document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=184317>Question 184317</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/032150108X/algebrahomeworkh>A Survey of Mathematics with Application</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> I am having problems with doing Venn Diagrams, I really need your help with this??? Please? Okay, here's the question:\r<BR>\n" );
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document.write( " A drug company is considering manufacturing a new product that has two different flavors, orange and cherry.  They surveyed 120 people.  The results are as follows:\r<BR>\n" );
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document.write( "62 liked cherry flavor<BR>\n" );
document.write( "74 liked orange flavor<BR>\n" );
document.write( "35 liked both flavors\r<BR>\n" );
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document.write( "We're asked to 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 like either one or the other or both\r<BR>\n" );
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document.write( "This is pretty confusing to me, i'm now sure if i'm making too much out of this or what i'm doing, but I definitely need some help </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #138345 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=138345\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "Draw a big rectangle.  That represents everybody that was surveyed; according to your givens, 120 people.\r<BR>\n" );
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document.write( "Draw two circles inside of the rectangle and make sure they overlap some.  That divides the area inside of your rectangle into four regions:  An area outside of both circles, an area that is ONLY in the first circle, an area that is ONLY in the second circle, and a little lozenge shaped area that is inside of BOTH circles.\r<BR>\n" );
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document.write( "The lozenge-shaped area represents the 35 people who liked both cherry and orange, so write the number 35 in that area.\r<BR>\n" );
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document.write( "Next pick one of the circles to represent cherry and the other will then represent orange.  You know that 62 people liked cherry, but 35 of those people also liked orange, so subtract 35 from 62 = 27 to get the number of people who ONLY liked cherry.  Write that number inside the 'cherry' circle but outside of the lozenge-shaped area.  Similarly, 74 - 35 = 39 people ONLY liked orange.  Write that number in the 'orange' circle but outside of the lozenge shaped area.\r<BR>\n" );
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document.write( "Now you can answer your questions directly:\r<BR>\n" );
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document.write( "Only liked Cherry:  27\r<BR>\n" );
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document.write( "Only liked Orange:  39\r<BR>\n" );
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document.write( "Liked one OR the other OR both:  27 + 39 + 35:\r<BR>\n" );
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document.write( "Answers to questions not asked here but that might come up if you discuss this one in class:\r<BR>\n" );
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document.write( "Liked one or the other but NOT both:  27 + 39.\r<BR>\n" );
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document.write( "Didn't like either:  120 - (27 + 39 + 35)\r<BR>\n" );
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document.write( "Didn't like orange:  120 - 39\r<BR>\n" );
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document.write( "Didn't like both:  120 - 35\r<BR>\n" );
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document.write( "Very handy things are Venn diagrams.\r<BR>\n" );
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document.write( "<i><b>Super-Double-Plus Extra Credit</b></i>  What would the diagram look like (without the numbers) if your survey included 3 flavors?\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large e^{i\pi} + 1 = 0\"><BR>\n" );
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