document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=293564>Question 293564</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am stuck on this problem can any one show me how to do this especially the VENNGRAM\r<BR>\n" );
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document.write( "In a survey of 160 dancers, 98 knew the Salsa, 120 knew the Merengue, and 86 knew the Cha Cha. Of these, 77 knew the Merengue and Salsa dances, 51 knew the Salsa and Cha Cha, and 70 knew the Merengue and Cha Cha. Forty-seven dancers knew all three dances. <BR>\n" );
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document.write( "(a)   How many knew only the Salsa? <BR>\n" );
document.write( "(b)   How many knew only the Merengue? <BR>\n" );
document.write( "(c)   How many knew exactly one of the three dances?<BR>\n" );
document.write( "(d)   How many knew the Merengue and Cha Cha, but not the Salsa? <BR>\n" );
document.write( "(e)   How many knew none of these dances?<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #211912 by </B><A HREF=/tutors/aboutme.mpl?userid=scott8148><B>scott8148(6628)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=scott8148><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=scott8148><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=211912\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the \"VENNGRAM\" is three intersecting circles, surrounded by a box\r<BR>\n" );
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document.write( "the box represents the 160 dancers surveyed<BR>\n" );
document.write( "___ the circles represent the Salsa, Merengue, and Cha Cha\r<BR>\n" );
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document.write( "start on the INNERMOST parts of the circles, and work your way out\r<BR>\n" );
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document.write( "47 dancers knew all three, so this number goes in the INTERSECTION OF ALL THREE CIRCLES\r<BR>\n" );
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document.write( "70 knew the Merengue and Cha Cha, so this number goes in the intersection of the M and CC circles<BR>\n" );
document.write( "___BUT ___ there are already 47 in the intersection from the people who knew all three<BR>\n" );
document.write( "___ so 23 (70 - 47) are added to the M and CC intersection [question(d)]\r<BR>\n" );
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document.write( "similarly for S and CC ___ 4 people added<BR>\n" );
document.write( "___ and M and S ___ 30 people added\r<BR>\n" );
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document.write( "86 knew the Cha Cha ___ BUT ___ 47 knew all three; 23 knew M and CC; and 4 knew S and CC<BR>\n" );
document.write( "___ so 12 (86 - 47 - 23 - 4) are added to the CC circle [part of question(c)]\r<BR>\n" );
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document.write( "similarly for Salsa ___ 17 added [question(a)] and [part of question(c)]<BR>\n" );
document.write( "___ and Merengue ___ 20 added [question(b)] and [part of question(c)]\r<BR>\n" );
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document.write( "(e) 160 dancers MINUS everyone in the three circles<BR>\n" );
document.write( "___ 160 - 47 - 23 - 4 - 30 - 12 - 17 - 20 = ? </SPAN>\n" );
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