In a room, there is a group of 11 people, with the average age being exactly 25 years. A second group of 7 people arrives, and the average age in the room then becomes exactly 32 years. What is the average age of the second group?
Answer: 43. Let $x$ be the average age of the second group. We have ( $11 \times$ $25+7 x) / 18=32$, so $275+7 x=18 \times 32$, which gives $x=(18 \times 32-275) / 7=43$.