30% of 1225 - 64% of 555 = $x$

### Concept & Strategy This question tests speed and accuracy in calculating exact percentages of numbers ending in $5$. The best strategy is multiplying the base number by the decimal equivalent of the percentage, or breaking down the percentages into standard $10\%$ and $1\%$ blocks. ### Step-by-Step Solution * **Given**: $30\% \text{ of } 1225 - 64\% \text{ of } 555 = x$ * **Calculation**: 1. Calculate $30\% \text{ of } 1225$: $10\% \text{ of } 1225 = 122.5$ $30\% = 122.5 \times 3 = 367.5$ 2. Calculate $64\% \text{ of } 555$: Convert to decimal multiplication: $0.64 \times 555$. Alternatively, $50\% + 10\% + 4\%$. $50\% \text{ of } 555 = 277.5$ $10\% \text{ of } 555 = 55.5$ $1\% \text{ of } 555 = 5.55 \rightarrow 4\% = 5.55 \times 4 = 22.2$ Total $= 277.5 + 55.5 + 22.2 = 355.2$ 3. Subtract the second result from the first: $$x = 367.5 - 355.2$$ $$x = 12.3$$ ### Exam Strategy & Shortcut An alternative mental math trick for $64\% \text{ of } 555$: Notice that $555$ is easy to multiply by single digits. $64 \times 5 = 320$. So, $64 \times 500 = 32000$. $64 \times 50 = 3200$. $64 \times 5 = 320$. Total $= 35520$. Since it's a percentage ($ \div 100$), shift the decimal two places: $355.2$. This avoids dealing with multiple fractional pieces and relies on simple integer multiplication. ### Common Pitfall When breaking down $64\%$ into $50\% + 10\% + 4\%$, a frequent mistake is misaligning the decimal points during the final addition phase (e.g., adding $22.2$ as $2.22$). Ensure all numbers are aligned by their decimal point before adding or subtracting. ### Final Answer **Therefore, the correct answer is 12.3.**