Solve for the unknown: 89% of a number plus 365 equals 1075.22. What is the number?

Introduction / Context:
This linear percentage equation involves isolating the unknown number from a mixed expression containing a percent of the number plus a constant. Converting to decimal and solving step-by-step yields the exact result.

Given Data / Assumptions:

• Equation: 0.89x + 365 = 1075.22.
• x represents the unknown number.

Concept / Approach:
Subtract the constant to isolate the percentage term, then divide by the decimal percentage (0.89) to obtain x. This is a direct algebraic manipulation.

Step-by-Step Solution:

Verification / Alternative check:
Plug back: 0.89 * 798 = 710.22; add 365 gives 1075.22, matching exactly.

Why Other Options Are Wrong:

• 897, 898, 752: Substitution fails to reach 1075.22 when processed through 0.89x + 365.

Common Pitfalls:
Dividing by 89 instead of 0.89, or rounding too early and losing accuracy. Keep at least two decimals until the final check.

Final Answer: