# Problem 5.

In 10 minutes, Zhenya eats 5 cottage cheese vatrushki, while Sasha eats only 3. On Saturday, all the baked vatrushki went to Zhenya, and on Sunday, they went to Sasha. In total, exactly 70 vatrushki were eaten in three hours of pure time. How many cottage cheese vatrushki did each of the children get?
# Solution.

Let Zhene get $n$, and Sasha get $-k$ pancakes. We need to solve the system of equations in integers

$$
\left\{\begin{array}{l}
n+k=70 \\
2 n+\frac{10}{3} k=180
\end{array}\right.
$$

Substituting $n=70-k$ into the second equation, we get

$$
140-2 k+\frac{10}{3} k=180
$$

Or

$$
\frac{4}{3} k=40
$$

From this, $k=30, n=70-30=40$.

Answer. Zhene got 40 pancakes, Sasha got 30.