Final answer:
In a fruit punch recipe, variable x is the cups of orange juice and y is the cups of apple juice, with the relationship x = 1.5y. To make 5 batches of punch using 3 cups of pineapple juice per batch, Evana would need 3.75 quarts of pineapple juice.
Step-by-step explanation:
In the situation described, where a fruit punch recipe uses 1.5 cups of orange juice for every cup of apple juice, we can define the variables x and y. The variable x will represent the number of cups of orange juice, and the variable y will represent the number of cups of apple juice used in the recipe. To maintain the ratio given in the recipe, the relationship between x and y would be x = 1.5y.
Additionally, to answer the question about Evana’s fruit punch recipe needing pineapple juice in quarts, we calculate the total amount of pineapple juice needed by multiplying the number of cups per batch by the number of batches:
Total cups of pineapple juice = 3 cups/batch × 5 batches = 15 cups.
We then set up a proportion to convert cups to quarts, knowing that there are 4 cups in 1 quart:
4 cups/1 quart = 15 cups/x quarts
Cross-multiplication gives:
4x = 15 × 1
x = 15/4
x = 3.75 quarts of pineapple juice needed for 5 batches.