document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1205709>Question 1205709</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A group of market women sell at least one of the following items of food stuffs. Yam,corn,and plantain.18 of them sell corn,17 sell yam and 19 sell plantain.8 sell plantain and corn and 12 sell yam and plantain and 5 sell all the food stuffs.Draw a venn diagram to illustrate the information above.Find the total number of women in the group.Find the total number of women who sell one of the food stuffs. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #842709 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=842709\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "As it stands right now, <font color=red size=4>this question is incomplete</font>. It is missing 1 key detail. I'll try my best to explain. \r<BR>\n" );
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document.write( "Draw 3 partially overlapping circles with these labels<BR>\n" );
document.write( "Y = yam<BR>\n" );
document.write( "C = corn<BR>\n" );
document.write( "P = plantain<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%0D%0Adrawing%28400%2C400%2C-5%2C5%2C-5%2C5%2C%0D%0Aline%28-4%2C4%2C4%2C4%29%2C%0D%0Aline%284%2C4%2C4%2C-4%29%2C%0D%0Aline%284%2C-4%2C-4%2C-4%29%2C%0D%0Aline%28-4%2C-4%2C-4%2C4%29%2C%0D%0A%0D%0Acircle%28-1%2C1%2C2%29%2Ccircle%281%2C1%2C2%29%2Ccircle%280%2C-0.7321%2C2%29%2C%0D%0A%0D%0Alocate%28-2.8%2C2.8%2CY%29%2C%0D%0Alocate%282.6%2C2.8%2CC%29%2C%0D%0Alocate%281%2C-2.6%2CP%29%2C%0D%0Alocate%28-2%2C1.8%2Ca%29%2C%0D%0Alocate%280%2C1.8%2Cb%29%2C%0D%0Alocate%282%2C1.8%2Cc%29%2C%0D%0Alocate%28-1.5%2C0%2Cd%29%2C%0D%0Alocate%280%2C0.4%2Ce%29%2C%0D%0Alocate%281.2%2C0%2Cf%29%2C%0D%0Alocate%280%2C-1.5%2Cg%29%2C%0D%0Alocate%283%2C-1.5%2Ch%29%0D%0A%29%0D%0A ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Letters 'a' through 'h' indicate the following <BR>\n" );
document.write( "a = yams only<BR>\n" );
document.write( "b = yams and corn only (but no plantains)<BR>\n" );
document.write( "c = corn only<BR>\n" );
document.write( "d = yams and plaintains only (but no corn)<BR>\n" );
document.write( "e = all 3 items mentioned<BR>\n" );
document.write( "f = corn and plaintains only (but no yams)<BR>\n" );
document.write( "g = plantains only<BR>\n" );
document.write( "h = none of the 3 items mentioned\r<BR>\n" );
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document.write( "Here's the given info<BR>\n" );
document.write( "<TABLE  border = \"1\" cellpadding = \"5\">\n" );
document.write( "<tr><TD >Number</TD><TD >Statement</TD></tr><tr><TD ><font color=blue>Fact 1</font></TD><TD >A group of market women sell at least one of the following items of food stuffs. Yam,corn,and plantain.</TD></tr><tr><TD ><font color=blue>Fact 2</font></TD><TD >18 of them sell corn</TD></tr><tr><TD ><font color=blue>Fact 3</font></TD><TD >17 sell yam</TD></tr><tr><TD ><font color=blue>Fact 4</font></TD><TD >19 sell plantain</TD></tr><tr><TD ><font color=blue>Fact 5</font></TD><TD >8 sell plantain and corn</TD></tr><tr><TD ><font color=blue>Fact 6</font></TD><TD >12 sell yam and plantain</TD></tr><tr><TD ><font color=blue>Fact 7</font></TD><TD >5 sell all the food stuffs</TD></tr>\n" );
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document.write( "<font color=blue>fact 1</font> means that h = 0. \r<BR>\n" );
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document.write( "<font color=blue>fact 7</font> leads to e = 5.\r<BR>\n" );
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document.write( "Let's combine <font color=blue>fact 6</font> and <font color=blue>fact 7</font><BR>\n" );
document.write( "12 sell yam and plantain. Five sell all three types, so 12-5 = 7 <BR>\n" );
document.write( "Therefore, d = 7\r<BR>\n" );
