In the city of King$$s Landing, Bronn lives and works as a sell$-$sword $($someone who is willing to fight with his sword for pay$).$ His most recent client, Tyrion Lannister, has been very generous this year $(2024)$ offering $$25,000$ per fight already for each of his first two fights this year. So$,$ in total, he has earned $$50,000$ so far. However, Tyrion recently approached Bronn offering an additional $$50,000$ if he would be willing to fight Gregore Clegane the next day $($still in $2024).$ This would be Bronn$$s third fight for the year. Assume Bronn files as a single taxpayer and that whatever he receives from Tyrion constitutes his taxable income.

Bronn will only take the third $($extra$)$ fight if the additional pay he receives for the fight exceeds the additional tax he has to pay by $$38,000$ because he believes Gregore is a very tough opponent. In other words, he will only take the job if the additional after$-$tax pay $($$$50,000$ less the additional tax on the new $$50,000$ of pay$)$ is greater than $$38,000.$ Ignoring your answers to part a$.,$ assume that Bronn's total tax is $$8,150$ when he does not take the extra fight and $$21,830$ when he does take the extra fight.

Fill in the blank: Bronn's additional after$-$tax pay with these assumptions is $$\_\_\_\_\_\_\_\_\_\_\_.$