SOLUTION: Sum of the ages of Sam and his father is 47 years, when Sam reaches his fathers age, the sum of their ages will be 97 years, how old is Sam?

Let x be the Sam age.


Then the father's age is 47-x years.


Sam will reach the father age in  ((47-x) - x) = 47-2x years.


In  (47-2x) years, Sam's age will be  (x + (47-2x))  years,

while the father's age will be  ((47-x) + (47-2x)) ages.


In  (47-2x) years, the sum of their ages will be 97 years. It gives you an equation


    (x + (47-2x) + ((47-x) + (47-2x)) = 97.


Simplify and solve for x


     (47-x)      +  (94-3x)           = 97

     (47 + 94)   - 4x                 = 97

     47  + 94    - 97                 = 4x

     44                               = 4x

      x                               = 44/4 = 11.


ANSWER.  Sam is 11 years old.


CHECK.  Then the father is 47-11 = 36 years old.

        Sam will reaches his father age in 36-11 = 25 years.

        Then the sum of their ages will be  (11+25) + (36+25) = 47 + 50 = 97 years.    ! Precisely correct !

Now the sum of their ages is 47 years; the sum of their ages of 97 will happen in  = 25 years.


So, Sam will reach his father current age in 25 years, which means that the father is 25 years older than Sam.


Thus the sum of their ages is 47 years, while the difference is 25 years.


Hence, the Sam's age is   =  = 11 years.   (the same answer)