# SOLUTION: Please help me with the following questions.I dont understand what Im doing. In a survey of 75 consumers, 12 indicated that they were going to buy a new car, 18 said they were g

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 Click here to see ALL problems on Miscellaneous Word Problems Question 184848: Please help me with the following questions.I dont understand what Im doing. 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. Construct a Venn diagram, label your diagram clearly. Use your diagram to answer the following questions: (a) How many were going to buy only a car? (b) How many were going to buy only a washer? (c) How many were going to buy only a refrigerator (d) How many were going to buy a car and a washer but not a refrigerator? (e) How many were going to buy none of these items? Please help meFound 2 solutions by josmiceli, Edwin McCravy:Answer by josmiceli(9671)   (Show Source): You can put this solution on YOUR website!What you have to draw is 3 interlocking circles with an area in the middle which is common to all 3. Kind of like the olympic rings. 1 ring will be consumers who bought refrigerators 1 ring will be consumers who bought cars 1 ring will be consumers who bought washers All the small and big areas making up the rings adds up to the total number of people buying items Right away I'm told that the car ring contains 12 people, the fridge ring contains 18 people, and the washer ring contains 24 people What I do is label each ring just outside of it like this: Of these, 6 were going to buy both a car and a refrigerator Locate the small area where c and f overlap, and put a inside it. 4 were going to buy a car and a washer. This is the area common to c and w. Put a 4 inside it 10 were going to buy a washer and a refrigerator Label the intersection of w and f with a 10 One person indicated that she was going to buy all three items. This last fact gives you all the answers. It's the key. The intersection of c and f = 6, but 1 of those is the last person, so 6 - 1 = 5 persons will buy ONLY both f and c. 10 - 1 = 9 persons will buy ONLY both w and f. 4 - 1 = 3 persons will buy ONLY both w and c. Now you should be able to label every area on the diagram (a) How many were going to buy only a car? 3 (b) How many were going to buy only a washer? 11 (c) How many were going to buy only a refrigerator 3 (d) How many were going to buy a car and a washer but not a refrigerator? 3 (e) How many were going to buy none of these items? 40 I come up with a total of 35 persons buying items c = 3 w = 11 f = 3 w+c only = 3 f+c only = 5 w+f only = 9 All 3 = 1 ------------ 35 total The trick is not to count the sme area twice. Hope I got the right answers and my method helps you Answer by Edwin McCravy(8908)   (Show Source): You can put this solution on YOUR website!Edwin's solution with Venn Diagram: ``` 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. First draw a big square or rectangle to hold all 75 consumers: Next draw a circle to hold all 12 consumers who said they were going to buy a new car and label it C (for "car"): Next draw a circle overlapping the first to hold all 18 consumers who said they were going to buy a refrigerator and label it R. (The overlapping part will contain the consumers who said they were going to buy a new car and a refrigerator). Next draw a circle overlapping the first two circles to hold all the consumers who said they were going to buy a new washer and label it W: This gives us 8 regions to classify cnsumers with according to what they said they were going to buy: There is only one statements which immediately give us complete information about any of the 8 regions are these: This one: >>...One person indicated that she was going to buy all three items...<< So we will fill 1 in the middle region which is the only region common to all three circles: Next we look at this statement >>...6 were going to buy both a car and a refrigerator...<< These 6 are in the region where circles C and R overlap. There is already 1 accounted for in there, so we write the other 5 of the 6 in the other part of the overlapping part of C and R: ----- Next we look at this statement >>...4 were going to buy a car and a washer...<< These 4 are in the region where circles C and W overlap. There is already 1 accounted for in there, so we put the other 3 of the 4 in the other part of the overlapping part of C and W: ----- Next we look at this statement >>...10 were going to buy a washer and a refrigerator...<< These 10 are in the region where circles W and R overlap. There is already 1 accounted for in there, so we put the other 9 of the 10 in the other part of the overlapping part of W and R: ----- Next we look at this statement >>...12 indicated that they were going to buy a new car...<< These 12 make up the total in the entire circle C There are already 5+1+3 or 9 of these 12 accounted for in circle C, so we put the other 3 of the 12 in the upper left part of circle C: ----- Next we look at this statement >>...18 said they were going to buy a new refrigerator...<< These 18 make up the total in the entire circle R. There are already 5+1+9 or 15 of these 18 accounted for in circle R, so we put the other 3 of the 18 in the upper right part of circle R: ----- Next we look at this statement >>...24 said they were going to buy a new washer...<< These 24 make up the total in the entire circle W. There are already 3+1+9 or 13 of these 24 accounted for in circle W, so we put the other 11 of the 24 in the lower part of circle W: ----- Next we look at these words: >>...In a survey of 75 consumers...<< Now we see how many of the 75 consumers we have accounted for. They are 3+5+3+3+1+9+11 or 35, so there are 75-35 or 40 more of the 75 left to account for. These 40 are outside all the circles. So let's write 40 in the region outside all the three circles, but inside the rectangle. I'll put it in the bottom left, although it could go anywhere in that outer region. Now we can answer the questions: (a) How many were going to buy only a car? These are the 3 in the upper left region of circle C. (b) How many were going to buy only a washer? These are the 11 in the lower region of circle W. (c) How many were going to buy only a refrigerator These are the 3 in the upper rightt region of circle R. (d) How many were going to buy a car and a washer but not a refrigerator? These are the 5 in the region in the middle above which is part of bot circles C and R but not part of W. (e) How many were going to buy none of these items? These are the 40 which are outside all the circles. Edwin```