A grandfather gifted his two grandchildren, who were born on the same calendar day (in different years), with as many 10 forints as their age every birthday. When the sum of the grandchildren's ages was 30 years, it turned out that they had received a total of 2410 forints this way (including the gifts of that day). How old were the grandchildren at that time?
Let one of the grandchildren be $x$ years old, then the other is $30-x$ years old. According to the problem,

$$
(10+2 \cdot 10+\ldots+x \cdot 10)+[10+2 \cdot 10+\ldots+(30-x) \cdot 10]=2410
$$

Dividing by 10 and using the formula for the sum of an arithmetic series,

$$
\frac{x}{2}(1+x)+\frac{30-x}{2}(31-x)=241
$$

which simplifies to

$$
x^{2}-30 x+224=0
$$

from which

$$
\begin{aligned}
x_{1}=16, & \text { and } \quad x_{2}=14 \\
30-x_{1}=14, & \text { and } \quad 30-x_{2}=16
\end{aligned}
$$

Therefore, one of the grandchildren is 16 years old, and the other is 14 years old.

Beregi Péter (Bp. VI., Kölcsey g. IV. o. t.)