document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1066746>Question 1066746</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In a sample of 150 people, 45 swim, 40 bike, and 50 jog. Moreover, 32 jog but don't bike, 27 jog and swim, and 10 do all three activities. <BR>\n" );
document.write( "a. How many jog but don't swim and don't bike?<BR>\n" );
document.write( "b. If 21 bike and swim, how many do not do any of the activities? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #682019 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=682019\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You need a Venn diagram which is 3 interlocking<BR>\n" );
document.write( "circles: swimmers, joggers, and bikers<BR>\n" );
document.write( "Realize there are 7 regions, and each has a different<BR>\n" );
document.write( "meaning. The center one is all 3:  swimmers, joggers, and bikers.<BR>\n" );
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document.write( "10 do all 3 activities<BR>\n" );
document.write( "27 jog and swim. That leaves <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+27+-+10+=+17+ ALIGN=MIDDLE  ALT=\"+27+-+10+=+17+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "that jog and swim, but don't do anything else<BR>\n" );
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document.write( "(a)<BR>\n" );
document.write( "32 jog but don't bike, so if you subtract the joggers and<BR>\n" );
document.write( "swimmers, there are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+32+-+17+=+15+ ALIGN=MIDDLE  ALT=\"+32+-+17+=+15+\"   DISABLED_style= \"max-width:90%; height:auto;\" > who ONLY jog<BR>\n" );
document.write( "but don't swim and bike<BR>\n" );
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document.write( "(b)<BR>\n" );
document.write( "21 bike and swim. Subtract those who do all 3.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+21+-+10+=+11+ ALIGN=MIDDLE  ALT=\"+21+-+10+=+11+\"   DISABLED_style= \"max-width:90%; height:auto;\" > so, 11 do ONLY swimming and biking.<BR>\n" );
document.write( "Now I can subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+17+%2B+10+%2B+11+ ALIGN=MIDDLE  ALT=\"+17+%2B+10+%2B+11+\"   DISABLED_style= \"max-width:90%; height:auto;\" > from total swimmers <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+45+-+38+=+7+ ALIGN=MIDDLE  ALT=\"+45+-+38+=+7+\"   DISABLED_style= \"max-width:90%; height:auto;\" > who ONLY swim<BR>\n" );
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document.write( "Likewise, subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+15+%2B+17+%2B+10+ ALIGN=MIDDLE  ALT=\"+15+%2B+17+%2B+10+\"   DISABLED_style= \"max-width:90%; height:auto;\" > from all the joggers<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+50+-+42+=+8+ ALIGN=MIDDLE  ALT=\"+50+-+42+=+8+\"   DISABLED_style= \"max-width:90%; height:auto;\" > who ONLY jog or bike<BR>\n" );
document.write( "There is only 1 of the 7 regions left. It is those who bike ONLY.<BR>\n" );
document.write( "Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+11+%2B+10+%2B+8+ ALIGN=MIDDLE  ALT=\"+11+%2B+10+%2B+8+\"   DISABLED_style= \"max-width:90%; height:auto;\" > from total of bikers<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+40+-+29+=+11+ ALIGN=MIDDLE  ALT=\"+40+-+29+=+11+\"   DISABLED_style= \"max-width:90%; height:auto;\" > who ONLY bike<BR>\n" );
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document.write( "Now add up all of the 7 regions and subtract from <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+150+ ALIGN=MIDDLE  ALT=\"+150+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+150+-+7+-+11+-15+-11+-17+-8+-+10+ ALIGN=MIDDLE  ALT=\"+150+-+7+-+11+-15+-11+-17+-8+-+10+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+150+-+79+=+71+ ALIGN=MIDDLE  ALT=\"+150+-+79+=+71+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "There are 71 who don't swim, bike or jog<BR>\n" );
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document.write( "Note there is no way to do this problem if you don't draw<BR>\n" );
document.write( "a Venn diagram and understand what each of the 7 regions<BR>\n" );
document.write( "means. Always start with the center one which is those who<BR>\n" );
document.write( "do all 3 activities. Hope this helps.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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