13.040. Three employees received a bonus of 2970 rubles, with the second receiving $1 / 3$ of what the first received, plus 180 rubles, and the third receiving $1 / 3$ of the second's amount, plus 130 rubles. How much did each receive?
## Solution.

Let $x$ rubles be the bonus of the first employee. Then $\frac{1}{3} x+180$ rubles for the second; $\frac{1}{3}\left(\frac{1}{3} x+180\right)+130$ rubles for the third. According to the condition, $x+\frac{1}{3} x+180+\frac{1}{3}\left(\frac{1}{3} x+180\right)+130=2970$, from which $x=1800$ rubles - the bonus of the first employee; $\frac{1}{3} \cdot 1800+180=780$ rubles - the bonus of the second; $\frac{1}{3} \cdot 780+130=390$ rubles - the third.

Answer: 1800, 780, and 390 rubles.