Question
You are placing bets on the outcome of a soccer match. Team Alpha has $(2:1)$ odds, meaning you receive $\$3$ if you win, resulting in a profit of $\$2$. Team Beta offers $(3:1)$ odds, while betting on a tie has $(10:1)$ odds. $$$$ Let $A$, $B$, and $C$ represent the minimum whole dollar amounts you bet on Team Alpha, Team Beta, and a tie, respectively. Assuming you want to make the same profit regardless of the game's outcome, how much do you profit? If you determine that betting on this game is not advisable, enter $0$.