$92.5\%$ of $550 = $x$

### Concept & Formula Finding large percentages can often be simplified by calculating the difference from $100\%$, a technique known as negative percentage calculation. $$ P\% \text{ of } N = (100\% - (100-P)\%) \text{ of } N $$ ### Step-by-Step Solution * **Given:** Find $92.5\%$ of $550$. * **Calculation:** Represent $92.5\%$ as $(100\% - 7.5\%)$. $$ 100\% \text{ of } 550 = 550 $$ * Now, calculate $7.5\%$ of $550$. Let's break down $7.5\%$ into $5\% + 2.5\%$. $$ 10\% \text{ of } 550 = 55 $$ $$ 5\% \text{ of } 550 = 27.5 $$ $$ 2.5\% \text{ of } 550 = 13.75 $$ * Add the parts together to find $7.5\%$. $$ 7.5\% = 27.5 + 13.75 = 41.25 $$ * Subtract this from the $100\%$ value. $$ 550 - 41.25 = 508.75 $$ ### Exam Strategy & Shortcut The subtraction method shown above is by far the most efficient exam shortcut for percentages near $100$. It replaces heavy multiplication involving $0.925$ with simple mental additions and one final subtraction, drastically reducing calculation errors. ### Common Pitfall Multiplying $0.925$ directly by $550$. While technically correct, this brute-force method relies on keeping track of three decimal places during a lengthy multiplication, which often results in arithmetic mistakes under time pressure. ### Final Answer **Therefore, the correct answer is 508.75.**