13.092. A monetary prize was distributed among three inventors: the first received half of the entire prize minus $3 / 22$ of what the other two received together. The second received $1 / 4$ of the entire prize and $1 / 56$ of the money received by the other two together. The third received 30000 rubles. How large was the prize and how much money did each inventor receive?
## Solution.

Let $x$ rubles be the prize for the first inventor, and $y$ rubles be the prize for the second. According to the condition, the total prize is $x+y+30000$ rubles. Then

$$
\left\{\begin{array}{l}
x=\frac{1}{2}(x+y+30000)-\frac{3}{22}(y+30000) \\
y=\frac{1}{4}(x+y+30000)+\frac{1}{56}(x+30000)
\end{array} \text {, from which } x=40000, y=25000 .\right. \text { The total }
$$

prize is $40000+25000+30000=95000$ rubles.

Answer: 95000 rubles; 40000, 25000, and 30000 rubles.