11. The mean age of three people is 22 and their median age is 20.
The range of their ages is 16. How old is each person?

The three ages are { 15, 20, 31 }

Step-by-step explanation:

Let the ages of these three people be x, y and z, in ascending order.

Then:

x + y + z

= mean age = 22.  This leads to x + y + z = 3(22) = 66.

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If the median age is 20, then y = 20, since y (20) is the middle value.

If the range of their ages is 16, then z - x = 16.

Rewrite x + y + z = 66 as x + 20 + z = 66, or x + z = 46.

Solve the system

-x + z = 16

x + z = 46

for x and z.     To do this, combine these two equations, obtaining:

2z = 62, so that z = 31.

Use z - x = 16 with z = 31 to find the value of x:

-x + 31 = 16, or -x = -15.  Then x = 15.

The three ages are { 15, 20, 31 }.

Check:  is the mean (average) of these three ages equal to 22?

Does:

 15 + 20 + 31

= 22?   Does (35 + 31)/3 = 22?  YES

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