A mother told her son that the son was already 10 years old when she was at his  age. 
    Then the mother said to the son, “I will be 88 years old when you are at my age.” 
    How old was the mother when her child was born?

Let x be the mother age when her son was born.

It means that the mother is x years older than the son is.      (*)


From the first statement of the problem, the son's current age is  (10+x) years (now).


Hence, the mother's current age is (10+x+x) = (10 + 2x) years (now).


From the second statement of the problem, the son's age will be  (10+2x) years, when the mother will be 88 years old.


At that time, the difference between their ages will be (88- (10+2x)) years,
and it will be exactly x years, as noticed in (*).


It gives you this equation

    88 - (10+2x) = x.


Simplify and find x

    88 - 10 - 2x = x

       78   =   3x

       x    = 78/3 = 26.


ANSWER.  The mother was 26 years old, when the son was born.


CHECK.   Hence, the son's current age is 26+10 = 36 years now; 

         the mother's current age is 36+26 = 62 years now;

         88-62 = 26 years.  In 26 years the mother will be 88 years old, while the son will be 36+26 = 62 years,

         which exactly is the mother's current age.    ! Correct !