document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=198485>Question 198485</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Thank you so much this teacher is picking me a part with these problem please help.\r<BR>\n" );
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document.write( ") In a survey of 100 consumers, 33 indicated that they were going to buy a new car, 18 said they were going to buy a new refrigerator, and 34 said they were going to buy a new washer. Of these, 7 were going to buy both a car and a refrigerator, 15 were going to buy a car and a washer, and 9 were going to buy a washer and a refrigerator. Three consumers indicated that they were going to buy all three items. \r<BR>\n" );
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document.write( "Construct a Venn diagram, label your diagram clearly.  <BR>\n" );
document.write( "Use your diagram to answer the following questions:\r<BR>\n" );
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document.write( "(a)	How many were going to buy only a car? <BR>\n" );
document.write( "(b)	How many were going to buy only a washer? <BR>\n" );
document.write( "(c)	How many were going to buy only a refrigerator<BR>\n" );
document.write( "(d)	How many were going to buy a car and a washer but not a refrigerator? <BR>\n" );
document.write( "(e)	How many were going to buy none of these items\r<BR>\n" );
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document.write( "thank you so much </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #149026 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=149026\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> (1) Draw a circle that represents the consumers that are going to buy <BR>\n" );
document.write( "a new car. What I do sometimes to avoid confusion is to label the  <BR>\n" );
document.write( "circle right in the center with a \"c\"<BR>\n" );
document.write( "Don't even worry about numbers at this point.<BR>\n" );
document.write( "(2) Some consumers are going to buy a refrigerator, and, reading<BR>\n" );
document.write( "ahead, some of these are also buying a new car. So, now draw a <BR>\n" );
document.write( "circle that intersects the refrigerator circle, and label it in the center<BR>\n" );
document.write( "with a small \"r\" Where the circle intersects the new car circle,<BR>\n" );
document.write( "label that intersection with \"c x r\" <BR>\n" );
document.write( "Make sure you leave some room for other circles. Don't worry about numbers. <BR>\n" );
document.write( "(3) This is the tricky part. A third circle will represent the<BR>\n" );
document.write( "washing machine buyers. Some of these are new car buyers also, and<BR>\n" );
document.write( "some are refrigerator buyers, so this new circle will intersect both<BR>\n" );
document.write( "the \"c\" circle and the \"r\" circle. Label the new circle \"w\"<BR>\n" );
document.write( "Label the intersection with \"c\", \"c x w\"<BR>\n" );
document.write( "Label the intersection with \"r\", \"r + w\"<BR>\n" );
document.write( "(4) There is one last bit of information: some of the washing machine<BR>\n" );
document.write( "buyers are buying all three things. This is the small intersection of<BR>\n" );
document.write( "the three circles. If your picture doesn't have this small intersection,<BR>\n" );
document.write( "redraw it. It will be \"w + c + r\". I just draw an arrow pointing to<BR>\n" );
document.write( "it and put this label outside the circles.<BR>\n" );
document.write( "(5) If the drawing is right, and you can make sense of it, then you<BR>\n" );
document.write( "can proceed with the numbers and answer any question about it.<BR>\n" );
document.write( "The labels you have are:<BR>\n" );
document.write( "\"c\" ALL the new car buyers<BR>\n" );
document.write( "\"r\" ALL the refrigerator buyers<BR>\n" );
document.write( "\"c x r\" ALL those who will buy both car and refrigerator<BR>\n" );
document.write( "\"w x c\" ALL those who will buy washing machine and car<BR>\n" );
document.write( "\"w x r\" ALL those who will buy washing machine and refrigerator<BR>\n" );
document.write( "\"w x c x r\" those who will buy all three things<BR>\n" );
document.write( "The really tricky part is to realize that intersections like<BR>\n" );
document.write( "\"c x r\" also INCLUDE the ones that buy all three.<BR>\n" );
document.write( "Try to see the circles two at a time, ignoring the third.<BR>\n" );
document.write( "I hope this helps:<BR>\n" );
document.write( "(A)  How many were going to buy only a car? That means no washer, no frige<BR>\n" );
document.write( "I'm told that 7 will buy \"c x r\" and 15 will buy \"c x w\"<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=33+-+7+-+15+=+11 ALIGN=MIDDLE  ALT=\"33+-+7+-+15+=+11\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "Tricky part: I an subtracting the \"c x r x w = 3\" group <BR>\n" );
document.write( "they are being subtracted twice, so to subtract them once, I need to add<BR>\n" );
