Q. Is it acceptable/legal to apply most of the scholarship monies to room and board, assuming the scholarships ( Pell etc) allow the monies to be used for tuition and room and board?
A. Yes. Pell grants, in particular, are allowed to be applied that way.* You actually haven't gone far enough. You can get little bit more refund. It takes $4000 of net qualified expenses to get the maximum $2500 tuition credit.
There is a tax “loop hole” available to claim an education credit, for the parents of students on scholarship. The student reports all his scholarship, up to the amount needed to claim the American Opportunity Credit (AOC), as income on his return. That way, the parents (or himself, if he is not a dependent) can claim the tuition credit on their return. They can do this because that much tuition was no longer paid by "tax free" scholarship. You cannot do this if the conditions of the grant are that it be used to pay for qualified expenses.
Using your numbers: Student has $9830 in box 5 of the 1098-T and $4851 in box 1. At first glance he/she has $4979 of taxable income and nobody can claim the American opportunity credit. But if she reports $8979 as income on her return, the parents can claim $4000 of qualified expenses on their return.
Books and computers are also qualifying expenses for the AOC. So, extending the example, the student had another $1000 in expenses for those course materials, paid out of pocket. She would only need to report $7979 of taxable scholarship income, instead of $8979.
*The IRS actually encourages use of this technique. From the form 1040 instructions: “You may be able to increase an education credit if the student chooses to include all or part of a Pell grant or certain other scholarships or fellowships in income. For more information, see Pub. 970, the instructions for Form 1040 and IRS.gov/EdCredit". PUB 970 even has examples of how to do the “loop hole”.
