Solve $[ 180\% \text{ of } ($x$) ] \div 2 = 504$

### Concept & Formula This is a direct algebraic simplification problem involving percentages. The core concept is converting the percentage into a decimal or fraction to isolate the unknown variable. $$ P\% \text{ of } x = \frac{P}{100} \times x $$ ### Step-by-Step Solution * **Calculation / Deduction:** * Convert $180\%$ into a decimal: $180\% = 1.8$. * Rewrite the equation using standard notation: * $(1.8 \times x) \div 2 = 504$ * Multiply both sides of the equation by $2$ to remove the denominator: * $1.8x = 504 \times 2$ * $1.8x = 1008$ * Divide by $1.8$ to isolate $x$: * $x = \frac{1008}{1.8}$ * Multiply the numerator and denominator by $10$ to remove the decimal: * $x = \frac{10080}{18}$ * Simplify the fraction (both are divisible by $9$): * $\frac{10080}{9} = 1120$, and $\frac{18}{9} = 2$. * $x = \frac{1120}{2} = 560$. ### Exam Strategy & Shortcut You can reframe the equation before calculating large numbers. Notice that $180\% \div 2 = 90\%$. The equation simplifies instantly to $90\% \text{ of } x = 504$. Since $90\%$ is $\frac{9}{10}$, you have $\frac{9}{10}x = 504$. Divide $504$ by $9$ (which is $56$) and multiply by $10$ to get $560$. This mental math completely avoids dealing with $10080 \div 18$. ### Common Pitfall A trivial but frequent error is multiplying $504$ by $180\%$ instead of isolating the variable, or forgetting to multiply by $2$ when transferring the division to the right-hand side. ### Final Answer **Therefore, the correct answer is 560.**