Bob and Sally are married, file a joint tax return, report AGI of $ $152,000,$ and have two children. Del is beginning her freshman year at State College during Fall $20232,$ and Owen is beginning his senior year at Southwest University during Fall $2023.$ Owen completed his junior year during the Spring semester of $2022($i$.$e$.,$ he took a $$leave of absence$$ during the $2022-2023$ school year$).$ Both Del and Owen are claimed as dependents on their parents$$ tax return.

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Del$$s qualifying tuition expenses and fees total $$5,000$ for the Fall semester, while Owen$$s qualifying tuition expenses were $$6,100$ for the Fall $2023$ semester. Del$$s room and board costs were $$3,200$ for the Fall semester. Owen did not incur room and board costs, as he lived with his aunt and uncle during the year.

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Full payment is made for the tuition and related expenses for both children at the beginning of each semester. In addition to the children$$s college expenses, Bob also spent $$3,000$ on professional education seminars during the year in order to maintain his license as a practicing dentist. Bob attended the seminars during July and August $2023.$ Compute the available education tax credits for Bob and Sally for $2023.$

a$.$

$$3,100$

b$.$

$$5,000$

c$.$

$$5,480$

d$.$

$$5,600$