$15\%$ of $578 + 22.5\%$ of $644 = $x$

### Concept & Formula Break down difficult decimal percentages into summable, manageable fractions (like $10\%$, $5\%$, and $2.5\%$) to perform calculations without needing a calculator. ### Step-by-Step Solution * **Given:** We must evaluate $15\%$ of $578 + 22.5\%$ of $644$. * **Calculation:** Calculate the first part using the split method ($10\% + 5\%$). $$ 10\% \text{ of } 578 = 57.8 $$ $$ 5\% \text{ of } 578 = \frac{57.8}{2} = 28.9 $$ $$ 15\% \text{ of } 578 = 57.8 + 28.9 = 86.7 $$ * Calculate the second part. $22.5\%$ is equivalent to the fraction $\frac{22.5}{100} = \frac{45}{200} = \frac{9}{40}$. $$ \frac{9}{40} \times 644 = \frac{9 \times 161}{10} $$ $$ = \frac{1449}{10} = 144.9 $$ * Add the two results together. $$ 86.7 + 144.9 = 231.6 $$ ### Exam Strategy & Shortcut Converting $22.5\%$ to its fractional equivalent $\frac{9}{40}$ is a massive time-saver. By turning a complex decimal multiplication into a simple division by $4$ and multiplication by $9$, you bypass the risk of misplaced decimal points and can quickly arrive at $144.9$. ### Common Pitfall Attempting to brute-force the multiplication of $0.225 \times 644$. This takes significantly longer and makes it highly likely you will misplace the decimal point during the multi-line addition step of standard multiplication. ### Final Answer **Therefore, the correct answer is 231.6.**