Since each batch of cookies will need 1/3 cup, Stacy would need 1/3 cup for the first batch , another 1/3 cup for the second batch, and 1/4 of 1/3 cup for the 1/4 batch.
This total can be determined by multiplying 2 and 1/4 (or 9/4) by 1/3:
9/4 * 1/3 = 9/12 or 3/4 cup sugar for all the batches