2. On the day when Dima's brother and sister were congratulating him on his birthday, Dima said: "Look how interesting, I am now twice as old as my brother and three times as old as my sister!" - "And your average age is 11 years," - added Dad. How old did Dima turn?
Answer: 18 years.

Solution. The first method. According to the problem, we can form an equation. Let Dima's age be $x$ years, then his sister's age is $x / 3$, and his brother's age is $-x / 2 ;(x+x / 3+x / 2): 3=11$. After solving this equation, we get that $x=18$. Dima is 18 years old.

It will be useful to provide another solution, "in parts."

The second method. If the ages of Dima, his brother, and sister are represented by segments, then "Dima's segment" consists of two "brother's segments" or three "sister's segments." Then, if Dima's age is divided into 6 parts, the sister's age is two such parts, and the brother's age is three such parts. Thus, the sum of their ages is 11 such parts. On the other hand, if the average age is 11 years, then the sum of the ages is 33 years. From this, it follows that one part is three years. Therefore, Dima is 18 years old.

## Grading criteria.

- Complete correct solution - 7 points.
- The equation is correctly set up, but errors are made in solving it - 3 points.
- The correct answer is provided and a check is performed - 2 points.
- Only the correct answer is provided - $\mathbf{0}$ points.