1. Ali, Igor, and Vladimir jointly invested money in a sports betting round. Their individual investments were 600 denars, 900 denars, and 1500 denars, respectively. They won 17000 denars. How much should each of them receive to fairly divide the winnings?
Solution. We will convert the individual investments into percentages of the total investment. To ensure the profit is fairly distributed, the same percentages will apply to the profit distribution. Thus, Ali invested 600 denars out of a total of 3000 denars, which represents $\frac{600}{3000}=\frac{1}{5}$ $=\frac{20}{100}=20\%$ of the total amount. Igor invested $\frac{900}{3000}=\frac{3}{10}=\frac{30}{100}=30\%$ of the total amount, and Vladimir invested the remaining 50%. Therefore, Ali should receive $20\%$ of 17000 denars, which is $\frac{20}{100} \cdot 17000=3400$ denars. Igor should receive $\frac{30}{100} \cdot 17000=5100$ denars, and Vladimir the remaining amount, which is equal to the combined share of Ali and Igor, that is 8500 denars, representing exactly $50\%$ of the profit.