AOTC help needed to verify I am doing this right please

@Hal_Al 
Hello, 
If possible could you please give your input if I have done this correctly to claim the AOTC? 

I am trying to claim the AOTC credit for my student that is in their second year of college. 
Our 1098 T info:
BOX 1: $37,019.95 
BOX 5: $44,085.00

Student at least half time: X
[The rest of the blanks on the form are empty.]


QEE (books): $128
Room & Board amounts for the 2024: $9,806
Scholarship Amount restricted to Tuition ONLY: $34,650

Can we allocate $9,435 of his scholarship money (the difference left after deducting the tuition only scholarship) to his room & board and claim that for my students income? (They earned $2,400 over summer with an on campus job, they received a W2 for this job and that was their only income - so even with the $9,435 that's not enough for them to be required to file their taxes, correct?)


This gives me the following: 
Education Credit $1,275 

Refundable American Opportunity Credit $850

 

For a total of $2,125

Does this look correct? Or do I need to do something differently? 
Thank you in advance.