[ Arithmetic. Mental calculation, etc. ] $[\quad$ Case enumeration $\quad]$

109 apples are distributed into bags. In some bags, there are $x$ apples, and in others, there are three apples.

Find all possible values of $x$, if the total number of bags is 20.
If there were 3 apples in each package, there would be 60 apples in total. But there are 49 more apples, so the "extra" apples need to be evenly distributed among some packages. Since $49=7 \cdot 7=49 \cdot 1$ and there are 20 packages in total, either 7 packages contain 7 "extra" apples each, or one package contains 49 "extra" apples. In the first case, $x=10$, in the second case, $x=52$.

## Answer

10 or 52.