1. **State the problem:** We have a corn chowder recipe with 3 cups of corn, 2 cups of water, and 1 1\/2 cups of cream. We want to find how much corn is needed if the cream is increased to 4 1\/2 cups. 2. **Identify the relationship:** The ingredients are proportional. The ratio of corn to cream remains constant when scaling the recipe. 3. **Write the ratio:** Original corn to cream ratio is $$\frac{3}{1.5}$$. 4. **Calculate the ratio:** Simplify $$\frac{3}{1.5} = \frac{3}{\cancel{1.5}} \times \frac{\cancel{2}}{2} = \frac{6}{3} = 2$$. 5. **Set up proportion for new cream amount:** Let $x$ be the new amount of corn needed for 4 1\/2 cups of cream. $$\frac{x}{4.5} = 2$$ 6. **Solve for $x$:** $$x = 2 \times 4.5 = 9$$ 7. **Answer:** You will need 9 cups of corn if you use 4 1\/2 cups of cream.