Three FM radio stations $($A$,$B$,$ and$$C$)$ are competing for customers in the same market area.

Through an aggressive advertising campaign, each month station$$A$$is capturing $10\%$ of station$$B$\text{'}$s customers and $5\%$ of station$$C$\text{'}$s customers. $($Hint: The phrase "station$$A$$is capturing $10\%$ of station$$B$\text{'}$s customers" means that $10\%$ of the listeners are moving from$$B$$to$$A$,$ not the other way around.$)$ At the same time, station$$A$$is losing only $2\%$ of its customers to$$B$$and $2\%$ of its customers to$$C$.$ Additionally, each month $1\%$ of$$B$\text{'}$s customers switch to$$C$,$ and $1\%$ of$$C$\text{'}$s customers switch to$$B$.$

Initially,$$A$$and$$B$$each have $30\%$ of the listeners and$$C$$has $40\%.$