Answer: We need to add 40 ounces of water to the 100 oz of concentrated juice and water to obtain a new mixture that is 20% concentrated juice.
Explanation:
We can begin by setting up an equation based on the given information.
Let's say we need to add x ounces of water to the 100 oz of concentrated juice and water to obtain the new 20% mixture.
The amount of pure juice in the original 100 oz mixture is 28% of 100 oz, which is 0.28(100) = 28 oz.
After x ounces of water are added, the total volume of the mixture becomes 100 + x oz. The amount of pure juice remains the same at 28 oz. We want to find the amount of water that needs to be added to reach a concentration of 20%.
Setting up the equation:
0.20(100 + x) = 28
Expanding and simplifying:
20 + 0.20x = 28
0.20x = 8
x = 40