1. **Problem Statement:** Amarilis started with a certain length of string in inches and used pieces of string of different lengths: 3 inches, 4\frac{1}{4} inches, and 4\frac{1}{2} inches. We need to find how much unused string she has left after using these pieces. 2. **Understanding the lengths used:** The lengths of the pieces used are: - 3 inches - 4\frac{1}{4} inches = 4.25 inches - 4\frac{1}{2} inches = 4.5 inches 3. **Total length used:** Add the lengths of all pieces used: $$3 + 4.25 + 4.5 = 11.75$$ inches 4. **Initial length of string:** The problem states Amarilis started with some length but does not specify it explicitly. Since the question asks for unused string rounded to the nearest inch, we assume the initial length is the sum of used pieces plus the unused part. 5. **Unused string calculation:** Let the initial length be $L$ inches. Then, $$\text{Unused string} = L - 11.75$$ 6. **Rounding:** The problem states all measurements are rounded to the nearest inch. If the unused string is rounded to the nearest inch, and assuming the initial length $L$ is the sum of used pieces plus unused string, the unused string is the difference rounded. 7. **Conclusion:** Without the exact initial length $L$, we cannot compute the exact unused string. If the initial length was, for example, 15 inches, then: $$15 - 11.75 = 3.25 \approx 3 \text{ inches unused}$$ **Final answer:** The unused string length is the initial length minus 11.75 inches, rounded to the nearest inch. If you provide the initial length, I can calculate the exact unused string.