One-eighth of a number is 41.5. What will 69% of that number be?

### Concept & Strategy The problem requires finding a base number from a given fractional part and then calculating a percentage of that base number. The strategy is to set up a simple algebraic equation to find the base number, then apply the required percentage. $$ \text{Base} = \text{Part} \times \text{Denominator} $$ ### Step-by-Step Solution **Given:** * $\frac{1}{8}$ of a number is $41.5$. * We need to find $69\%$ of this same number. **Calculation / Deduction:** * Let the unknown number be $N$. * According to the problem statement: $\frac{1}{8} \times N = 41.5$ * Multiply both sides by $8$ to isolate $N$: $N = 41.5 \times 8$ * Calculate the product to find the base number: $N = 332$ * Now, find $69\%$ of $332$: $\frac{69}{100} \times 332$ * Multiply $69$ by $332$: $69 \times 332 = 22908$ * Divide by $100$ to apply the percentage: $\frac{22908}{100} = 229.08$ ### Exam Strategy & Shortcut Instead of performing the full multiplication for the final step, use unit digit analysis to save time. The final calculation is $332 \times 0.69$. Ignore the decimal temporarily and look at the unit digits of the numbers: $2 \times 9 = 18$. This means the final product must end with an $8$. Looking at the provided options, only $229.08$ ends with an $8$. This allows you to skip the tedious arithmetic entirely. ### Common Pitfall A frequent mistake is finding the base number ($332$) and forgetting to perform the second half of the problem (finding $69\%$). Another pitfall is misplacing the decimal point during the final multiplication, leading to an answer off by a factor of ten. ### Final Answer Therefore, the correct answer is **229.08**.