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2005 AMC 10A Problem 6

Problem 6 of 25EasierAlgebra

The average (mean) of 2020 numbers is 30,30, and the average of 3030 other numbers is 20.20. What is the average of all 5050 numbers?

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Solution

The combined sum is 20⋅30+30⋅20=600+60020 \cdot 30 + 30 \cdot 20 = 600 + 600 =1200.= 1200. The average of all 5050 numbers is 120050=24.\dfrac{1200}{50} = 24. Thus, the correct answer is B.

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Concepts: mean · ratio and proportion

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