Task 1. Three girls, Ana, Maja, and Aleksandra, collected 770 strawberries in the forest and decided to divide them proportionally according to their ages. Whenever Maja took 4 strawberries, Ana took 3 strawberries, and for every 6 strawberries Maja took, Aleksandra took 7 strawberries. How old is each of the girls if it is known that together they are 35 years old? How many strawberries did each of them get?
Solution. Let the ages of Ana, Maja, and Aleksandar be denoted by $x, y$, and $z$, respectively. From the condition of the problem, we have,

$$
\left\{\begin{array}{c}
x+y+z=35 \\
y: x=4: 3 \\
y: z=6: 7
\end{array}\right.
$$

It follows that $x=\frac{3}{4} y$ and $z=\frac{7}{6} y$, so by substituting into $x+y+z=35$, we get $x=9$, $y=12$, and $z=14$. Since $770: 35=22$, we find that Ana received $9 \cdot 22=198$ eggs, Maja received $12 \cdot 22=264$ eggs, and Aleksandar received $22 \cdot 14=308$ eggs.