and math<BR>\n" );
document.write( "7 are members of all 3 Clubs\r<BR>\n" );
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document.write( "1.How many members in Math club only ?<BR>\n" );
document.write( "2.How many members in Music Club only?<BR>\n" );
document.write( "3.How many members in Art Club only ?<BR>\n" );
document.write( "4.How many members in Art and Music but not members of Math Club?<BR>\n" );
document.write( "5.How many are members of both math and music?<BR>\n" );
document.write( "6.how many are not members of Math Club?<BR>\n" );
document.write( "7.How many students do not belong to any of the three clubs ? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #597851 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=597851\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Two questions can be answered without much work:<BR>\n" );
document.write( "5.How many are members of both math and music?<BR>\n" );
document.write( "The problem says that \"<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%2814%29 ALIGN=MIDDLE  ALT=\"highlight%2814%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > are members of Math and Music Club.\"<BR>\n" );
document.write( "6.How many are not members of Math Club?<BR>\n" );
document.write( "The problem says that<BR>\n" );
document.write( "\"In a a group of 60 students ... 32 are members of Math Club,\"<BR>\n" );
document.write( "so obviously <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=60-32=highlight%2828%29 ALIGN=MIDDLE  ALT=\"60-32=highlight%2828%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > are not members of Math club.<BR>\n" );
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document.write( "Other questions require more work, and it is best to work with diagrams.<BR>\n" );
document.write( "The diagram below shows that we know that<BR>\n" );
document.write( "some students may not belong to any of the three clubs,<BR>\n" );
document.write( "some students may belong to only one of the clubs,<BR>\n" );
document.write( "some students may belong to two clubs, <BR>\n" );
document.write( "and exactly 7 students belong to all three clubs.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28330%2C300%2C-5.5%2C5.5%2C-6.5%2C3.5%2C%0D%0Arectangle%28-5.4%2C-6.4%2C5.4%2C3.4%29%2Clocate%28-5.3%2C3.38%2Cstudents%29%2C%0D%0Ared%28circle%28-2%2C0%2C3%29%29%2Clocate%28-2.6%2C2.9%2Cred%28MUSIC%29%29%2C%0D%0Ablue%28circle%282%2C0%2C3%29%29%2Clocate%281.5%2C2.9%2Cblue%28ART%29%29%2C%0D%0Agreen%28circle%280%2C-3%2C3%29%29%2Clocate%28-0.5%2C-5.5%2Cgreen%28MATH%29%29%2C%0D%0Alocate%28-0.2%2C-1%2C7%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > We can calculate some more facts and fill them into the diagram.<BR>\n" );
document.write( "The group of 25 students who are members of Art and Music clubs includes those 7 students who belong to all three clubs.<BR>\n" );
document.write( "It also includes<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25-7=18 ALIGN=MIDDLE  ALT=\"25-7=18\"   DISABLED_style= \"max-width:90%; height:auto;\" > students who belong to the Art and Music clubs, but not to the Math club. That is the answer to one of the questions:<BR>\n" );
document.write( "4.How many members in Art and Music but not members of Math Club? <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%2818%29 ALIGN=MIDDLE  ALT=\"highlight%2818%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The group of 14 students who are members of Math and Music clubs includes those 7 students who belong to all three clubs.<BR>\n" );
document.write( "It also includes<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=14-7=7 ALIGN=MIDDLE  ALT=\"14-7=7\"   DISABLED_style= \"max-width:90%; height:auto;\" > students who belong to the Math and Music clubs, but not to the Art club.<BR>\n" );
