Mr. Patrick teaches math to $15$ students. He was grading tests and found that when he graded everyone's test except Payton's, the average grade for the class was $80$. After he graded Payton's test, the test average became $81$. What was Payton's score on the test?
$\textbf{(A)}\ 81\qquad\textbf{(B)}\ 85\qquad\textbf{(C)}\ 91\qquad\textbf{(D)}\ 94\qquad\textbf{(E)}\ 95$
If the average of the first $14$ peoples' scores was $80$, then the sum of all of their tests is $14 \cdot 80 = 1120$.  When Payton's score was added, the sum of all of the scores became $15 \cdot 81 = 1215$.  So, Payton's score must be $1215-1120 = \boxed{\textbf{(E) }95}$