In $2023,$ Elaine paid $$2,120$ of tuition and $$1,300$ for books for her dependent son to attend State University this past fall as a freshman. Elaine files a joint return with her husband.

What is the maximum American opportunity tax credit that Elaine can claim for the tuition payment and books in each of the following alternative situations?

Note: Leave no answer blank. Enter zero if applicable.

a$.$ Elaine's AGI is $$104,250.$

b$.$ Elaine's AGI is $$173,500.$