Let's start by finding out how much cranberry juice is currently in the 30 oz. mixture. If the mixture is 40% cranberry juice, then the amount of cranberry juice in ounces is:
0.4 x 30 = 12 oz.
We want to end up with a 30 oz. mixture that is 20% cranberry juice. So the amount of cranberry juice in ounces we need in the new mixture is:
0.2 x 30 = 6 oz.
To achieve this, we need to remove some of the original mixture, which contains 12 oz. of cranberry juice, and replace it with seltzer, which contains 0 oz. of cranberry juice. Let's say we remove x oz. of the original mixture.
The amount of cranberry juice left in the mixture after we remove x oz. is:
12 - x
The amount of seltzer left in the mixture after we remove x oz. is:
30 - x
If we replace the x oz. of mixture we removed with seltzer, the amount of cranberry juice in the new mixture is:
12 - x + 0 = 12 - x
And the amount of seltzer in the new mixture is:
30 - x + x = 30
We want the new mixture to contain 6 oz. of cranberry juice, which is 20% of the total 30 oz. So we can set up an equation:
(12 - x) / 30 = 0.2
Simplifying this equation, we get:
12 - x = 6
x = 6
So we need to remove 6 oz. of the original mixture and replace it with 6 oz. of seltzer to end up with a 30 oz. mixture that is 20% cranberry juice.