Daniel likes to make desserts for bake sales. Last month, he made 2 batches of brownies and 2 batches of cookies, which called for 12 eggs total. The month before, he baked 3 batches of brownies and 1 batch of cookies, which required a total of 12 eggs. How many eggs did Daniel use for a batch of eggs and how many eggs did Daniel use for a batch of cookies?
Let's call the number of eggs used for a batch of brownies "B" and the number of eggs used for a batch of cookies "C."
From the information given, we can make two equations:
2B + 2C = 12, and
3B + 1C = 12.
Simplifying the first equation, we have 2B + 2C = 12 is equivalent to B + C = 6.
Rearranging the second equation, we have 1C = 12 - 3B is equivalent to C = 12 - 3B.
Substituting C in the first equation, we have B + (12 - 3B) = 6.
Expanding and combining like terms, we have B + 12 - 3B = 6, which simplifies to 12 - 2B = 6.
Subtracting 12 from both sides, we have -2B = -6.
Dividing both sides by -2, we have B = 3.
Substituting B into the second equation, we have C = 12 - 3 * 3.
Performing the calculation, we have C = 12 - 9 = 3.
Therefore, Daniel used 3 eggs for a batch of brownies and 3 eggs for a batch of cookies. Answer: \boxed{3}.