Problem 3. Three girls, Ana, Maria, and Elena, collected 770 acorns in the forest and decided to divide them among themselves proportionally to their ages. Every time Maria took 4 acorns, Ana took 3, and for every 6 that Maria took, Elena took 7 acorns. How old is each girl if together they are 35 years old? How many acorns did each of them get?
Solution. Let $a$ be the age of Ana, $m$ be the age of Maria, and $e$ be the age of Elena. Then, according to the problem, $a+m+e=35$. The ages are related like the bones, and that is:

$$
\begin{aligned}
& m: a=4: 3, \quad m: e=6: 7 \\
& a=\frac{3}{4} m, \quad e=\frac{7}{6} m
\end{aligned}
$$

Now,

$$
\begin{aligned}
& m+\frac{3}{4} m+\frac{7}{6} m=35 \\
& \frac{12 m+9 m+14 m}{12}=35 \\
& \frac{35}{12} m=35 \\
& m=12, \quad a=\frac{3}{4} \cdot 12=9, \quad e=\frac{7}{6} \cdot 12=14
\end{aligned}
$$

Since $770: 35=22$, it follows that Maria has $22 \cdot 12=264$ bones, Ana has $22 \cdot 9=198$ bones, and Elena has $22 \cdot 14=308$ bones.