Question

The sum of the ages of a son and father is 56 years; after four years the age of the father will be three times that of the son. What is the age of the father and the son, respectively?

• A. \(41 \text{ years}, 12 \text{ years}\)
• B. \(30 \text{ years}, 12 \text{ years}\)
• C. \(34 \text{ years}, 11 \text{ years}\)
• D. \(44 \text{ years}, 12 \text{ years}\)

Hint:

When working with age-related problems, setting up the initial conditions and future predictions as equations can simplify the solution process considerably.

Answer 1

The Correct Option is D

Step 1: Define the variables and set up the equations.
Let \( f \) be the father's current age and \( s \) be the son's current age. Given: \[ f + s = 56 \] \[ f + 4 = 3(s + 4) \]

Step 2: Solve the equations.
From the second equation: \[ f + 4 = 3s + 12 \] \[ f = 3s + 8 \] Substitute \( f \) in the first equation: \[ 3s + 8 + s = 56 \] \[ 4s = 48 \] \[ s = 12 \] \[ f = 44 \]