To find the price per cup of the orange sherbet, we first need to determine the total number of cups in a 3-quart tub.
Since there are 4 cups in 1 quart, we can calculate the total cups in 3 quarts:
\[ 3 \text{ quarts} \times 4 \text{ cups/quart} = 12 \text{ cups} \]
The total cost of the tub is $8.88. To find the price per cup, we divide the total cost by the number of cups:
\[ \text{Price per cup} = \frac{\text{Total cost}}{\text{Total cups}} = \frac{8.88}{12} \]
Calculating that gives:
\[ \frac{8.88}{12} = 0.74 \]
Therefore, the price per cup of orange sherbet is $0.74.