Final answer:
Using the ratio 5:2:3 for pear, pineapple, and plum juices respectively and given 6 cups of plum juice, the total punch Jane can make is closest to 18 cups, considering the calculation error in the provided options.
Step-by-step explanation:
Jane's favorite fruit punch consists of pear, pineapple, and plum juices in the ratio 5:2:3. If she has 6 cups of plum juice, we can determine the total amount of punch she can make. To keep the ratio intact and given that the amount of plum juice corresponds to the '3' part of the ratio, we use a simple proportion.
- Ratio for plum juice = 3 parts
- Total ratio parts = 5 (pear) + 2 (pineapple) + 3 (plum) = 10 parts
We calculate how many parts one cup of plum juice represents:
3 parts (for plum) / 6 cups (available plum juice) = 0.5 part per cup
Now we find out how many cups are needed for pear and pineapple to maintain the ratio:
- Pear juice: 5 parts x 0.5 part per cup = 2.5 cups
- Pineapple juice: 2 parts x 0.5 part per cup = 1 cup
Total punch: 6 cups (plum) + 2.5 cups (pear) + 1 cup (pineapple) = 9.5 cups. However, since 9.5 cups is not one of the multiple-choice options provided, we should consider whether we've made a multiplication error. Since the total ratio parts are 10, and plum juice fills 3 of these parts, we need to do the following multiplication:
(Total ratio parts / Plum juice ratio parts) x Plum juice quantity = Total punch quantity
(10 / 3) x 6 cups = 20 cups
Therefore, Jane can make 20 cups of punch which suggests there might be an error in the list of options provided. However, we should choose the answer that is closest to our calculated result, which would make the correct answer:
B) 18 cups