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?

Now: 6 yr mean age
in 10 yrs? 16 yr mean age
in 20 yrs? 26 yr mean age

Why?  Because regardless of the relationship between each sibling’s age, your always adding the 10yrs to each individual, which you are then dividing out to determine the mean age.   See proof below:

Including anita, there are 6 people.   We’ll define each age as an unknown variable.   Assume we know nothing about the relationships between their ages

for example sake
anita’s age = a
sister 1’s age = b
sister 2’s age = c
brother 1’s age = d
brother 2’s age = e
brother 3’s age = f

Now:
mean age = (a + b + c + d + e + f)/(6 people) = 6 yrs

in 10 yrs:
mean age = ((a+10) + (b+10) + (c+10) + (d+10) + (e+10) + (f+10))/(6 people)
mean age = (a + b + c + d + e + f + 60)/(6 people)
mean age = (a + b + c + d + e + f)/(6 people) + (60)/(6 people)
mean age = (a + b + c + d + e + f)/(6 people) + 10

Notice the first term is the same expression of the mean age for "Now"
Thus, in 10 yrs:
mean age = 6 + 10 = 16 yrs

The same principle applies for "x" yrs from now, as long as we know what the mean age is "Now"

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