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Anita has two sisters and three brothers. The mean of all their ages is 6 years. What will their mean age be 10 years from now? Twenty years from now?

1 Answer

Apr 12, 2018

10 years from now, it will be 16

20 years from now, it will be 26

Explanation:

Right now, their ages are: #{a_1, a_2, ..., a_N}# with mean age:

# bar a = (sum_1^N a_i)/N #

In #n# years time, ages will be: #{a_1 + n, a_2 + n ... a_N + n}#, with mean age :

#bar a_n = (sum_1^N (a_i + n))/N = (sum_1^N (a_i) + (Nn))/N #

#= (sum_1^N (a_i))/N + n = bar a + n#

IOW, #bar a_n = bar a + n#, or:

10 years from now, ave age will be 16
20 years from now, ave age will be 26

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