Question

A recipe for pineappleorange juice calls for mixing 2/3 cup of pineapple juice with 2 1/3 cups of orange juice. If you want to make a larger batch using this recipe and 4 cups of pineapple juice, how much orange juice should you use?

Answer 1

To make a larger batch of pineappleorange juice with 4 cups of pineapple juice, the recipe proportion indicates that one would need 14 cups of orange juice.

Step-by-step explanation:

The student wants to know how much orange juice is required when scaling up a recipe for pineappleorange juice, which uses 2/3 cup of pineapple juice and 2 1/3 cups of orange juice. To find the answer, we'll set up a proportion because the amount of pineapple juice used in the large batch (4 cups) compared to the original recipe amount (2/3 cup) will be the same ratio as the amount of orange juice needed for the large batch compared to the original recipe amount (2 1/3 cups).

Firstly, the proportion can be written as:

(2/3 cups pineapple juice) / (2 1/3 cups orange juice) = (4 cups pineapple juice) / (x cups orange juice)

To find the value of x, we cross-multiply and solve for x.

(2/3) * x = 4 * (2 1/3)

Convert mixed number to improper fraction:

2 1/3 = 7/3

Now, the equation is:

(2/3) * x = 4 * (7/3)

Multiply 4 with 7/3:

(2/3) * x = (4 * 7) / 3 = 28/3

Now solve for x:

x = (28/3) / (2/3) = (28/3) * (3/2) = 14

So, for a large batch using 4 cups of pineapple juice, you need 14 cups of orange juice.