Question

Mary was making sandwiches for the class picnic. 13 of the sandwiches had a slice of cheese. 14 had a slice of salami. 13 had a slice of tomato. 8 had a slice of cheese & a slice of tomato. Only 3 had a just a slice of salami. 5 had a slice of tomato, a slice of cheese, & a slice of salami. 8 had a slice of tomato & a slice of salami. How many sandwiches did Mary make for the class picnic?

Answer 1

Using Venn diagram, start filling in the information

Put 5 in the intersection of all three
C+T --> 8, but we have already accounted for 5 of those, so put 3 into the intersection of only C and T
only S --> 3, so put 3 into S which is not part of any intersection
C+S --> 8 , but we have already accounted for 5 of those, so put 3 into the intersection of only C and S

the whole C circle is 13 , but 3+3+5 or 11 are already counted, so the only C part is 2
We don't know what only S and T is, call it x
For S, x+5+3+3=14
x = 3
For T, we already have 11, but the total of T is 13
so we would need 2 for "only T" part.

Complete C the same way, I get 2 for the "only C" part
Now add up all the components,
for a total of 21 sandwiches

Answer 2

How does this work though?