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2015 AMC 10A Problem 5

Problem 5 of 25EasierAlgebra

Mr. Patrick teaches math to 1515 students. He was grading tests and found that when he graded everyone’s test except Payton’s, the average grade for the class was 80.80. After he graded Payton’s test, the class average became 81.81. What was Payton’s score on the test?

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Solution

The total for the first 1414 graded tests was 1480=112014\cdot 80=1120. After Payton’s test was included, the total became 1581=121515\cdot 81=1215. Therefore Payton’s score was 12151120=951215-1120=95. Thus, E is the correct answer.

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Concepts: mean

Problem text and solution from the LIVE past-contest archive. See also the AoPS wiki page for community solutions.