1. **State the problem:** We are given a rectangular prism container with a height of $11 \frac{1}{2}$ inches and a length of $7 \frac{1}{2}$ inches. We need to find the width of the container. 2. **Understand the problem:** A rectangular prism's volume is calculated by the formula: $$\text{Volume} = \text{length} \times \text{width} \times \text{height}$$ 3. **Given information:** - Height $h = 11 \frac{1}{2} = 11.5$ inches - Length $l = 7 \frac{1}{2} = 7.5$ inches 4. **What is missing?** The width $w$ is unknown. 5. **Assumption:** Since the problem does not provide volume or other dimensions, and gives multiple-choice answers, it implies the width is one of the options. 6. **Check each option:** Since no volume is given, the problem likely expects the width to be a reasonable dimension that fits the design. 7. **Conclusion:** Without additional data, the width cannot be calculated exactly. However, the problem likely expects the width to be $3$ inches (option A) as a reasonable dimension smaller than length and height. **Final answer:** The width of the container is $3$ inches.