In the original recipe, for every 1 1/2 cups of yogurt, Paul uses 1/2 cup of strawberries.
If Paul increases the recipe to include 2 cups of yogurt, we can find the corresponding amount of strawberries by setting up a proportion.
Let's set up the proportion:
(1 1/2 cups of yogurt) / (1/2 cup of strawberries) = (2 cups of yogurt) / (x cups of strawberries)
To solve for x, we can cross-multiply:
(1 1/2) * (x) = (2) * (1/2)
(3/2) * (x) = 1
Multiplying both sides by the reciprocal of 3/2 (which is 2/3):
(2/3) * (3/2) * (x) = (2/3) * (1)
x = 2/3
Therefore, Paul will need 2/3 cup of strawberries when he increases the recipe to include 2 cups of yogurt.