Question 257069: A survey of residents in a community showed the following
information about their lunch eating habits:
29 ate salads
26 ate sandwiches
25 ate sweets
13 ate both a salad and a sandwich
11 ate both a sandwich and sweets
18 ate both a salad and sweets
6 ate all three types
7 ate none of them
How many ate sandwiches and sweets but not a salad?
Answer by drk(1908)   (Show Source):
You can put this solution on YOUR website! Draw a 3 circle Venn diagram and label each circle: salad, sandwich, and sweets.
PLace a small horizontal line in each space and then one on the outside of the Venn diagram. Numbers will go on these lines.
step 1 - place 7 on the outside line
step 2 - ALWAYS start from the "all three" number and work your way out.
6 goes into the center oval
I have
7, 6 in the salad - sandwich ovals
5, 6 in the sandwich, sweets ovals
12, 6 in the salad, sweets ovals
All by itself I have 8 sandwich, 2 sweet, and 9 salad
--
sandwiches and sweets is: 8 + 7 + 6 + 5 + 2 + 12 = 37
we minus the overlapping region of salad or 12 + 6 = 18 .
So, it appears we get 37-18 = 19 people.
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