1. **State the problem:** Kareem mixes lemonade with a ratio of 3 cups lemon juice to 4 cups water. He uses 32 cups of water and we need to find how many cups of lemon juice are in the large batch. 2. **Understand the ratio:** The ratio of lemon juice to water is $3:4$. This means for every 3 cups of lemon juice, there are 4 cups of water. 3. **Set up the ratio equation:** Let $x$ be the number of times the ratio is multiplied to get the large batch. $$\text{Water} = 4x$$ Given water is 32 cups: $$4x = 32$$ 4. **Solve for $x$:** $$x = \frac{32}{4}$$ $$x = 8$$ 5. **Find lemon juice amount:** $$\text{Lemon juice} = 3x = 3 \times 8 = 24$$ 6. **Diagram explanation:** The total batch can be represented as a rectangle divided into 7 sections (3 for lemon juice, 4 for water). Each section represents 8 cups. **Final answer:** There are **24 cups** of lemon juice in the large batch.