Cascade two ratios to a three-term result: If A : B = 7 : 9 and B : C = 3 : 5, determine A : B : C by aligning the common term B and simplifying.

Introduction / Context:
Combining chained ratios requires equalizing the shared variable. Here, B links the two given ratios. After setting B equal in both, read off the values for A and C to form a combined three-term ratio.

Given Data / Assumptions:

• A : B = 7 : 9.
• B : C = 3 : 5.

Concept / Approach:
Write A : B = 7x : 9x and B : C = 3y : 5y. Match B so 9x = 3y; choose convenient integers to maintain integrality, then compute A, B, C and simplify if needed.

Step-by-Step Solution:

Verification / Alternative check:
Check subratios: A : B = 7 : 9 and B : C = 9 : 15 = 3 : 5, both satisfied.

Why Other Options Are Wrong:
7 : 9 : 5 uses wrong C; 21 : 35 : 45 is not consistent with B : C; 7 : 3 : 15 breaks A : B; 14 : 18 : 30 reduces to 7 : 9 : 15 but is an unsimplified multiple (not minimal form usually expected).

Common Pitfalls:
Multiplying corresponding terms across ratios or mixing up the order; always align the shared term first.

Final Answer:
7 : 9 : 15