document.write( "The group of 11 students who are members of Art and Math clubs includes those 7 students who belong to all three clubs.<BR>\n" );
document.write( "It also includes<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=11-7=4 ALIGN=MIDDLE  ALT=\"11-7=4\"   DISABLED_style= \"max-width:90%; height:auto;\" > students who belong to the Art and Math  clubs, but not to the Music club.<BR>\n" );
document.write( "So we re-draw the diagram with the calculated information:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28330%2C300%2C-5.5%2C5.5%2C-6.5%2C3.5%2C%0D%0Arectangle%28-5.4%2C-6.4%2C5.4%2C3.4%29%2Clocate%28-5.3%2C3.38%2Cstudents%29%2C%0D%0Ared%28circle%28-2%2C0%2C3%29%29%2Clocate%28-2.6%2C2.9%2Cred%28MUSIC%29%29%2C%0D%0Ablue%28circle%282%2C0%2C3%29%29%2Clocate%281.5%2C2.9%2Cblue%28ART%29%29%2C%0D%0Agreen%28circle%280%2C-3%2C3%29%29%2Clocate%28-0.5%2C-5.5%2Cgreen%28MATH%29%29%2C%0D%0Alocate%28-0.2%2C-1%2C7%29%2C%0D%0Alocate%28-0.6%2C1.2%2C57-7%29%2Clocate%28-0.4%2C0.8%2C%22=+18%22%29%2C%0D%0Alocate%28-2.5%2C-2%2C14-7=7%29%2Clocate%280.5%2C-2%2C11-7=4%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > , and we calculate more and add the new calculations to the diagram.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28330%2C300%2C-5.5%2C5.5%2C-6.5%2C3.5%2C%0D%0Arectangle%28-5.4%2C-6.4%2C5.4%2C3.4%29%2Clocate%28-5.3%2C3.38%2Cstudents%29%2C%0D%0Ared%28circle%28-2%2C0%2C3%29%29%2Clocate%28-2.6%2C2.9%2Cred%28MUSIC%29%29%2C%0D%0Ablue%28circle%282%2C0%2C3%29%29%2Clocate%281.5%2C2.9%2Cblue%28ART%29%29%2C%0D%0Agreen%28circle%280%2C-3%2C3%29%29%2Clocate%28-0.5%2C-5.5%2Cgreen%28MATH%29%29%2C%0D%0Alocate%28-0.2%2C-1%2C7%29%2Clocate%28-0.2%2C1%2C18%29%2C%0D%0Alocate%28-1.5%2C-1.5%2C7%29%2Clocate%281.2%2C-1.5%2C4%29%2C%0D%0Alocate%28-4.9%2C0.5%2C34-%2818%2B7%2B7%29=2%29%2C%0D%0Alocate%281.1%2C0.5%2C30-%2818%2B7%2B4%29=1%29%2C%0D%0Alocate%28-1.8%2C-3.5%2C32-%287%2B7%2B4%29=14%29%0D%0A+%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > from the diagram we can answer some of the questions:<BR>\n" );
document.write( "1.How many members in Math club only ? <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%2814%29 ALIGN=MIDDLE  ALT=\"highlight%2814%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "2.How many members in Music Club only? <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%282%29 ALIGN=MIDDLE  ALT=\"highlight%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "3.How many members in Art Club only ? <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%281%29 ALIGN=MIDDLE  ALT=\"highlight%281%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "We have just one question left:<BR>\n" );
document.write( "7.How many students do not belong to any of the three clubs ?<BR>\n" );
document.write( "At this point, we can calculate how many of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=60 ALIGN=MIDDLE  ALT=\"60\"   DISABLED_style= \"max-width:90%; height:auto;\" > students belong to one or more clubs:<BR>\n" );
document.write( "32 belong to the Math club and maybe one or two other clubs,<BR>\n" );
document.write( "2 belong to only the Music club,<BR>\n" );
document.write( "1 student belongs to only the Art club,<BR>\n" );
document.write( "and 18 students belong to both the Music and Art clubs.<BR>\n" );
document.write( "So the total belonging to at least one club is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=32%2B2%2B1%2B18=53 ALIGN=MIDDLE  ALT=\"32%2B2%2B1%2B18=53\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "Therefore, there must be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=60-53=highlight%287%29 ALIGN=MIDDLE  ALT=\"60-53=highlight%287%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > students that do not belong to any of the three clubs.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );