A clothing supplier stores 800 coats in a warehouse, of which 15 percent are full-length coats. If 500 of the short-length coats are removed form the warehouse, then what percent of the remaining coats are full length?

### Concept & Strategy This is a **Volume Change Problem**. The key logic is recognizing that removing one type of item (short-length coats) does not change the absolute quantity of the other type (full-length coats), but it *does* change the total quantity. To solve this, we will find the absolute number of full-length coats, find the new total number of coats after the removal, and then calculate the new percentage. ### Step-by-Step Solution * **Initial Total Coats:** $800$ * **Full-length Coats:** $15\%$ of $800 = 0.15 \times 800 = 120$ This means initially, there are $800 - 120 = 680$ short-length coats. The supplier removes $500$ short-length coats. Let's calculate the new total in the warehouse: * **New Total Coats:** Initial Total $-$ Coats Removed * **New Total Coats:** $800 - 500 = 300$ Notice that the number of full-length coats has not changed; it remains $120$. Now, we calculate the new percentage of full-length coats out of the new total: $$ \text{New Percentage} = \left( \frac{\text{Full-length Coats}}{\text{New Total Coats}} \right) \times 100 $$ $$ \text{New Percentage} = \left( \frac{120}{300} \right) \times 100 $$ $$ \text{New Percentage} = \left( \frac{12}{30} \right) \times 100 = \left( \frac{2}{5} \right) \times 100 = 40\% $$ ### Exam Strategy & Shortcut You don't actually need to calculate the initial number of short coats at all. Just calculate the full-length coats ($15\%$ of $800 = 120$). You know $500$ coats of the *other* type are leaving. So the new total inventory is simply $800 - 500 = 300$. The full-length coats are untouched, so they are still $120$. Calculate the fraction: $120 / 300 = 40\%$. Skipping the short-coat calculation saves 10-15 seconds. ### Common Pitfall The trap is assuming the percentage of full-length coats stays the same or calculating the removal from the wrong category. Students occasionally subtract the $500$ from the wrong place or try to do complex percentage subtractions (e.g., $15\%$ of $800$ minus something). Stick to absolute numbers when items are physically removed. ### Final Answer Therefore, the correct answer is **40%**.