The present ages of a father and his son sum to 60 years. Six years ago, the father was five times the son's age. What will be the son's age after 6 years?

Problem restatementUse a system of equations with present ages and a past ratio to find the son's current age, then add 6 years.

Given data

• F + S = 60 (present ages of father and son).
• Six years ago: F − 6 = 5(S − 6).

Concept/ApproachSolve the linear system for S; the future age is S + 6.

Step-by-step calculation F − 6 = 5S − 30 → F = 5S − 24 (5S − 24) + S = 60 6S = 84 → S = 14 After 6 years: S + 6 = 20

Verification/AlternativePresent father's age F = 60 − 14 = 46. Six years ago: 40 and 8, and 40 = 5 × 8 (satisfies the condition).

Common pitfalls

• Applying the five-times relation to present ages instead of ages six years ago.

Final Answer20 years