document.write( "Question 184848: Please help me with the following questions.I dont understand what Im doing.\r
\n" ); document.write( "\n" ); document.write( "In a survey of 75 consumers, 12 indicated that they were going to buy a new car, 18 said they were going to buy a new refrigerator, and 24 said they were going to buy a new washer. Of these, 6 were going to buy both a car and a refrigerator, 4 were going to buy a car and a washer, and 10 were going to buy a washer and a refrigerator. One person indicated that she was going to buy all three items.
\n" ); document.write( "Construct a Venn diagram, label your diagram clearly. Use your diagram to answer the following questions:
\n" ); document.write( "(a) How many were going to buy only a car?
\n" ); document.write( "(b) How many were going to buy only a washer?
\n" ); document.write( "(c) How many were going to buy only a refrigerator
\n" ); document.write( "(d) How many were going to buy a car and a washer but not a refrigerator?
\n" ); document.write( "(e) How many were going to buy none of these items? \r
\n" ); document.write( "\n" ); document.write( "Please help me \n" ); document.write( "

Algebra.Com's Answer #138722 by Edwin McCravy(20060) $\"\"$ $\"About$

You can put this solution on YOUR website!
Edwin's solution with Venn Diagram:
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document.write( "In a survey of 75 consumers, 12 indicated that they were going to buy a new\r\n" );
document.write( "car, 18 said they were going to buy a new refrigerator, and 24 said they were\r\n" );
document.write( "going to buy a new washer. Of these, 6 were going to buy both a car and a\r\n" );
document.write( "refrigerator, 4 were going to buy a car and a washer, and 10 were going to buy\r\n" );
document.write( "a washer and a refrigerator. One person indicated that she was going to buy all\r\n" );
document.write( "three items. \r\n" );
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document.write( "First draw a big square or rectangle to hold all 75 consumers:\r\n" );
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document.write( " \r\n" );
document.write( "Next draw a circle to hold all 12 consumers who said they\r\n" );
document.write( "were going to buy a new car and label it C (for \"car\"):\r\n" );
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document.write( " \r\n" );
document.write( "Next draw a circle overlapping the first to hold all \r\n" );
document.write( "18 consumers who said they were going to buy a refrigerator and label\r\n" );
document.write( "it R. (The overlapping part will contain the consumers who said\r\n" );
document.write( "they were going to buy a new car and a refrigerator).\r\n" );
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document.write( " \r\n" );
document.write( "Next draw a circle overlapping the first two circles\r\n" );
document.write( "to hold all the consumers who said they were going to\r\n" );
document.write( "buy a new washer and label it W: \r\n" );
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document.write( " \r\n" );
document.write( "This gives us 8 regions to classify cnsumers with\r\n" );
document.write( "according to what they said they were going to buy:\r\n" );
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document.write( "There is only one statements which immediately give \r\n" );
document.write( "us complete information about any of the 8 regions are these:\r\n" );
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document.write( "This one:\r\n" );
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document.write( ">>...One person indicated that she was going to buy all\r\n" );
document.write( "three items...<<\r\n" );
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document.write( "So we will fill 1 in the middle region which is the\r\n" );
document.write( "only region common to all three circles:\r\n" );
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document.write( "\r\n" );
document.write( "Next we look at this statement\r\n" );
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document.write( ">>...6 were going to buy both a car and a refrigerator...<<\r\n" );
document.write( " \r\n" );
document.write( "These 6 are in the region where circles C and R overlap.\r\n" );
document.write( "There is already 1 accounted for in there, so we write\r\n" );
document.write( "the other 5 of the 6 in the other part of the overlapping \r\n" );
document.write( "part of C and R:\r\n" );
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document.write( "\r\n" );
document.write( " \r\n" );
document.write( "-----\r\n" );
document.write( "\r\n" );
document.write( "Next we look at this statement\r\n" );
document.write( " \r\n" );
document.write( ">>...4 were going to buy a car and a washer...<<\r\n" );
document.write( " \r\n" );
document.write( "These 4 are in the region where circles C and W overlap.\r\n" );
document.write( "There is already 1 accounted for in there, so we put\r\n" );
document.write( "the other 3 of the 4 in the other part of the \r\n" );
