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2011 AMC 10B Problem 2

Problem 2 of 25EasierAlgebra

Josanna’s test scores to date are 90,90, 80,80, 70,70, 60,60, and 85.85. Her goal is to raise her test average at least 33 points with her next test. What is the minimum test score she would need to accomplish this goal?

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Solution

Her current average is 90+80+70+60+855=77,\dfrac{90+80+70+60+85}5 = 77, and the sum of her scores is 385.385. The desired average is then 80,80, so the sum of scores required is 80⋅6.80\cdot 6. Therefore, the answer is 80⋅6−385=95.80\cdot 6-385 = 95. Thus, the correct answer is E .

More practice

Concepts: mean · work backwards

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