Seventy-five percent of a number, when added to 75, equals the number. Find the number.

Introduction / Context:
This is a simple linear equation with a percentage term. Translating the text into an equation and solving for the unknown yields the number directly.

Given Data / Assumptions:

• Let the number be x.
• Condition: 0.75x + 75 = x.

Concept / Approach:
Rearrange to isolate x: move the 0.75x term to the other side to get 25% of x equals 75, then solve by division. Recognize that 25% is one-quarter to speed up computation.

Step-by-Step Solution:

Verification / Alternative check:
75% of 300 = 225; 225 + 75 = 300, satisfying the condition.

Why Other Options Are Wrong:

• 150, 200, 225: Substitution shows the equality does not hold.

Common Pitfalls:
Adding 75 to 100% of x instead of 75% of x, or interpreting 75% incorrectly as 0.75 of 75.

Final Answer: