13.176. The total capacity of three tanks is 1620 liters. Two of them are filled with kerosene, while the third one is empty. To fill it, you need to use either all the contents of the first tank plus $1 / 5$ of the contents of the second, or all the contents of the second plus $1 / 3$ of the contents of the first. Find the capacity of each tank.
Solution.

Let $x$ be the capacity of the first tank in liters, $y_{\text {l }}$ be the capacity of the second tank in liters, and $z \pi-$ be the capacity of the third tank in liters. According to the conditions, $\left\{\begin{array}{l}x+y+z=1620, \\ z=x+\frac{1}{5} y, \\ z=y+\frac{1}{3} x,\end{array}\right.$ from which $x=540$ liters, $y=450$ liters, $z=630$ liters.

Answer: 540, 450, and 630. .t.