document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1204589>Question 1204589</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In a recent survey of 180 housewives. The following were determined with regard to their detergent soap preferences\r<BR>\n" );
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document.write( "65 use brand A<BR>\n" );
document.write( "140 use brand B<BR>\n" );
document.write( "145 use brand C <BR>\n" );
document.write( "115 use B and C<BR>\n" );
document.write( "23 use A but not B<BR>\n" );
document.write( "12 use A but not C<BR>\n" );
document.write( "18 use A and C but not B\r<BR>\n" );
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document.write( "A) Draw a Venn diagram to summarize the given data.<BR>\n" );
document.write( "B) Determine the number of housewives who use all 3 soaps.<BR>\n" );
document.write( "C) How many do not use any of the above brands. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #840949 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=840949\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Here's a template of a venn diagram with 3 circles that partially overlap.<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%2CA%29%2C%0D%0Alocate%282.6%2C2.8%2CB%29%2C%0D%0Alocate%281%2C-2.6%2CC%29%0D%0A%29%0D%0A ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The goal is to place a number into each of the 8 separate regions.\r<BR>\n" );
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document.write( "18 people use A and C, but not B. This means we'll place 18 in circles A and C, but outside circle B as shown below<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%2CA%29%2C%0D%0Alocate%282.6%2C2.8%2CB%29%2C%0D%0Alocate%281%2C-2.6%2CC%29%2C%0D%0Alocate%28-1.5%2C0%2C18%29%0D%0A%29%0D%0A ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "23 housewives use brand A but not brand B<BR>\n" );
document.write( "This must mean the value in circle A outside the other circles must be 5, since 5+18 = 23. Or you could think of it like 23-18 = 5.<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%2CA%29%2C%0D%0Alocate%282.6%2C2.8%2CB%29%2C%0D%0Alocate%281%2C-2.6%2CC%29%2C%0D%0Alocate%28-2%2C1.8%2C5%29%2C%0D%0Alocate%28-1.5%2C0%2C18%29%0D%0A%29%0D%0A ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "12 use brand A but not brand C.<BR>\n" );
document.write( "We already have 5 people who use brand A exclusively, so the remaining 12-5 = 7 people must use brand A but not brand C.\r<BR>\n" );
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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%2CA%29%2C%0D%0Alocate%282.6%2C2.8%2CB%29%2C%0D%0Alocate%281%2C-2.6%2CC%29%2C%0D%0Alocate%28-2%2C1.8%2C5%29%2C%0D%0Alocate%280%2C1.8%2C7%29%2C%0D%0Alocate%28-1.5%2C0%2C18%29%0D%0A%29%0D%0A ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "At this point, we almost have all of the regions pertaining to circle A. The missing part is where all 3 circles overlap.\r<BR>\n" );
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document.write( "The values so far in circle A are: 5, 7, 18<BR>\n" );
document.write( "They add to 5+7+18 = 30<BR>\n" );
document.write( "There are 30 housewives so far that use brand A (and some use other brands as well).<BR>\n" );
document.write( "The instructions state that 65 women use brand A, so 65-30 = 35 must use all three brands.\r<BR>\n" );
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document.write( "We'll place this value in the overlapped portion of all 3 circles.<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%2CA%29%2C%0D%0Alocate%282.6%2C2.8%2CB%29%2C%0D%0Alocate%281%2C-2.6%2CC%29%2C%0D%0Alocate%28-2%2C1.8%2C5%29%2C%0D%0Alocate%280%2C1.8%2C7%29%2C%0D%0Alocate%28-1.5%2C0%2C18%29%2C%0D%0Alocate%280%2C0.4%2C35%29%0D%0A%29%0D%0A ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Circle A is completely filled out.\r<BR>\n" );
document.write( "<BR>\n" );
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document.write( "Next, we're told that \"115 use B and C\"<BR>\n" );
document.write( "So the numbers in the overlapped region of circles B and C must add to 115<BR>\n" );
document.write( "There are already 35 who use all three brands, so 115-35 = 80 use brand B and brand C, but not brand A.<BR>\n" );
document.write( "Let's update the venn diagram\r<BR>\n" );
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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%2CA%29%2C%0D%0Alocate%282.6%2C2.8%2CB%29%2C%0D%0Alocate%281%2C-2.6%2CC%29%2C%0D%0Alocate%28-2%2C1.8%2C5%29%2C%0D%0Alocate%280%2C1.8%2C7%29%2C%0D%0Alocate%28-1.5%2C0%2C18%29%2C%0D%0Alocate%280%2C0.4%2C35%29%2C%0D%0Alocate%281.2%2C0%2C80%29%0D%0A%29%0D%0A ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
