Linked percentages across variables: If 90% of A equals 30% of B and B = C% of A, find the value of C.

Introduction / Context:
This item connects two percentage relationships among A, B, and C. The goal is to express B as a percent of A once we compare 90% of A with 30% of B.

Given Data / Assumptions:

• 0.90A = 0.30B.
• B = (C/100) * A.

Concept / Approach:
Solve the first equation for B in terms of A, then equate it to (C/100) * A. Cancel A (assuming A ≠ 0), and solve for C.

Step-by-Step Solution:

Verification / Alternative check:
Check: If B = 300% of A, then 30% of B = 30% of 3A = 0.90A, which matches the left side.

Why Other Options Are Wrong:

• 900, 800, 600 are multiples that do not satisfy both relationships simultaneously.
• 150 would make B = 1.5A; then 30% of B would be 0.45A, not 0.90A.

Common Pitfalls:
Solving 0.90/0.30 incorrectly or forgetting that “B = C% of A” means (C/100) * A.

Final Answer:
300