Father–son linear system: A man is five times as old as his son. Four years later, the sum of their ages will be 56. Find the son’s present age.

Introduction / Context:We combine a present multiplicative relation with a future sum. Express the father’s age in terms of the son’s age, then apply the future sum to solve for the son directly.

Given Data / Assumptions:

• Let present ages be M and S
• M = 5S
• (M + 4) + (S + 4) = 56

Concept / Approach:Substitute M = 5S into the future-sum equation and solve for S. This yields the son’s current age immediately.

Step-by-Step Solution:

Verification / Alternative check:Father now = 40. After 4 years: 44 and 12; sum = 56 ✓.

Why Other Options Are Wrong:12, 5, and 6 do not satisfy both constraints simultaneously.

Common Pitfalls:Adding 4 to only one of them; both ages advance by 4 years.

Final Answer:8 years