Math

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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?

  • Math -

    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

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