2015 AMC 12A Problem 3

Attempt Problem 3 of the 2015 AMC 12A below, then check your answer against the professionally curated solution 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.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

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
Answer: E
Concepts:mean
Small hint:
The other 1414 students together scored 14×8014\times 80
Big hint:
All 1515 scores together total 15×8115\times 81; subtract
Solution:
The sum of the 1414 other scores was 14⋅80=1120.14\cdot 80 = 1120. The sum of all 1515 scores was 15⋅81=1215.15\cdot 81 = 1215.
Therefore Payton’s score was 1215−1120=95.1215 - 1120 = 95.
Thus, the correct answer is E.
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