I am Ivan and I am three times younger than my father. I have brothers Vincent and Jakub, who are 11 and 9 years old. My age is equal to five times the third of the age of the younger of the brothers. A peculiarity of our family is that we were all born on April 12th, so today we are celebrating our birthdays.

How many years will it take for the age of our father to be equal to the sum of the ages of the three of us? (L. Hozová)
The younger of the brothers is 9 years old, so I am 15 years old $\left(\frac{9}{3} \cdot 5=15\right)$. I am three times younger than my father, so my father is 45 years old $(3 \cdot 15=45)$. The sum of the ages of the three of us brothers is 35 years $(11+9+15=35)$.

The father's age is 10 years older than the sum of the ages of the three of us brothers, and this difference decreases by 2 each year (the father gains 1 year, while the sum of our ages gains 3 years). The father's age will be the same as the sum of the ages of the three of us brothers in 5 years $(10: 2=5)$.

Evaluation. 3 points for partial results; 3 points for the calculation and quality of the commentary.

Note. The problem can be solved by successively adding years $k$ to the father's age and the sum of the brothers' ages until the difference is zero. Symbolically: in $r$ years, the father's age will be $45+r$, while the sum of the brothers' ages will be $35+3r$. The required equality, after rearrangement, gives

$$
\begin{aligned}
35+3 r & =45+r, \\
2 r & =10, \\
r & =5 .
\end{aligned}
$$

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