Last month: 1 batch of cookies and 1 batch of brownies (7 eggs in total)
[tex]c+b=7...(1)[/tex]The month before: 2 batches of brownies and 3 batches of cookies (18 eggs in total)
[tex]3c+2b=18...(2)[/tex]Where c and b are the numbers of eggs needed to make a batch of cookies and brownies, respectively. From equation (1):
[tex]c=7-b[/tex]Using this in (2):
[tex]\begin{gathered} 3(7-b)+2b=18 \\ 21-3b+2b=18 \\ \Rightarrow b=3 \end{gathered}[/tex]Finally, from (1):
[tex]\begin{gathered} c=7-b=7-3 \\ \\ \Rightarrow c=4 \end{gathered}[/tex]He needs 4 eggs to make a batch of cookies and 3 eggs to make a batch of brownies.
