Final answer:
In total, 4 ounces of grapefruit juice were added to the pitcher to make grapefruit juice 1/3 of the total mixture.
Step-by-step explanation:
The question is asking how many ounces of grapefruit juice were added to a pitcher initially containing 32 ounces of orange juice and 12 ounces of grapefruit juice to make grapefruit juice 1/3 of the total mixture. To solve this, we assume x ounces of grapefruit juice are added. The total content of the pitcher will be 32 + 12 + x ounces. Since we want the grapefruit juice to be 1/3 of the total, we can set up the equation 1/3 (32 + 12 + x) = 12 + x. Simplifying the equation gives us 1/3 * (44 + x) = 12 + x. Multiplying through by 3 gives us 44 + x = 36 + 3x, which simplifies to 2x = 8. Therefore, x = 4 ounces. So, 4 ounces of grapefruit juice were added to the pitcher.