11/3 = 55/x
11x = 165
x = 15
11x = 165
x = 15
Let's assign variables to the father's age (F) and the son's age (S).
According to the problem, the ratio of the father's age to the son's age is 8:3. This can be written as:
F/S = 8/3 (Equation 1)
It is also given that the sum of their ages is 55 years:
F + S = 55 (Equation 2)
To solve this system of equations, we can use the method of substitution.
From Equation 1, we can isolate F by multiplying both sides by S:
F = (8/3)S
Now, substitute this expression for F in Equation 2:
(8/3)S + S = 55
Combining like terms:
(8/3)S + (3/3)S = 55
(11/3)S = 55
To isolate S, we can multiply both sides by the reciprocal of (11/3), which is (3/11):
S = (55) * (3/11)
Simplifying:
S = 15
Therefore, the son is 15 years old.