Difficulty: Easy
Correct Answer: 10
Explanation:
Introduction / Context:Linear relations among three ages combined with a total allow quick variable substitution. This problem is a straightforward arithmetic exercise intended to reinforce systematic setup and solution.
Given Data / Assumptions:
Concept / Approach:Eliminate A and B in favor of C (or any single variable). Solve for C from the sum, then compute B directly from B = 2C.
Step-by-Step Solution:
Substitute into total: (B + 2) + B + C = 27. With B = 2C ⇒ (2C + 2) + 2C + C = 27 ⇒ 5C + 2 = 27 ⇒ C = 5. Hence B = 2C = 10; A = B + 2 = 12.Verification / Alternative check:Sum 12 + 10 + 5 = 27 (✓); relations A = B + 2 and B = 2C both hold (✓).
Why Other Options Are Wrong:They correspond to incorrect solutions for C that do not satisfy the total or the given relations.
Common Pitfalls:Adding instead of substituting, or mixing which person is twice as old as whom, which flips the relation.
Final Answer:10
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