13.416 There is a certain number of barrels of two samples (sizes) with a total capacity of 7000 liters. If all the barrels were of the first sample, the total capacity would increase by 1000 liters. If all the barrels were of the second sample, the total capacity would decrease by 4000 liters. Calculate the capacity of all barrels of each sample separately.
Solution. Let $x$ and $y$ be the total capacities of the barrels of the first and second types, respectively, and $n$ and $k$ be their quantities. Then $\frac{x}{n}$ and $\frac{y}{k}$ are the capacities of one barrel of each type. According to the conditions of the problem,

$$
\left\{\begin{array} { l } 
{ x + y = 7 0 0 0 , } \\
{ \frac { x } { n } ( n + k ) = 8 0 0 0 , } \\
{ \frac { y } { k } ( n + k ) = 3 0 0 0 }
\end{array} \Rightarrow \left\{\begin{array} { l } 
{ x + y = 7 0 0 0 } \\
{ \frac { x } { 8 0 0 0 } = \frac { n } { n + k } } \\
{ \frac { y } { 3 0 0 0 } = \frac { k } { n + k } }
\end{array} \Rightarrow \left\{\begin{array}{l}
x+y=7000 \\
\frac{x}{8000}+\frac{y}{3000}=1
\end{array} \Rightarrow x=6400, y=600\right.\right.\right.
$$

Answer: 6400 liters, 600 liters.