In $2022,$ Amanda and Jaxon Stuart have a daughter who is $1$ year old. The Stuarts are full$-$time students and are both $23$ years old. Their only sources of income are gains from stock they held for three years before selling and wages from part$-$time jobs.

What is their earned income credit in the following alternative scenarios if they file jointly? Use Exhibit $8-11.$ a$.$ Their AGI is $$16,400,$ consisting of $$12,700$ of capital gains and $$3,700$ of wages. b$.$ Their AGI is $$16,400,$ consisting of $$10,100$ of lottery winnings $($unearned income$)$ and $$6,300$ of wages. c$.$ Their AGI is $$28,150,$ consisting of $$23,100$ of wages and $$5,050$ of lottery winnings $($unearned income$).$ d$.$ Their AGI is $$28,150,$ consisting of $$5,050$ of wages and $$23,100$ of lottery winnings $($unearned income$).$