13.319. A vessel with a capacity of 8 liters is filled with a mixture of oxygen and nitrogen, with oxygen accounting for $16 \%$ of the vessel's capacity. From this vessel, a certain amount of the mixture is released and an equal amount of nitrogen is added, after which the same amount of the mixture is released again and the same amount of nitrogen is added once more. In the new mixture, the oxygen content is $9 \%$. What amount of the mixture was released each time?
Solution.

Initially, the vessel contained $16 \cdot \frac{8}{100}=\frac{32}{25}$ liters of oxygen. The released $x$ liters of the mixture contain $\frac{16 x}{100}=\frac{4 x}{25}$ liters of oxygen. Now, for every 8 liters of the mixture in the vessel, there are $\frac{32-4 x}{25}$ liters of oxygen, which constitutes $(16-2 x) \%$. The second release of $x$ liters of the mixture contains $(16-2 x) \frac{x}{100}=(8-x) \frac{x}{50}$ liters of oxygen. According to the problem, $\frac{32-4 x}{25}-\frac{(8-x) x}{50}=9 \cdot \frac{8}{100}$, from which $x_{1}=2, x_{2}=14$.

Answer: 2 liters.