Linked age statements: In ten years, A will be twice as old as B was 10 years ago. If A is now 9 years older than B, find B’s present age.

Introduction / Context:Time-shifted age relations are best handled by setting up simultaneous equations. Translate each sentence carefully into algebra and solve the linear system for present ages.

Given Data / Assumptions:

• Let A and B be present ages
• A + 10 = 2 * (B − 10)
• A = B + 9

Concept / Approach:Substitute A = B + 9 into the first equation to get B directly; then retrieve A if needed. Ensure sign handling is correct when shifting time forward/backward.

Step-by-Step Solution:

Verification / Alternative check:10 years from now, A = 58; 10 years ago, B = 29; twice 29 is 58 ✓.

Why Other Options Are Wrong:40, 36, 49 do not satisfy both the time-shift constraint and the current age difference of 9 years.

Common Pitfalls:Reversing the 10-year shifts or forgetting parentheses around (B − 10) when doubling.

Final Answer:39 year