The ratio of father's age and son's age is 8:3. If the sum of their ages is 55 years, how old is the son ?
11/3 = 55/x
11x = 165
x = 15
To find the age of the son, we can set up a system of equations based on the information given.
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.