document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=464865>Question 464865</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A survey of flower gardeners showed the following:<BR>\n" );
document.write( " <BR>\n" );
document.write( "45 grew roses     7 grew both roses and tulips  4 grew all three types<BR>\n" );
document.write( "16 grew tulips    5 grew both orchids and tulips 9 grew none of these three<BR>\n" );
document.write( "13 grew orchids   10 grew both roses and orchids     <BR>\n" );
document.write( " <BR>\n" );
document.write( "Create a Venn diagram to reflect the above data, label your diagram clearly and submit to the Dropbox. Use your diagram to answer the following questions here.<BR>\n" );
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document.write( "(a)   How many grew only roses?<BR>\n" );
document.write( "(b)   How many grew both roses and tulips, but not orchids?<BR>\n" );
document.write( "(c)   How many grew only tulips?<BR>\n" );
document.write( "(d)   How many grew none of these three or only orchids?<BR>\n" );
document.write( "(e)   How many flower gardeners were surveyed? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #318460 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=318460\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The trick is to get a count for each little<BR>\n" );
document.write( "region of the Venn diagram.<BR>\n" );
document.write( "Label the big interlocking circles:<BR>\n" );
document.write( "R = 45<BR>\n" );
document.write( "T = 16<BR>\n" );
document.write( "O = 13<BR>\n" );
document.write( "A key item is: 4 grew all three types<BR>\n" );
document.write( "Look at just the intersection of Roses and Tulips<BR>\n" );
document.write( "There are 7 gardeners in this intersection, but 4 grew all 3 types,<BR>\n" );
document.write( "so there are 7 - 4 = 3 who grew ONLY Roses and Tulips<BR>\n" );
document.write( "--------------------------------------------<BR>\n" );
document.write( "Look at just the intersection of Tulips and Orchids<BR>\n" );
document.write( "There are 5 gardeners in this intersection, but 4 grew all 3 types,<BR>\n" );
document.write( "so there are 5 - 4 = 1 who grew ONLY Orchids and Tulips<BR>\n" );
document.write( "---------------------------------------------<BR>\n" );
document.write( "Look at just the intersection of Roses and Orchids<BR>\n" );
document.write( "There are 10 gardeners in this intersection, but 4 grew all 3 types, <BR>\n" );
document.write( "so there are 10 - 4 = 6 who grew ONLY Roses and Orchids<BR>\n" );
document.write( "----------------------------------------------<BR>\n" );
document.write( "Now all that is left is to count how many grew<BR>\n" );
document.write( "ONLY Roses<BR>\n" );
document.write( "ONLY Tulips<BR>\n" );
document.write( "ONLY Orchids<BR>\n" );
document.write( "----------<BR>\n" );
document.write( "ONLY Roses = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=45+-+%286+%2B+3+%2B+4%29+=+45+-+13 ALIGN=MIDDLE  ALT=\"45+-+%286+%2B+3+%2B+4%29+=+45+-+13\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+45+-+13+=+32+ ALIGN=MIDDLE  ALT=\"+45+-+13+=+32+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "ONLY Tulips = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+16+-+%283+%2B+1+%2B+4%29++=+16+-+8 ALIGN=MIDDLE  ALT=\"+16+-+%283+%2B+1+%2B+4%29++=+16+-+8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+16+-+8+=+8+ ALIGN=MIDDLE  ALT=\"+16+-+8+=+8+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "ONLY Orchids = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+13+-+%286+%2B+1+%2B+4%29+=+13+-+11+ ALIGN=MIDDLE  ALT=\"+13+-+%286+%2B+1+%2B+4%29+=+13+-+11+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+13+-+11+=+2+ ALIGN=MIDDLE  ALT=\"+13+-+11+=+2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "--------------<BR>\n" );
document.write( "There were 9 gardeners who didn't grow any of these 3 types<BR>\n" );
document.write( "Now you can answer any question<BR>\n" );
document.write( "(a) How many grew only roses?<BR>\n" );
document.write( "32 grew only Roses<BR>\n" );
document.write( "(b) How many grew both roses and tulips, but not orchids?<BR>\n" );
document.write( "This is the intersection of Roses and Tulips, which is 7,<BR>\n" );
document.write( "minus the ones that grew all 3 types, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+7+-+4+=+3+ ALIGN=MIDDLE  ALT=\"+7+-+4+=+3+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(c) How many grew only tulips?<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+16+-+%283+%2B+1+%2B+4%29+=+16+-+8+ ALIGN=MIDDLE  ALT=\"+16+-+%283+%2B+1+%2B+4%29+=+16+-+8+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+16+-+8+=+8+ ALIGN=MIDDLE  ALT=\"+16+-+8+=+8+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(d) How many grew none of these three or only orchids?<BR>\n" );
document.write( "Only Orchids is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+13+-+%286+%2B+1+%2B+4%29+=+2+ ALIGN=MIDDLE  ALT=\"+13+-+%286+%2B+1+%2B+4%29+=+2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and<BR>\n" );
document.write( "none of the 3 types is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9 ALIGN=MIDDLE  ALT=\"9\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2+%2B+9+=+11+ ALIGN=MIDDLE  ALT=\"+2+%2B+9+=+11+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(e) How many flower gardeners were surveyed?<BR>\n" );
document.write( "Add up all the little areas of the Venn diagram to get<BR>\n" );
document.write( "a true count of gardeners who grew SOME of the 3 types<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+32+%2B+8+%2B+2+%2B+3+%2B+6+%2B+1+%2B+4+=+56+ ALIGN=MIDDLE  ALT=\"+32+%2B+8+%2B+2+%2B+3+%2B+6+%2B+1+%2B+4+=+56+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Add this to gardeners who grew NONE of the 3 types<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+56+%2B+9+=+65+ ALIGN=MIDDLE  ALT=\"+56+%2B+9+=+65+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "And, I hope I didn't mess something up, but this is the method I use </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );