13.243. One of the three barrels is filled with water, while the others are empty. If the second barrel is filled with water from the first barrel, then $1 / 4$ of the water that was in the first barrel will remain. If the third barrel is then filled from the second, then $2 / 9$ of the amount of water that was in the second barrel will remain. If, finally, water is poured from the third barrel into the empty first barrel, it will take 50 more buckets to fill it. Determine the capacity of each barrel.
Solution.

Let $x$ barrels be the capacity of the first barrel, then the capacity of the second is $-\frac{3}{4} x$, and the third is $-\frac{7}{9}\left(\frac{3}{4} x\right)$.

According to the condition $\frac{7}{9} \cdot \frac{3}{4} x + 50 = x$,

from which $x = 120$ barrels,

$$
\frac{3}{4} x = 90 \text{ barrels}
$$

$\frac{7}{9} \cdot \frac{3}{4} x = 70$ barrels.

Answer: 120, 90, and 70 barrels.