After the final exam, Mr. Liang asked each of his 17 students to guess the average final exam score. David, a very smart student, received a score of 100 and guessed the average would be 97. Each of the other 16 students guessed $30 + \frac{n}{2}$, where $n$ was that student's score. If the average of the final exam scores was the same as the average of the guesses, what was the average score on the final exam?

Let's think step by step and output the final answer within \boxed{}.
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