1. **State the problem:** We have a mixture of juices with ingredients Apple, Orange, and Cranberry in the ratio 4:3:1, and the total amount of juice is 48 cups. 2. **Formula and rules:** The ratio parts add up to the total parts of the mixture. To find the amount of each ingredient, use the formula: $$\text{Amount of ingredient} = \frac{\text{Ratio part of ingredient}}{\text{Sum of all ratio parts}} \times \text{Total cups}$$ 3. **Calculate the sum of ratio parts:** $$4 + 3 + 1 = 8$$ 4. **Calculate each ingredient's amount:** - Apple: $$\frac{4}{8} \times 48 = 24$$ cups - Orange: $$\frac{3}{8} \times 48 = 18$$ cups - Cranberry: $$\frac{1}{8} \times 48 = 6$$ cups 5. **Explanation:** The ratio tells us how many parts of each ingredient are in the mixture. Since the total is 48 cups, we divide it according to the ratio parts to find the exact amount of each juice. **Final answer:** Apple = 24 cups, Orange = 18 cups, Cranberry = 6 cups.