What the condition says is THIS:


Sam + Ben = 55,     (equation 1)    ("The total of their ages is 55 years.")
Sam = Ben - 15.     (equation 2)    ("Sam is 15 years younger than his friend Ben.")


In other words (in Math symbols)


S + B = 55,    (1)
S = B - 15.    (2)


Now substitute the expression (2) into equation (1), replacing S. You will get a single equation for B


(B-15) + B = 55.


Simplify and solve for B:


2B - 15 = 55  

2B = 55 + 15 = 70  ====>  B =  = 35.


Answer.  Ben is 35 years old.  Sam is  35 - 15 = 20 years old.