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There are 68 children in the cafeteria of a school and all [#permalink]
04 May 2006, 17:34

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There are 68 children in the cafeteria of a school and all of the children have something for lunch. Thirty-four of the children brought lunches from home, 23 of the children bought a drink from the cafeteria beverage machine, and 32 of the children bought fruit in the cafeteria. If 18 children did at least 2 of these things, how many children did exactly two of these things?

(# All 3) = x
(# Drink + Home) = w
(# Drink + Fruit) = y
(# Home + Fruit) = z
(# Drink only) = 23-w-x-y
(# Home only) = 34-w-x-z
(# Fruit only) = 32-x-y-z

So:

34-x-w-z + 32-x-y-z + 23-w-x-y + x + y + z + w = 68