document.write( "back <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" > so, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=33+-+7+-+15+%2B+3+=+14 ALIGN=MIDDLE  ALT=\"33+-+7+-+15+%2B+3+=+14\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "14 will buy only a car<BR>\n" );
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document.write( "(B) Those only buying a washer will not buy car or frige.<BR>\n" );
document.write( "I need to subtract from <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w+=+34 ALIGN=MIDDLE  ALT=\"w+=+34\"   DISABLED_style= \"max-width:90%; height:auto;\" > the intersections \"w x c\"<BR>\n" );
document.write( "and \"w x r\", so I get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=34+-+15+-+9+=+10 ALIGN=MIDDLE  ALT=\"34+-+15+-+9+=+10\"   DISABLED_style= \"max-width:90%; height:auto;\" >, but remember, by<BR>\n" );
document.write( "subtracting these two groups, I am subtracting \"w x c x r\" twice<BR>\n" );
document.write( "so, I'll add back 3 once<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=34+-+15+-+9+%2B+3+=+13 ALIGN=MIDDLE  ALT=\"34+-+15+-+9+%2B+3+=+13\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "13 will buy only a washer<BR>\n" );
document.write( "---------------------------<BR>\n" );
document.write( "(C) How many were going to buy only a refrigerator?<BR>\n" );
document.write( "I need to subtract from \"r\" the intersections \"r x w\" and \"r x c\"<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=18+-+9+-+7+=+12 ALIGN=MIDDLE  ALT=\"18+-+9+-+7+=+12\"   DISABLED_style= \"max-width:90%; height:auto;\" >, again, I am subtracting \"c x r x w\" twice,<BR>\n" );
document.write( "so I'll add it back once. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=18+-+9+-+7+%2B+3+=+5 ALIGN=MIDDLE  ALT=\"18+-+9+-+7+%2B+3+=+5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "5 will buy only a frige<BR>\n" );
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document.write( "(D) How many were going to buy a car and a washer but not a refrigerator?<BR>\n" );
document.write( "\"c x w = 15\", but some of those will buy friges. How many? It's<BR>\n" );
document.write( "the ones who will buy \"c x r x w\", so subtract 3<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15+-+3+=+12 ALIGN=MIDDLE  ALT=\"15+-+3+=+12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "12 will buy \"c x w\" but not \"r\"<BR>\n" );
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document.write( "(E) How many were going to buy none of these items?<BR>\n" );
document.write( "Not an easy question. What I have to do is add up the contents <BR>\n" );
document.write( "of the three circles WITHOUT overlaps, that is not counting<BR>\n" );
document.write( "anything twice.<BR>\n" );
document.write( "I can make use of the questions I've answered.<BR>\n" );
document.write( "ONLY \"c\" plus ONLY \"w\" plus ONLY \"r\" = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=14+%2B+13+%2B+5+=+32 ALIGN=MIDDLE  ALT=\"14+%2B+13+%2B+5+=+32\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "OK, but this ignores all the intersections, so I have to add in<BR>\n" );
document.write( "\"c x w\" PLUS \"c x r\" PLUS \"r x w\" = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7+%2B+15+%2B+9+=+31 ALIGN=MIDDLE  ALT=\"7+%2B+15+%2B+9+=+31\"   DISABLED_style= \"max-width:90%; height:auto;\" >, but<BR>\n" );
document.write( "by doing this, I have added \"c x r x w\" three times, so I need to<BR>\n" );
document.write( "subtract it twice. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7+%2B+15+%2B+9+-+3+-+3+=+25 ALIGN=MIDDLE  ALT=\"7+%2B+15+%2B+9+-+3+-+3+=+25\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "And <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=32+%2B+25+=+57 ALIGN=MIDDLE  ALT=\"32+%2B+25+=+57\"   DISABLED_style= \"max-width:90%; height:auto;\" > so, there are 57 buyers without counting<BR>\n" );
document.write( "anyone twice. There were 100 consumers surveyed, so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=100+-+57+=+43 ALIGN=MIDDLE  ALT=\"100+-+57+=+43\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "43 will buy none of the items<BR>\n" );
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document.write( "Chcking my answer, If I add up<BR>\n" );
document.write( "ONLY \"c\" PLUS \"r\" PLUS ONLY \"w\" PLUS \"c x w\" MINUS \"c x r x w\", then I<BR>\n" );
document.write( "should get the result <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=57 ALIGN=MIDDLE  ALT=\"57\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "ONLY \"c\" = 14<BR>\n" );
document.write( "\"r\" = 18<BR>\n" );
document.write( "ONLY \"w\" = 13<BR>\n" );
document.write( "\"c x w\" = 15<BR>\n" );
document.write( "\"c x r x w = 3<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=14+%2B+18+%2B+13+%2B+15+-+3+=+57 ALIGN=MIDDLE  ALT=\"14+%2B+18+%2B+13+%2B+15+-+3+=+57\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "OK \r<BR>\n" );
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