Problem 5. For his birthday, Filip received 405 denars from his grandmother and grandfather. From his grandmother, he received 3 times more money than her age, and from his grandfather, four times more money than his age. How old are Filip's grandmother and grandfather if it is known that his grandfather is 5 years older than his grandmother.
Solution. If Philip's grandmother is $x$ years old, his grandfather is $x+5$ years old. For his birthday, his grandmother gave him $3 x$ denars and his grandfather gave him $4 x+20$ denars. Together, they gave him $7 x+20$ denars. Therefore,

$$
\begin{aligned}
& 7 x+20=405 \\
& 7 x=385 \\
& x=385: 7=55
\end{aligned}
$$

Thus, his grandmother was 55 years old, and his grandfather was 60 years old.

## V section