Question

Manny likes to make desserts for bake sales. Last month, he made 1 batch of brownies and 1 batch of cookies, which called for 7 eggs total. The month before, he baked 2 batches of brownies and 3 batches of cookies, which required a total of 18 eggs. How many eggs did Manny use for a batch of each dessert? a eggs to make a batch of brownies and eggs to make a batch of Manny uses cookies.

Answer 1

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

`c+b=7...(1)`

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

`3c+2b=18...(2)`

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

`c=7-b`

Using this in (2):

`\begin{gathered} 3(7-b)+2b=18 \\ 21-3b+2b=18 \\ \Rightarrow b=3 \end{gathered}`

Finally, from (1):

`\begin{gathered} c=7-b=7-3 \\ \\ \Rightarrow c=4 \end{gathered}`

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