document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=206978>Question 206978</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A company is considering manufacturing a new product that has two different flavors, orange and cherry. They surveyed 150 people. The results are as follows.<BR>\n" );
document.write( "75 liked cherry <BR>\n" );
document.write( "94 liked orange<BR>\n" );
document.write( "22 like both flavors<BR>\n" );
document.write( "Construct a Venn diagram and answer the following:<BR>\n" );
document.write( "a) how many liked only orange flavor?<BR>\n" );
document.write( "b) how many liked only cherry flavor?<BR>\n" );
document.write( "c) how many liked either one or the other or both?<BR>\n" );
document.write( "d) how many liked neither? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #156504 by </B><A HREF=/tutors/aboutme.mpl?userid=mickclns><B>mickclns(59)</B></A><img src=\"/images/stars/stars-08.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=mickclns><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=156504\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+drawing%28200%2C200%2C0%2C200%2C0%2C200%2C%0D%0A+++++circle%2875%2C100%2C70%29%2C%0D%0A+++++circle%28125%2C100%2C70%29%2C%0D%0A%0D%0A+++++locate%2830%2C175%2CO%29%2C%0D%0A+++++locate%28165%2C175%2CC%29%2C%0D%0A%0D%0A+++++rectangle%281%2C199%2C199%2C1%29%0D%0A%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "There are 4 separate (mutually exclusive) regions in this diagram: 1) the part inside both circles (their intersection), 2) The part inside O but not inside C, 3) the part inside C but not inside O 4) The part outside both O and C.\r<BR>\n" );
document.write( "\n" );
document.write( "Since 22 like both flavors, that number goes in the intersection of O and C.<BR>\n" );
document.write( "Since 75 like Cherry, and 22 like both, 75-22=53 like Cherry but not Orange.<BR>\n" );
document.write( "Since 94 like Orange, and 22 like both, 94-22=72 like Orange but not Cherry.\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+drawing%28200%2C200%2C0%2C200%2C0%2C200%2C%0D%0A+++++circle%2875%2C100%2C70%29%2C%0D%0A+++++circle%28125%2C100%2C70%29%2C%0D%0A%0D%0A+++++locate%2830%2C175%2CO%29%2C%0D%0A+++++locate%28165%2C175%2CC%29%2C%0D%0A%0D%0A+++++rectangle%281%2C199%2C199%2C1%29%2C+%0D%0A%0D%0A+++++locate%2889.5%2C110%2C+22%29%2C%0D%0A+++++locate%28155%2C110%2C+53%29%2C%0D%0A+++++locate%2833%2C110%2C+72%29%2C%0D%0A+++++locate%2820%2C30%2C+3%29%0D%0A%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "Together the 4 sections include 150 people and the 3 sections so far filled include 22+53+72=147 people, so 150 - 147 = 3 people like neither Orange nor Cherry.<BR>\n" );
document.write( " <BR>\n" );
document.write( "The answers to the questions:<BR>\n" );
document.write( "a) how many liked only orange flavor?  *** 72<BR>\n" );
document.write( "b) how many liked only cherry flavor?  *** 53<BR>\n" );
document.write( "c) how many liked either one or the other or both?  *** 147<BR>\n" );
document.write( "d) how many liked neither?  *** 3 </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );