Number equals its own 75% plus 75: Seventy-five percent of a number, when added to 75, equals the number itself. What is that number?

Introduction / Context:This problem is a linear equation framed in percentage language. The number is equal to a fraction (75%) of itself plus a constant (75). Translating words into an algebraic equation is the main skill tested here, followed by simple solving.

Given Data / Assumptions:

• If N is the number, then 75% of N plus 75 equals N.
• 75% = 0.75 in decimal form.

Concept / Approach:Write the statement as an equation: 0.75N + 75 = N. Isolate N by moving like terms and then dividing by the coefficient. Double-check computation to avoid arithmetic slips when handling decimals and constants together.

Step-by-Step Solution:

Verification / Alternative check:Compute 75% of 300 = 225; add 75 to get 300, which equals the original number, confirming the solution.

Why Other Options Are Wrong:280, 305, 360, and 400 do not satisfy 0.75N + 75 = N. Substitution will show mismatches in each case.

Common Pitfalls:Forgetting to convert 75% to 0.75 or mismanaging the subtraction step N − 0.75N. Keeping track of decimal places is crucial in percentage equations.

Final Answer:300