From 8× in the past to 4× now: Four years ago a father's age was eight times his son's age. At present the father's age is four times the son's age. What is the son's current age?

Introduction / Context:Two time-spaced multiplicative relations in ages yield a tidy linear system. Translate both statements into equations in today's variables and solve.

Given Data / Assumptions:

• Let present ages be F (father) and S (son).
• Now: F = 4S.
• Four years ago: F − 4 = 8(S − 4).

Concept / Approach:Substitute F = 4S into the past condition and solve for S.

Step-by-Step Solution:1) 4S − 4 = 8S − 32.2) Move terms: 28 = 4S ⇒ S = 7.

Verification / Alternative check:Check: Now F = 28. Four years ago: F=24, S=3 → 24 = 8 × 3; now 28 = 4 × 7. Consistent.

Why Other Options Are Wrong:They fail one of the multiplicative checks when validated.

Common Pitfalls:Forgetting both ages decrease by 4 in the “four years ago” equation.

Final Answer:7 years