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document.write( "Circle B is almost complete.<BR>\n" );
document.write( "The values in this circle add to: 7+35+80 = 122<BR>\n" );
document.write( "And there are 140 who use brand B, which tells us there are 140-122 = 18 people who use brand B only.<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%2CA%29%2C%0D%0Alocate%282.6%2C2.8%2CB%29%2C%0D%0Alocate%281%2C-2.6%2CC%29%2C%0D%0Alocate%28-2%2C1.8%2C5%29%2C%0D%0Alocate%280%2C1.8%2C7%29%2C%0D%0Alocate%282%2C1.8%2C18%29%2C%0D%0Alocate%28-1.5%2C0%2C18%29%2C%0D%0Alocate%280%2C0.4%2C35%29%2C%0D%0Alocate%281.2%2C0%2C80%29%0D%0A%29%0D%0A ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "We're done with Circle B.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Now onto circle C.<BR>\n" );
document.write( "The values add to 18+35+80 = 133<BR>\n" );
document.write( "There are 145 people who use brand C, so the remaining 145-133 = 12 housewives use brand C exclusively.<BR>\n" );
document.write( "Let's update the venn diagram.\r<BR>\n" );
document.write( "\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%2CA%29%2C%0D%0Alocate%282.6%2C2.8%2CB%29%2C%0D%0Alocate%281%2C-2.6%2CC%29%2C%0D%0Alocate%28-2%2C1.8%2C5%29%2C%0D%0Alocate%280%2C1.8%2C7%29%2C%0D%0Alocate%282%2C1.8%2C18%29%2C%0D%0Alocate%28-1.5%2C0%2C18%29%2C%0D%0Alocate%280%2C0.4%2C35%29%2C%0D%0Alocate%281.2%2C0%2C80%29%2C%0D%0Alocate%280%2C-1.5%2C12%29%0D%0A%29%0D%0A ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "All of the circles are now completely filled in.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The missing number is what goes outside the three circles. This represents the subset of women who don't use any of the three brands mentioned.\r<BR>\n" );
document.write( "<BR>\n" );
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document.write( "Let's add up all of the values inside those circles.<BR>\n" );
document.write( "5+7+18+18+35+80+12 = 175\r<BR>\n" );
document.write( "<BR>\n" );
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document.write( "There are 175 housewives who use one or more of brand A,B, and/or C.<BR>\n" );
document.write( "This is out of the 180 housewives surveyed. <BR>\n" );
document.write( "Therefore, there must be 180-175 = 5 housewives who don't use any of the 3 brands.<BR>\n" );
document.write( "We place this new value outside of the circles.\r<BR>\n" );
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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%2CA%29%2C%0D%0Alocate%282.6%2C2.8%2CB%29%2C%0D%0Alocate%281%2C-2.6%2CC%29%2C%0D%0Alocate%28-2%2C1.8%2C5%29%2C%0D%0Alocate%280%2C1.8%2C7%29%2C%0D%0Alocate%282%2C1.8%2C18%29%2C%0D%0Alocate%28-1.5%2C0%2C18%29%2C%0D%0Alocate%280%2C0.4%2C35%29%2C%0D%0Alocate%281.2%2C0%2C80%29%2C%0D%0Alocate%280%2C-1.5%2C12%29%2C%0D%0Alocate%283%2C-1.5%2C5%29%0D%0A%29%0D%0A ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The venn diagram is complete.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "You can use this venn diagram to answer parts (b) and (c). <BR>\n" );
document.write( "I'll let the student take over from here.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "More practice with venn diagrams (that have 3 circles)<BR>\n" );
document.write( "<a  rel=nofollow HREF= \"https://www.algebra.com/algebra/homework/Subset/Subset.faq.question.1196992.html\">https://www.algebra.com/algebra/homework/Subset/Subset.faq.question.1196992.html</a><BR>\n" );
document.write( "and<BR>\n" );
document.write( "<a  rel=nofollow HREF= \"https://www.algebra.com/algebra/homework/Finance/Finance.faq.question.1201924.html\">https://www.algebra.com/algebra/homework/Finance/Finance.faq.question.1201924.html</a><BR>\n" );
document.write( "and<BR>\n" );
document.write( "<a  rel=nofollow HREF= \"https://www.algebra.com/algebra/homework/sets-and-operations/sets-and-operations.faq.question.1199899.html\">https://www.algebra.com/algebra/homework/sets-and-operations/sets-and-operations.faq.question.1199899.html</a><BR>\n" );
document.write( "and<BR>\n" );
document.write( "<a  rel=nofollow HREF= \"https://www.algebra.com/algebra/homework/Subset/Subset.faq.question.1192015.html\">https://www.algebra.com/algebra/homework/Subset/Subset.faq.question.1192015.html</a><BR>\n" );
document.write( "I also recommend searching out for other examples on YouTube so you can see how the venn diagram is filled out in a step-by-step process.<BR>\n" );
document.write( "</font> </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );