3. The class mini bookshelf has a total of 12 science popularization books. According to statistics, each member of the math group has borrowed exactly two of them, and each science popularization book has been borrowed by exactly 3 members of the math group. How many people are there in this math group?
3. The class mini bookshelf has a total of 12 science popularization books. According to statistics, each member of the math group has borrowed exactly two of them, and each science popularization book has been borrowed by exactly 3 members of the math group. How many people are there in this math group?
【Analysis】Since the mini bookshelf has a total of 12 science popularization books, and each book has been borrowed by exactly 3 members of the math group, the total number of borrowings is $12 \times 3=36$ (person-times). Let the math group have $x$ people. Since each member of the math group has borrowed exactly two books, the total number of borrowings is $2 x$ person-times. Therefore, we have $2 x=36$, and then solve it.
【Solution】Let the math group have $x$ people,
Each science popularization book has been borrowed by exactly 3 members of the math group, so the total number of borrowings is $12 \times 3=36$ (person-times). Since each member of the math group has borrowed exactly two books, the total number of borrowings is $2 x$ person-times,
So, $2 x=36$,
Solving for $x$, we get: $x=18$,
Answer: This math group has 18 people.