2015 AMC 12A Problem 3

Below is the professionally curated solution for Problem 3 of the 2015 AMC 12A, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2015 AMC 12A solutions, or check the answer key.

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Concepts:mean

Difficulty rating: 1130

3.

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?

8181

8585

9191

9494

9595

Solution:

The sum of the 1414 other scores was 1480=1120.14\cdot 80 = 1120. The sum of all 1515 scores was 1581=1215.15\cdot 81 = 1215.

Therefore Payton's score was 12151120=95.1215 - 1120 = 95.

Thus, the correct answer is E.

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