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document.write( "Combine <font color=blue>fact 5</font> and <font color=blue>fact 7</font> to determine that 8-5 = 3 women sell plantain and corn but no yams.<BR>\n" );
document.write( "3 goes inside region f<BR>\n" );
document.write( "f = 3\r<BR>\n" );
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document.write( "Here's what we found so far<BR>\n" );
document.write( "d = 7<BR>\n" );
document.write( "e = 5<BR>\n" );
document.write( "f = 3<BR>\n" );
document.write( "h = 0<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%0D%0Adrawing%28400%2C400%2C-5%2C5%2C-5%2C5%2C%0D%0Aline%28-4%2C4%2C4%2C4%29%2C%0D%0Aline%284%2C4%2C4%2C-4%29%2C%0D%0Aline%284%2C-4%2C-4%2C-4%29%2C%0D%0Aline%28-4%2C-4%2C-4%2C4%29%2C%0D%0A%0D%0Acircle%28-1%2C1%2C2%29%2Ccircle%281%2C1%2C2%29%2Ccircle%280%2C-0.7321%2C2%29%2C%0D%0A%0D%0Alocate%28-2.8%2C2.8%2CY%29%2C%0D%0Alocate%282.6%2C2.8%2CC%29%2C%0D%0Alocate%281%2C-2.6%2CP%29%2C%0D%0Alocate%28-2%2C1.8%2Ca%29%2C%0D%0Alocate%280%2C1.8%2Cb%29%2C%0D%0Alocate%282%2C1.8%2Cc%29%2C%0D%0Alocate%28-1.5%2C0%2C7%29%2C%0D%0Alocate%280%2C0.4%2C5%29%2C%0D%0Alocate%281.2%2C0%2C3%29%2C%0D%0Alocate%280%2C-1.5%2Cg%29%2C%0D%0Alocate%283%2C-1.5%2C0%29%0D%0A%29%0D%0A ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Focus on circle P.\r<BR>\n" );
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document.write( "<font color=blue>Fact 4</font> tells us that 19 women sell plantains (some sell other vegetables as well).<BR>\n" );
document.write( "The items inside circle P must add to 19.<BR>\n" );
document.write( "g+7+5+3 = 19<BR>\n" );
document.write( "g+15 = 19<BR>\n" );
document.write( "g = 19-15<BR>\n" );
document.write( "g = 4<BR>\n" );
document.write( "There are 4 women who sell plantains only.\r<BR>\n" );
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document.write( "Now focus on circle Y and <font color=blue>fact 3</font><BR>\n" );
document.write( "Because of this given fact, the items in this circle must add to 17.<BR>\n" );
document.write( "a+b+7+5 = 17<BR>\n" );
document.write( "a+b+12 = 17<BR>\n" );
document.write( "a+b = 17-12<BR>\n" );
document.write( "a+b = 5\r<BR>\n" );
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document.write( "Through similar logic (focus on circle C and <font color=blue>fact 2</font>), you'll find that b+c+5+3 = 18 leads to b+c = 10\r<BR>\n" );
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document.write( "We have this system of equations<BR>\n" );
document.write( "a+b = 5<BR>\n" );
document.write( "b+c = 10<BR>\n" );
document.write( "It has 3 variables. Since there are more variables than equations, we do <u>not</u> have enough information to find the numeric value of a,b, nor c.<BR>\n" );
document.write( "We need 3 equations to solve for 3 variables.<BR>\n" );
document.write( "This is where we come up short.\r<BR>\n" );
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document.write( "The general rule for Venn Diagram problems is this: There are 8 regions ('a' through h) so we need 8 given facts of information.<BR>\n" );
document.write( "Unfortunately we're only given 7 facts so we're one fact short.<BR>\n" );
document.write( "The problem is incomplete. <BR>\n" );
document.write( "Please make sure you didn't miss something to type in, or ask your teacher to see if s/he might have made a typo somewhere.\r<BR>\n" );
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document.write( "Refer to these similar Venn Diagram questions to see examples of 8 given facts to help fill out the Venn Diagram.<BR>\n" );
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document.write( "and<BR>\n" );
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document.write( "and<BR>\n" );
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document.write( "and<BR>\n" );
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document.write( "</font> </SPAN>\n" );
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