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).

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:

Verification / 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