The ratios 2 cups : 2/3 cups and 15/2 cups : 2 1/2 cups have a unit rate of 3, as they simplify to 3 cups : 1 cup.
A unit rate is the ratio of two measurements in which one of the quantities is 1. To determine which ratios have a unit rate of 3, we need to examine each option:
2 cups : 2/3 cups:
This ratio simplifies to 3 cups : 1 cup, which is a unit rate of 3.
1/2 cups : 5/6 cup:
This ratio simplifies to 3/5 cups : 1 cup, which is not a unit rate of 3.
2/3 cup : 1 cup:
This ratio simplifies to 2/3 cup : 1 cup, which is not a unit rate of 3.
15/2 cups : 2 1/2 cups:
This ratio simplifies to 3 cups : 1 cup, which is a unit rate of 3.
1 cup: 1/4 cup:
This ratio simplifies to 4 cups : 1 cup, which is not a unit rate of 3.
3 3/4 cups : 2 cups:
This ratio simplifies to 15/4 cups : 2 cups, which is not a unit rate of 3.
Therefore, the ratios with a unit rate of 3 are 2 cups : 2/3 cups and 15/2 cups : 2 1/2 cups.