want to average a bunch of values found with vlookup

Hi everyone, I'm trying to use vlookup in my gradebook. For any given student I want to enter a letter grade for each assignment. Then I want to create a vlookup table where those letters have equivalent number values. Then I want a formula that will find the average of all those number values the student earned.

For instance, according to my vlookup table, A = 95, B = 85 and C = 75.

And John gets the following grades: A B C C.

I want a formula that will calculate his overall grade of 82.5 without having to create separate columns that show the actual vlookup results (the number grades for each assignment).

I am really a beginner with Excel so right now I have something like this, which is completely annoying:
=(VLOOKUP(C4,$AH$28:$AI$37,2,FALSE)+VLOOKUP(D4,$AH$28:$AI$37,2,FALSE)+VLOOKUP(E4,$AH$28:$AI$37,2,FALSE))/3

I hope that makes sense. I appreciate your help!

Thanks, Tony! That worked like a charm.