Given A : B = 3 : 4 and B : C = 8 : 9, determine A : B : C in simplest integer form.

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