Linked variable definitions to ratio: If A = B/4 and B = C/2, find the simplest whole-number ratio A : B : C.

Introduction / Context:
Expressing variables in terms of a common parameter often simplifies ratio problems. Here, A and B are defined in terms of each other, and B is defined in terms of C, so we align all three to construct the ratio A : B : C.

Given Data / Assumptions:
A = B/4 and B = C/2.

Concept / Approach:
Use the second relation to express B and A in terms of C, then read off the ratio and simplify to the least integers.

Step-by-Step Solution:
From B = C/2, we get C = 2B. From A = B/4, we get A expressed via B. Hence A : B : C = (B/4) : B : (2B) = 1/4 : 1 : 2. Multiply by 4 to remove fractions → 1 : 4 : 8.

Verification / Alternative check:
Put B = 4 (convenient). Then A = 1 and C = 8. Relations hold: A = B/4 → 1 = 4/4; B = C/2 → 4 = 8/2.

Why Other Options Are Wrong:

• 4 : 2 : 1 or 1 : 2 : 4 invert and mis-scale the relationships.
• 8 : 4 : 1 reverses the order.
• 2 : 4 : 8 scales inconsistently with A = B/4.

Common Pitfalls:
Inverting the direction of relationships (e.g., assuming B = 4A instead of A = B/4) and mixing up order when writing ratios.

Final Answer:
1 : 4 : 8