2010 AMC 8 Problem 9

Attempt Problem 9 of the 2010 AMC 8 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 2010 AMC 8 solutions, or check the answer key.

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

9.

Ryan got 80%80\% of the problems correct on a 2525-problem test, 90%90\% on a 4040-problem test, and 70%70\% on a 1010-problem test. What percent of all the problems did Ryan answer correctly?
 63 \ 63
 75 \ 75
 80 \ 80
 84 \ 84
 86 \ 86
Answer: D
Concepts:percentage
Small hint:
Divide the total correct answers by the total number of problems.
Big hint:
Convert each test percentage into a number of correct answers.
Solution:
There were a total of 25+40+10=7525+40+10 = 75 problems.
On the first test, he solved 0.8⋅25=200.8\cdot25 = 20 problems.
On the second test, he solved 0.9⋅40=360.9\cdot40 = 36 problems.
On the third test, he solved 0.7⋅10=70.7\cdot10 = 7 problems.
Therefore, he solved a total of 20+36+7=63.20+36+7=63. This means the fraction he solved is 6375=84%. \dfrac{63}{75} = 84\%.
Therefore, the answer is D .
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