One year ago, the father was four times as old as his son. Six years from now, the father will be 9 years more than twice his son’s age. What is the ratio of their present ages (father : son)?

Question

Solve this multiple-choice question and choose the correct option.

Accepted Answer

Introduction / Context:We have two time-shifted linear relations: one from the past comparing father to son by a factor, and another from the future comparing father to twice the son plus a fixed number. Solve these equations to obtain current ages and then simplify the ratio. Given Data / Assumptions: One year ago: F − 1 = 4(S − 1). Six years later: F + 6 = 2(S + 6) + 9. Find present ratio F : S. Concept / Approach:Form linear equations in F and S and solve. The presence of constants (−1, +6, +9) requires careful algebra to avoid mistakes. Step-by-Step Solution: From the past: F − 1 = 4S − 4 ⇒ F = 4S − 3.From the future: F + 6 = 2S + 21 ⇒ F = 2S + 15.Equate: 4S − 3 = 2S + 15 ⇒ 2S = 18 ⇒ S = 9 ⇒ F = 33.Ratio F : S = 33 : 9 = 11 : 3. Verification / Alternative check: One year ago: 32 vs 8 ⇒ father = 4 × son ✔. Six years later: 39 vs 15 ⇒ 39 = 2 × 15 + 9 ✔. Why Other Options Are Wrong: 13 : 4, 12 : 5, 9 : 2 contradict one or both time-shifted conditions. Common Pitfalls: Mishandling the constants −1, +6, and +9 when translating to equations. Final Answer:11 : 3

One year ago, the father was four times as old as his son. Six years from now, the father will be 9 years more than twice his son’s age. What is the ratio of their present ages (father : son)?

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