Build a three-term ratio from two equations: If A = B/3 and B = C/2 (all positive), express the simplified ratio A : B : C, showing the substitution path from C to A.

Introduction / Context: Expressing all variables in terms of one helps create a clean ratio. Here, A is related to B, and B is related to C. Substituting stepwise leads to a direct representation of A and B in terms of C, which can then be scaled.

Given Data / Assumptions:

• A = B/3.
• B = C/2.
• All quantities are positive so ratios are meaningful.

Concept / Approach: Substitute B from the second equation into the first to express A in terms of C. Then write A : B : C and clear any fractions using a common multiple to get integer terms.

Step-by-Step Solution:

Verification / Alternative check: Take C = 6. Then B = 3 and A = 1. Check: A = B/3 = 1, B = C/2 = 3—consistent.

Why Other Options Are Wrong: 2 : 3 : 6 doubles only A incorrectly; 3 : 2 : 6 swaps terms; 3 : 1 : 2 and 1 : 2 : 3 do not satisfy the defining equations.

Common Pitfalls: Forgetting to divide by 3 after substituting for B, or mixing the order of A, B, C when forming the ratio.

Final Answer: 1 : 3 : 6