Two-time ratios to present ages: Seven years ago, A : B = 3 : 4. Nine years hence, A : B = 7 : 8. What is B’s present age?

Question

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

Accepted Answer

Introduction / Context:Again, two ratios at different times produce a solvable linear system for present ages. Translate carefully and solve systematically to avoid arithmetic slips. Given Data / Assumptions: (A − 7) : (B − 7) = 3 : 4 (A + 9) : (B + 9) = 7 : 8 Concept / Approach:Cross-multiply each, reduce to standard linear form, and solve by elimination or substitution. Step-by-Step Solution: 4(A − 7) = 3(B − 7) ⇒ 4A − 3B = 78(A + 9) = 7(B + 9) ⇒ 8A − 7B = −9Solve ⇒ A = 19, then 4A − 3B = 7 ⇒ 76 − 3B = 7 ⇒ B = 23 Verification / Alternative check:Seven years ago: 12 : 16 = 3 : 4; in nine years: 28 : 32 = 7 : 8 ✓. Why Other Options Are Wrong:16, 19, 28 are not B’s present age under the constraints; only 23 fits. Common Pitfalls:Arithmetic slips when distributing and moving constants; ensure both persons’ ages shift by the same amount in each time frame. Final Answer:23 yr

Two-time ratios to present ages: Seven years ago, A : B = 3 : 4. Nine years hence, A : B = 7 : 8. What is B’s present age?

More Questions from Problems on Ages

Discussion & Comments