85% of 485.5 = 50% of $x$

### Concept & Strategy When one side of an equation equals 50% (or exactly half) of an unknown variable, the unknown variable must be exactly double the value of the other side. $$ \text{Value} = 0.5 \times x \implies x = 2 \times \text{Value} $$ ### Step-by-Step Solution * **Given:** Equation: $ 85\% \text{ of } 485.5 = 50\% \text{ of } x $ * **Calculation:** Step 1: Simplify the equation by removing the 50% fraction. $ 0.85 \times 485.5 = 0.5 \times x $ Multiply both sides by 2 to isolate $x$: $ x = 2 \times (0.85 \times 485.5) $ Step 2: Reorder the multiplication to make it easier. $ x = (2 \times 0.85) \times 485.5 $ $ x = 1.7 \times 485.5 $ Step 3: Perform the final multiplication. $ x = 1.7 \times 485.5 = 825.35 $ ### Exam Strategy & Shortcut You can entirely avoid decimal multiplication by using fractions. 85% is $ \frac{17}{20} $ and 50% is $ \frac{1}{2} $. $ \frac{17}{20} \times 485.5 = \frac{1}{2} \times x $ Multiply both sides by 2: $ x = \frac{17}{10} \times 485.5 $ Dividing by 10 shifts the decimal point: $ x = 17 \times 48.55 $ $ 17 \times 48 = 816 $, and $ 17 \times 0.55 = 9.35 $. $ 816 + 9.35 = 825.35 $. ### Common Pitfall The most common mistake is calculating 85% of 485.5 (which is 412.675) and forgetting that this number is only *half* of the answer. Always ensure you complete the final isolation step for $x$. ### Final Answer **Therefore, the correct answer is 825.35.**