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2013 AMC 10B Problem 6

Problem 6 of 25EasierAlgebra

The average age of 3333 fifth-graders is 11.11. The average age of 5555 of their parents is 33.33. What is the average age of all of these parents and fifth-graders?

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Solution

The sum of the ages of all the fifth-graders and their parents is: 33⋅11+55⋅33=66⋅33.33\cdot 11+55\cdot 33 = 66\cdot 33. Then, as the average is the sum divided by the number of people, the average age must be: 66⋅3388=34⋅33=24.75.\dfrac{66\cdot 33}{88} = \dfrac 34 \cdot 33 = 24.75 . Thus, the correct answer is C .

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Concepts: mean

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