13.155. In the first week of their vacation trip, the friends spent 60 rubles less than $2 / 5$ of the amount of money they brought with them; in the second week, $1 / 3$ of the remainder and another 12 rubles on theater tickets; in the third week, $3 / 5$ of the new remainder and another 31 rubles 20 kopecks on boat rides, after which they had 420 rubles left. How much money was spent over the three weeks of the trip?
Solution.

Let the initial amount be $x$ rubles.

| Week | Spent | Balance |
| :--- | :---: | :---: |
| First | $\frac{2}{5} x-60$ (rubles) | $\frac{3}{5} x+60$ (rubles) |
| Second | $\frac{1}{3}\left(\frac{3}{5} x+60\right)+12=\frac{1}{5} x+32$ (rubles) | $\frac{2}{5} x+28$ (rubles) |
| Third | $\frac{3}{5}\left(\frac{2}{5} x+28\right)+31 \frac{1}{5} x=$ | $\frac{2}{5} x+28-\frac{6}{25} x-48=$ |
|  | $=\frac{6}{25} x+48$ (rubles) | $=\frac{4}{25} x-20$ (rubles) |

According to the condition $\frac{4}{25} x-20=420$, from which $x=2750$ rubles. Over three weeks, $2750-420=2330$ (rubles) were spent.

Answer: 2330 rubles.