Final answer:
To find the present ages of the father and son, we set up and solved a system of linear equations based on the provided information. The solution reveals that the son is currently 12 years old, and the father is 42 years old.
Step-by-step explanation:
The question involves solving a system of linear equations to find the present ages of a father and his son. We are provided with two pieces of information that will help us set up two equations. The first piece of information tells us that three years ago, the sum of the father's and son's ages was 48 years. Second, we know that three years from now, the father's age will be three times the son's age.
Let's denote the present age of the son as 's' and the present age of the father as 'f'. Our first equation, based on the information from three years ago, becomes:
(f - 3) + (s - 3) = 48
This simplifies to:
f + s - 6 = 48
which further simplifies to:
f + s = 54 (Equation 1)
Our second equation, based on the information about the future ages, becomes:
(f + 3) = 3(s + 3)
This simplifies to:
f + 3 = 3s + 9
which further simplifies to:
f - 3s = 6 (Equation 2)
Now we have two equations:
- Equation 1: f + s = 54
- Equation 2: f - 3s = 6
If we solve these equations simultaneously, we can find the values of 'f' and 's'. By subtracting Equation 2 from Equation 1, we get:
f + s - (f - 3s) = 54 - 6
f + s - f + 3s = 48
4s = 48
s = 12 (Son's present age)
Substituting 's = 12' into Equation 1 gives us:
f + 12 = 54
f = 42 (Father's present age)
Hence, the son is currently 12 years old and the father is 42 years old.