# 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, 35 vatrushki were eaten in one and a half hours of pure time. How many cottage cheese vatrushki did each of the children get?
# Solution.

The problem can be solved by formulating a system of equations with two unknowns (similar to a 7th-grade problem). However, it is unlikely that 6th-grade students would take this approach.

An alternative method of reasoning might be as follows.

One and a half hours is 9 times 10 minutes. Suppose the children ate in ten-minute intervals. Let's say Sasha spent $x$ such ten-minute intervals. Then Sasha ate $3 x$ pancakes.

Therefore, Zhenya ate $35-3 x$ pancakes. If each child spent a whole number of ten-minute intervals, then the value $35-3 x$ must be divisible by 5, which means $3 x$ must be divisible by 5.

Since $x \leq 9$, the only possible value is $x=5$. Thus, Sasha ate $5 \cdot 3=15$ pancakes, and Zhenya ate $35-15=20$.

Answer. Zhenya got 20 pancakes, and Sasha got 15.