document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1177473>Question 1177473</A>: <I><SPAN STYLE=\"word-break: break-all;\"> II. A survey was done of 200 8-year olds asking if they like certain types of vegetables (broccoli, carrots, and green beans). The following were obtained. <BR>\n" );
document.write( "28 kids only liked green beans. 	<BR>\n" );
document.write( "73 kids liked broccoli. <BR>\n" );
document.write( "40 kinds liked broccoli and green beans. <BR>\n" );
document.write( "79 kids liked exactly 2 of these vegetables. <BR>\n" );
document.write( "12 kinds liked broccoli and carrots, but not green beans. <BR>\n" );
document.write( "34 kinds only liked carrots. <BR>\n" );
document.write( "104 kids liked carrots or green beans, but not broccoli. 	\r<BR>\n" );
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document.write( "1. How many kids liked carrots, but not green beans? \r<BR>\n" );
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document.write( "2. How many kids liked exactly 1 of the three vegetables? \r<BR>\n" );
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document.write( "3. How many kids do not like carrots?  <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 #850451 by </B><A HREF=/tutors/aboutme.mpl?userid=CPhill><B>CPhill(1959)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=CPhill><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=CPhill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=850451\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> It's helpful to solve this kind of problem with a Venn Diagram. Here's how we can approach this:\r<BR>\n" );
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document.write( "**1. Draw a Venn Diagram**\r<BR>\n" );
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document.write( "Draw three overlapping circles representing broccoli, carrots, and green beans.\r<BR>\n" );
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document.write( "**2. Fill in the Diagram**\r<BR>\n" );
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document.write( "* **28 kids only liked green beans:** Place \"28\" in the green beans only section.<BR>\n" );
document.write( "* **40 kids liked broccoli and green beans:** Since 73 like broccoli total, and 40 like broccoli and green beans, 73 - 40 = 33 like only broccoli and green beans. Of those, 12 also like carrots. So, place \"12\" in the broccoli-carrot-green bean overlap, and 33 - 12 = 21 in the broccoli-green bean overlap.<BR>\n" );
document.write( "* **79 kids liked exactly 2 of these vegetables:** We've already accounted for 12 who like broccoli and carrots, and 21 who like broccoli and green beans. So, 79 - 12 - 21 = 46 must like carrots and green beans only.<BR>\n" );
document.write( "* **12 kids liked broccoli and carrots, but not green beans:** Place \"12\" in the broccoli-carrot overlap.<BR>\n" );
document.write( "* **34 kids only liked carrots:** Place \"34\" in the carrots only section.<BR>\n" );
document.write( "* **104 kids liked carrots or green beans, but not broccoli:** This includes those who like only carrots, only green beans, and the overlap between carrots and green beans. We've already accounted for 28 + 46 = 74, so 104 - 74 = 30 must like carrots only.\r<BR>\n" );
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document.write( "**3. Calculate the Remaining Values**\r<BR>\n" );
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document.write( "* **Total who like carrots:** 30 (carrots only) + 12 (broccoli-carrot) + 46 (carrot-green bean) + 12 (all three) = 100<BR>\n" );
document.write( "* **Total who like any vegetable:** Add up all the numbers in the Venn diagram.<BR>\n" );
document.write( "* **Those who dislike carrots:** 200 (total) - 100 (like carrots) = 100\r<BR>\n" );
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document.write( "**Answers**\r<BR>\n" );
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document.write( "1. **How many kids liked carrots, but not green beans?** 30 (carrots only) + 12 (broccoli-carrot) = 42<BR>\n" );
document.write( "2. **How many kids liked exactly 1 of the three vegetables?** 30 (carrots only) + 28 (green beans only) + 12 (broccoli and carrots only) = 70<BR>\n" );
document.write( "3. **How many kids do not like carrots?** 100 </SPAN>\n" );
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