Task 1. Zoran, Goran, and Ruza need to divide 2000 denars such that the shares of Zoran and Goran are in the ratio of $2: 3$, and the shares of Goran and Ruza are in the ratio of 9:5. How much denars will each of them receive?
Solution. If Zoran wins $6 x$ denars, then Goran will win $9 x$ denars, and Ruzha $5 x$ denars. Together they have $20 x$ denars. It follows that $20 x=2000$, from which $x=100$ denars. Therefore, Zoran, Goran, and Ruzha should receive 600, 900, and 500 denars, respectively.