Three-person ages from totals: The sum of ages of A, B, and C is 185 years. Also, B is twice A, and C is 17 years older than A. Find A, B, and C (in years).
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A40, 86 and 59 years
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B42, 84 and 59 years
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C40, 80 and 65 years
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DNone of these
Answer
Correct Answer: 42, 84 and 59 years
Explanation
Introduction / Context:Classic linear-relationship age problems can be reduced to a single variable by expressing every person’s age in terms of A. Then a single linear equation from the total yields A, and hence B and C.
Given Data / Assumptions:
- A + B + C = 185
- B = 2A
- C = A + 17
Concept / Approach:Substitute the relations into the sum to solve for A. Once A is found, compute B and C directly from the given relationships.
Step-by-Step Solution:
A + (2A) + (A + 17) = 185 ⇒ 4A + 17 = 1854A = 168 ⇒ A = 42B = 2A = 84, C = A + 17 = 59Verification / Alternative check:Sum check: 42 + 84 + 59 = 185 ✓. Conditions B = 2A and C = A + 17 both satisfied.
Why Other Options Are Wrong:Other triples do not sum to 185 while satisfying B = 2A and C = A + 17 simultaneously.
Common Pitfalls:Mixing up who is older by 17, or doubling the wrong person’s age. Always restate relationships consistently before solving.
Final Answer:42, 84 and 59 years