The average age of the Kebulov family, consisting of a father, a mother, and several children, is 18 years. When the father, who is 38 years old, is not included, the average age of the family is 14 years. How many children do the Kebulovs have?

(L. Hozová)
Let the number of members in this family be $n$. The sum of the ages of all members is equal to the product of the average age of the family and the number of members, that is, $18 \cdot n$. The family without the father has $n-1$ members, and the sum of the ages of these members is $14 \cdot(n-1)$. We know that this sum is 38 less than the sum of the ages of all members. Therefore, we arrive at the equation

$$
18 \cdot n=14 \cdot(n-1)+38
$$

after rearrangement, we get

$$
\begin{aligned}
4 n & =24 \\
n & =6 .
\end{aligned}
$$

The entire family has 6 members, so the Kebulovis have 4 children.

Evaluation. 2 points for setting up the equation; 2 points for justifying this setup; 1 point for solving the equation; 1 point for the correct conclusion.

Alternative solution. Ignoring the fact that there must be a certain age gap between children and parents, after reading the first sentence in the problem, one can imagine a family consisting only of 18-year-old members. After reading the second sentence, we can adjust our imagination and see a 38-year-old father and the rest of the members being 14 years old. The father's age has been increased by 20, and the age of the other members has been reduced by 4 each. To keep the sum of the ages of all family members the same when adjusting our imagination, the number of family members without the father must be $20: 4=5$. One of them is the mother, so the children must be 4.

Evaluation. 6 points.