2015 AMC 10A Problems/Problem 5

Problem

Mr. Patrick teaches math to students. He was grading tests and found that when he graded everyone's test except Payton's, the average grade for the class was . After he graded Payton's test, the test average became . What was Payton's score on the test?

$\textbf{(A)}\ 81\qquad\textbf{(B)}\ 85\qquad\textbf{(C)}\ 91\qquad\textbf{(D)}}\ 94\qquad\textbf{(E)}\ 95$ (Error compiling LaTeX. Unknown error_msg)

Solution

If the average of the first peoples' scores was , then the sum of all of their tests is . When Payton's score was added, the sum of all of the scores became . So, Payton's score must be