3.2% of 500 × 2.4% of $x$ = 288

### Concept & Formula This problem features the multiplication of two percentage terms. The goal is to simplify the known term first, treat it as a constant multiplier, and isolate $x$. $$ (\text{Value}_1) \times \left( \frac{\text{Percent}_2}{100} \times x \right) = \text{Result} $$ ### Step-by-Step Solution * **Given:** Equation: $ 3.2\% \text{ of } 500 \times 2.4\% \text{ of } x = 288 $ * **Calculation:** Step 1: Simplify the first term completely. $ 3.2\% \text{ of } 500 = \left(\frac{3.2}{100}\right) \times 500 = 3.2 \times 5 = 16 $ Step 2: Substitute this value into the equation. $ 16 \times (2.4\% \text{ of } x) = 288 $ Step 3: Isolate the term containing $x$. $ 2.4\% \text{ of } x = \frac{288}{16} $ $ 2.4\% \text{ of } x = 18 $ Step 4: Solve for $x$. $ \left(\frac{2.4}{100}\right) \times x = 18 $ $ x = \frac{18 \times 100}{2.4} $ $ x = \frac{1800}{2.4} = \frac{18000}{24} = 750 $ ### Exam Strategy & Shortcut Recognize that "Percent of a number" is commutative. 3.2% of 500 is exactly the same as 500% of 3.2. Since 500% means multiplying by 5, $ 3.2 \times 5 = 16 $. Then, immediately divide the result side (288) by 16 to get 18. Now you just need to solve $ 2.4\% \text{ of } x = 18 $. Since 2.4% is close to 2.5% (which is $ \frac{1}{40} $), $ x $ will be slightly larger than $ 18 \times 40 = 720 $. 750 fits perfectly and is the only logical option. ### Common Pitfall A common trap is attempting to multiply the two percentages together first ($ 3.2\% \times 2.4\% $). This leads to extremely small, error-prone decimals ($ 0.000768 $). Always simplify known constants against whole numbers first before combining terms. ### Final Answer **Therefore, the correct answer is 750.**