$30\%$ apples out of $450$ are rotten. How many apples are in good condition?

### Concept & Strategy When a total is divided into two distinct groups (e.g., rotten and good), the percentages of the two groups must add up to $100\%$. Calculating the percentage of the target group directly is more efficient than calculating the unwanted group and subtracting. $$ \text{Target Quantity} = \text{Total} \times (100\% - \text{Unwanted Percentage}) $$ ### Step-by-Step Solution * **Given:** * Total apples = $450$ * Rotten apples percentage = $30\%$ * **Deduction:** * If $30\%$ are rotten, the percentage of apples in good condition is $100\% - 30\% = 70\%$. * **Calculation:** * Calculate $70\%$ of the total number of apples: * $\text{Good Apples} = 70\% \text{ of } 450$ * $\text{Good Apples} = \frac{70}{100} \times 450$ * Cancel out the zeros: * $\text{Good Apples} = 7 \times 45$ * $7 \times 40 = 280$ * $7 \times 5 = 35$ * $280 + 35 = 315$ ### Exam Strategy & Shortcut Use percentage building blocks. $10\%$ of $450$ is $45$. Since we need $70\%$, we just multiply by $7$. $45 \times 7 = 315$. Alternatively, if you find subtraction easier: $10\%$ is $45$, so $30\%$ is $45 \times 3 = 135$. Then subtract: $450 - 135 = 315$. The direct $70\%$ method is usually slightly faster. ### Common Pitfall A common error is calculating $30\%$ of $450$ ($135$) and hastily selecting it as the answer if it were an option. Always double-check what the question is asking for: the *rotten* quantity or the *good* condition quantity. ### Final Answer **Therefore, the correct answer is 315.**