13.341. Three workers participated in a competition. The first and third of them produced twice as much product as the second, while the second and third produced three times as much as the first. What place did each worker take in the competition?
## Solution.

Let $x_{1}, x_{2}, x_{3}$ be the volume of production by the first, second, and third worker, respectively. According to the problem, we have the system

$$
\left\{\begin{array}{l}
x_{1}+x_{3}=2 x_{2}, \\
x_{2}+x_{3}=3 x_{1},
\end{array}\right.
$$

Answer: In first place - the third, in second place - the second, in third place - the first. The quantities of their production are in the ratio 5:4:3.