Final answer:
To calculate the amount of punch Jane can make with 6 cups of plum juice, we need to convert cups to liters and use proportions based on the original juice ratios. She can make approximately 4.8 liters of punch with 1.44 liters of plum juice, 2.4 liters of pear juice, and 0.96 liters of pineapple juice.
Step-by-step explanation:
Jane's favorite fruit punch consists of pear, pineapple, and plum juices in the ratio 5:2:3. To find out how much punch she can make with only 6 cups of plum juice, we need to set up a ratio based on the original proportions. First, we convert the given amount of plum juice to liters because the original recipe is in liters (1 cup is approximately 0.24 liters). Six cups of plum juice is roughly 1.44 liters.
Using the original ratio of 5:2:3 for pear, pineapple, and plum juice, and knowing that the amount of plum juice is 1.44 liters, we can set up the following proportions:
- Plum Juice: 3 parts (original ratio) = 1.44 liters (actual)
- Pear Juice: 5 parts (original ratio) = x liters (actual)
- Pineapple Juice: 2 parts (original ratio) = y liters (actual)
To find the values of x and y, we use cross multiplication:
- For pear juice: (5/3) = x/1.44
- For pineapple juice: (2/3) = y/1.44
By solving these equations, we find x (pear juice) is approximately 2.4 liters and y (pineapple juice) is approximately 0.96 liters. Adding these up, Jane can make a total of 4.8 liters of punch with the available plum juice.