Jackson and Ashley Turner $($both $45$ years old$)$ are married and want to contribute to a Roth IRA for Ashley. In $2023,$ their AGI is $$224,000.$ Jackson and Ashley each earned half of the income.

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a$.$ How much can Ashley contribute to her Roth IRA if they file a joint return?

b$.$ How much can Ashley contribute if she files a separate return?

c$.$ Assume that Ashley earned all of the couple's income and that she contributed the maximum amount she is allowed to contribute to a Roth IRA. What amount can be contributed to Jackson's Roth IRA if they file a joint return?