Question 484526: I'm having a problem with this set. The question is..
Prior to the 7:15 show at the local movie theater, 70 people visited the concession stand, Listed below is what they ordered
42 ordered popcorn
18 ordered candy
30 ordered a soda
10 ordered popcorn and candy
8 ordered soda and candy
12 ordered popcorn and soda
5 ordered popcorn, candy and soda
1. How many people ordered something other than popcorn, candy or soda?
2. How many people ordered popcorn and a soda but not candy?
3. How many people ordered candy or a soda but not popcorn?
4. How many people ordered popcorn or candy?
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
Draw a large rectangle. Inside of the rectangle draw three circles that partially overlap.
Label the circles P, C, and S.
In the very center where the three circles overlap, that is to say the one region on your diagram where you are inside of all three circles, put the number 5 representing the 5 people who ordered P, C, AND S.
The region where P and C overlap needs to contain the number of people who ordered ONLY P and C. The number 10 given for people who ordered P and C also includes those who ordered P, C, and S. So from the given 10 subtract those that ordered all three, that is 10 minus 5 = 5. And you put 5 into the P and C only region. Similarly, since 12 minus 5 equals 7, you put 7 in the P & S only region. Then, since the number who ordered P includes those who ordered P & C, those who ordered P & S, AND those who ordered all three, add up 5 plus 7 plus 5 = 17, then subtract 17 from the 42 we are told ordered P to arrive at 25 who ordered ONLY P. Use similar logic to fill in the rest of your diagram.
Next add all of the numbers that you have entered in your diagram. Subtract that result from 70, the number of people surveyed, to get the number of people who did not order P, S, OR C. Several of us only wanted ice cream. Write that number in the rectangle outside of all of the circles.
You should be able to answer all of the questions posed just from the data in your diagram.
John
My calculator said it, I believe it, that settles it
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