42% of a number is 892.5. What is 73% of that number?

### Concept & Strategy Just like the previous problem, bypass finding the 100% base value. Use the unitary method to directly map the known percentage value to the desired percentage value using a fractional multiplier. $$ \text{Desired Value} = \text{Given Value} \times \left( \frac{\text{Desired Percentage}}{\text{Given Percentage}} \right) $$ ### Step-by-Step Solution * **Given:** Given Percentage = 42% Given Value = 892.5 Desired Percentage = 73% * **Calculation:** Step 1: Set up the direct ratio equation. Let the desired value be $y$. $ y = 892.5 \times \left( \frac{73}{42} \right) $ Step 2: Simplify the division first. Divide 892.5 by 42. $ \frac{892.5}{42} = 21.25 $ (This means 1% of the number is 21.25). Step 3: Multiply the 1% value by the desired percentage (73). $ y = 21.25 \times 73 $ $ y = 1551.25 $ ### Exam Strategy & Shortcut Break the multiplication down to avoid heavy calculation. You need to calculate $ 21.25 \times 73 $. Think of 73 as $ 70 + 3 $. $ 21.25 \times 70 = 212.5 \times 7 = 1487.5 $. $ 21.25 \times 3 = 63.75 $. Add them together: $ 1487.5 + 63.75 = 1551.25 $. This is much cleaner and less prone to carry-over errors than a standard vertical multiplication stack. ### Common Pitfall Dividing 892.5 by 42 can look intimidating, leading students to try and convert 42% and 73% into complicated fractional approximations. However, 892.5 divides cleanly into 42. Trust the unitary method and carry out the division; exam questions are usually designed to result in clean decimals like 0.25 or 0.5. ### Final Answer **Therefore, the correct answer is 1551.25.**