Problem:
Isabella must take four -point tests in her math class. Her goal is to achieve an average grade of at least on the tests. Her first two test scores were and . After seeing her score on the third test, she realized that she could still reach her goal. What is the lowest possible score she could have made on the third test?
Answer Choices:
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B.
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E.
Solution:
To achieve an average grade of on the four tests, Isabella must score a total of points. She scored a total of points on her first two tests, so she must score a total of at least points on her last two tests. Because she can score at most on her fourth test, she must have scored at least on her third test.
Isabella's first score was , her second score was , and her fourth score can be at most . Because she can still achieve an average score of , her third score must have been at least .
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions