1. Alex's friends Boris and Tsane in one round of sports betting placed the following amounts: Alex 600 denars, Boris 900 denars, and Tsane 1500 denars. On the bet, they won a total of 17000 denars. How should they fairly divide the winnings?
Solution. Let $a, b, c$ be the respective shares of 17000 denars that Alex, Boris, and Tsane should receive. Then $a: b: c=600: 900: 1500=2: 3: 5$.

Therefore, we will first divide 17000 into $2+3+5=10$ parts, and then each will receive their proportional share:

$$
a=2 \cdot 1700=3400, b=3 \cdot 1700=5100 \text { and } c=5 \cdot 1700=8500 \text { denars. }
$$