1. **State the problem:** Emma made a punch using 4 cups of mango juice and 12 cups of lemonade. She wants to keep the same ratio of mango juice to lemonade but only has 9 cups of lemonade for the new batch. We need to find how much mango juice she should use. 2. **Identify the ratio:** The original ratio of mango juice to lemonade is $$\frac{4}{12}$$. 3. **Simplify the ratio:** Simplify $$\frac{4}{12}$$ by dividing numerator and denominator by their greatest common divisor 4: $$\frac{\cancel{4}}{\cancel{12}} = \frac{1}{3}$$ 4. **Set up the proportion for the new batch:** Let $$x$$ be the amount of mango juice needed for 9 cups of lemonade. The ratio must remain $$\frac{x}{9} = \frac{1}{3}$$. 5. **Solve for $$x$$:** Multiply both sides by 9: $$x = 9 \times \frac{1}{3}$$ 6. **Calculate:** $$x = 3$$ **Answer:** Emma should use 3 cups of mango juice to keep the same ratio with 9 cups of lemonade.