Anna and Josef are a married couple with eleven offspring. The average age of their two children is 63 years, the average age of their four grandchildren is 35 years, and the average age of their five great-grandchildren is 4 years. Anna's age is three and a half times the average age of all eleven offspring. If they live long enough, the average age of Anna and Josef will be 100 years in five years.

How old is Anna and how old is Josef?

(E. Semerádová)
The sum of the ages of all descendants is

$$
2 \cdot 63 + 4 \cdot 35 + 5 \cdot 4 = 286 \text{ years. }
$$

Their average age is $286: 11 = 26$ years. Therefore, Anna is $3.5 \cdot 26 = 91$ years old.

In five years, Anna will be 96 years old. For the average age of Anna and Josef to be 100 years, Josef will be 104 years old in five years. Therefore, Josef is currently 99 years old.

Note. The information about the average age of Anna and Josef can be written as follows:

$$
(91 + 5 + j + 5): 2 = 100
$$

where $j$ represents Josef's current age. From this, it follows that $j = 99$.

Evaluation. 3 points for the average age of all descendants; 1 point for Anna's age; 2 points for Josef's age.