## Birthday Party

#### Problem

At a birthday party, one-half drank only lemonade, one-third drank only cola, fifteen people drank neither, and nobody drinks both.

How many people were at the party?

#### Solution

As $1/2 + 1/3 = 3/6 + 2/6 = 5/6$, we know that $1/6$ drank neither.

So there must have been $6 \times 15 = 90$ people at the party.

Problem ID: 273 (21 Apr 2006) Difficulty: 1 Star