1. **State the problem:** We have two similar rectangular prisms with dimensions: - First prism: height = 8 in, length = 12 in, width = 3 in - Second prism: height = y, length = 9 in, width = x We need to find the values of $x$ and $y$. 2. **Use the similarity ratio:** For similar prisms, corresponding dimensions are proportional. So, $$\frac{y}{8} = \frac{9}{12} = \frac{x}{3}$$ 3. **Calculate the ratio:** Simplify $\frac{9}{12}$: $$\frac{9}{12} = \frac{\cancel{3} \times 3}{\cancel{3} \times 4} = \frac{3}{4}$$ 4. **Find $y$:** Using $\frac{y}{8} = \frac{3}{4}$, $$y = 8 \times \frac{3}{4}$$ $$y = 8 \times \frac{3}{4} = \cancel{8}^2 \times \frac{3}{\cancel{4}}^1 = 2 \times 3 = 6$$ 5. **Find $x$:** Using $\frac{x}{3} = \frac{3}{4}$, $$x = 3 \times \frac{3}{4}$$ $$x = 3 \times \frac{3}{4} = \cancel{3}^1 \times \frac{3}{\cancel{4}}^1 = \frac{9}{4} = 2.25$$ **Final answers:** $$x = 2.25$$ $$y = 6$$