Three squirrel friends set out to gather hazelnuts. Zrzinka found twice as many as Pizizubka, and Ouska found three times as many as Pizizubka. On their way home, they chatted and peeled and ate their hazelnuts. Pizizubka ate half of all the hazelnuts she had gathered, Zrzinka ate a third of all her hazelnuts, and Ouska ate a quarter of hers. When they got home, the squirrels found that they had 196 hazelnuts left in total.

How many hazelnuts did each squirrel find?

(M. Petrová)

Hint. What fraction of all the collected hazelnuts did the squirrels bring home?
If the number of nuts that Pizizubka found is denoted by $x$, then Zrzečka found $2x$ nuts and Ouška found $3x$ nuts.

- Pizizubka ate half of her nuts, leaving her with $\frac{x}{2}$ nuts.
- Zrzečka ate a third of her nuts, leaving her with $\frac{2}{3} \cdot 2x = \frac{4}{3} x$ nuts.
- Ouška ate a quarter of her nuts, leaving her with $\frac{3}{4} \cdot 3x = \frac{9}{4} x$ nuts.

All the squirrels together were left with

$$
\left(\frac{1}{2} + \frac{4}{3} + \frac{9}{4}\right) x = \frac{49}{12} x
$$

nuts, which according to the problem is equal to 196. Thus,

$$
\begin{aligned}
\frac{49}{12} x & = 196 \\
\frac{x}{12} & = 4 \\
x & = 48
\end{aligned}
$$

Pizizubka found 48 nuts, Zrzečka found $2 \cdot 48 = 96$ nuts, and Ouška found $3 \cdot 48 = 144$ nuts.