Last month: 1 batch of cookies and 1 batch of brownies (7 eggs in total)

The month before: 2 batches of brownies and 3 batches of cookies (18 eggs in total)

Where c and b are the numbers of eggs needed to make a batch of cookies and brownies, respectively. From equation (1):

Using this in (2):

Finally, from (1):

He needs 4 eggs to make a batch of cookies and 3 eggs to make a batch of brownies.