Question 1175810
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Let x be the youngest; then the oldest is 3x years old.


You have then this equation for the average age


    {{{(x + 10 + 22 + 3x)/4}}} = 16.


It implies


    4x = 4*16 - 10 - 22 = 32

     x                  = 32/4 = 8.


<U>ANSWER</U>.  The youngest child in the family is 8 years old.
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Solved.