Linear Equations

Step 1: Understanding the Concept:
This is a word problem involving ages that can be solved by setting up a system of linear equations.
Step 2: Key Formula or Approach:
Let F be the present age of the father and S be the present age of the son.
Translate the given statements into two equations.
1. "The present age of a father is 4 years more than double the age of his son."
2. "After 10 years, the father's age is 30 years more than his son."
Father's age after 10 years = F + 10
Son's age after 10 years = S + 10

Step 3: Detailed Explanation:
We have two equations:
(1)
(2)
Now we can solve this system. Since both equations are equal to F, we can set them equal to each other:

Subtract S from both sides:

Subtract 4 from both sides:

The son's present age is 26 years.
Now, find the father's present age using either equation. Let's use equation (2):

Let's verify with equation (1):

Both equations give the same result. The father's present age is 56 years.
Step 4: Final Answer:
The present age of the father is 56 years.