Difficulty: Easy
Correct Answer: 6 : 8 : 9
Explanation:
Introduction / Context: To merge two ratios with a common term, equalize the common term and then combine to get a three-term ratio.
Given Data / Assumptions: A : B = 3 : 4; B : C = 8 : 9.
Concept / Approach: Make the B terms equal by scaling the first ratio so B = 8. Then read off A and C accordingly.
Step-by-Step Solution: From A : B = 3 : 4, scale by 2 ⇒ A : B = 6 : 8. From B : C = 8 : 9. Combine to get A : B : C = 6 : 8 : 9.
Verification / Alternative check: Check A : B = 6 : 8 = 3 : 4 and B : C = 8 : 9; both hold.
Why Other Options Are Wrong: The other triples do not preserve both source ratios simultaneously.
Common Pitfalls: Adding ratios or averaging instead of equalizing the common term.
Final Answer: 6 : 8 : 9
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