Percentage reverse-calculation Solve for x in: x% of 10.8 = 32.4. What is x?

Introduction / Context:
Reverse percentage questions require translating a word statement into a simple equation and isolating the unknown percentage. This is a common test of algebraic manipulation and understanding of percent-as-over-100.

Given Data / Assumptions:

• x% of 10.8 equals 32.4.
• Percent means divide by 100.
• All values are exact; no rounding required.

Concept / Approach:
If x% of A = B, then (x/100) * A = B, so x = (B * 100) / A. Apply this formula directly with A = 10.8 and B = 32.4 to get x.

Step-by-Step Solution:
(x/100) * 10.8 = 32.4x = (32.4 * 100) / 10.8Compute 32.4 / 10.8 = 3Hence x = 3 * 100 = 300.

Verification / Alternative check:
300% of 10.8 = 3 * 10.8 = 32.4, confirming the result precisely.

Why Other Options Are Wrong:
3, 0.3, 30: These correspond to 3%, 0.3%, and 30%, yielding values far less than 32.4.

Common Pitfalls:
Forgetting to multiply by 100 when converting from percentage form; dividing the wrong way (10.8/32.4). Keep the structure (x/100)*10.8 = 32.4 to avoid confusion.

Final Answer:
300