Find the whole from a part percentage: If 31% of a number is 46.5, what is the number?

Introduction / Context:
Given a part of a whole expressed via a percentage, we are asked to recover the original whole. This is the reverse of “finding a percentage of a number.”

Given Data / Assumptions:

• x is the unknown number.
• 31% of x equals 46.5.

Concept / Approach:
Translate “31% of x” to 0.31 * x. Then solve the simple linear equation 0.31x = 46.5 by dividing both sides by 0.31.

Step-by-Step Solution:

Verification / Alternative check:
Check forward: 31% of 150 = 0.31 * 150 = 46.5, confirming the value.

Why Other Options Are Wrong:

• 155, 160, 165, 180 produce 31% values different from 46.5.

Common Pitfalls:
Misplacing the decimal when converting 31% to 0.31 or attempting to divide by 31 (instead of 0.31). Keep percent-to-decimal conversion precise.

Final Answer:
150