document.write( "overlapping part of C and W:\r\n" );
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document.write( "\r\n" );
document.write( "\r\n" );
document.write( "-----\r\n" );
document.write( "\r\n" );
document.write( "Next we look at this statement\r\n" );
document.write( "\r\n" );
document.write( ">>...10 were going to buy a washer and a refrigerator...<<\r\n" );
document.write( " \r\n" );
document.write( "These 10 are in the region where circles W and R overlap.\r\n" );
document.write( "There is already 1 accounted for in there, so we put\r\n" );
document.write( "the other 9 of the 10 in the other part of the overlapping \r\n" );
document.write( "part of W and R:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "-----\r\n" );
document.write( "Next we look at this statement\r\n" );
document.write( "\r\n" );
document.write( ">>...12 indicated that they were going to buy a new car...<<\r\n" );
document.write( " \r\n" );
document.write( "These 12 make up the total in the entire circle C\r\n" );
document.write( "There are already 5+1+3 or 9 of these 12 accounted for \r\n" );
document.write( "in circle C, so we put the other 3 of the 12 in the \r\n" );
document.write( "upper left part of circle C:\r\n" );
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document.write( "\r\n" );
document.write( "\r\n" );
document.write( "-----\r\n" );
document.write( "\r\n" );
document.write( "Next we look at this statement\r\n" );
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document.write( ">>...18 said they were going to buy a new refrigerator...<<\r\n" );
document.write( " \r\n" );
document.write( "These 18 make up the total in the entire circle R.\r\n" );
document.write( "There are already 5+1+9 or 15 of these 18 accounted for \r\n" );
document.write( "in circle R, so we put the other 3 of the 18 in the \r\n" );
document.write( "upper right part of circle R:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "-----\r\n" );
document.write( "\r\n" );
document.write( "Next we look at this statement\r\n" );
document.write( "\r\n" );
document.write( ">>...24 said they were going to buy a new washer...<<\r\n" );
document.write( " \r\n" );
document.write( "These 24 make up the total in the entire circle W.\r\n" );
document.write( "There are already 3+1+9 or 13 of these 24 accounted for \r\n" );
document.write( "in circle W, so we put the other 11 of the 24 in the \r\n" );
document.write( "lower part of circle W:\r\n" );
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document.write( "\r\n" );
document.write( "\r\n" );
document.write( "-----\r\n" );
document.write( "\r\n" );
document.write( "Next we look at these words:\r\n" );
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document.write( ">>...In a survey of 75 consumers...<<\r\n" );
document.write( " \r\n" );
document.write( "Now we see how many of the 75 consumers we\r\n" );
document.write( "have accounted for.  They are\r\n" );
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document.write( "3+5+3+3+1+9+11 or 35, so there are 75-35 or\r\n" );
document.write( "40 more of the 75 left to account for.  These\r\n" );
document.write( "40 are outside all the circles.  So let's\r\n" );
document.write( "write 40 in the region outside all the\r\n" );
document.write( "three circles, but inside the rectangle.  I'll\r\n" );
document.write( "put it in the bottom left, although it could go\r\n" );
document.write( "anywhere in that outer region.\r\n" );
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document.write( "Now we can answer the questions:\r\n" );
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document.write( "(a)	How many were going to buy only a car? \r\n" );
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document.write( "These are the 3 in the upper left region of circle C.\r\n" );
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document.write( "(b)	How many were going to buy only a washer? \r\n" );
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document.write( "These are the 11 in the lower region of circle W.\r\n" );
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document.write( "(c)	How many were going to buy only a refrigerator\r\n" );
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document.write( "These are the 3 in the upper rightt region of circle R.\r\n" );
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document.write( "(d)	How many were going to buy a car and a washer but not a refrigerator? \r\n" );
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document.write( "These are the 5 in the region in the middle above which\r\n" );
document.write( "is part of bot circles C and R but not part of W.\r\n" );
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document.write( "(e)	How many were going to buy none of these items?\r\n" );
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document.write( "These are the 40 which are outside all the circles.\r\n" );
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document.write( "Edwin

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