Question

If the baker has 26 cups of flour and 9 cups of butter, how many batches of each type of cookie can she make?

Answer 1

Given:

2 cups of flour and 3/4 cup of butter needed to make one batch of peanut butter cookies.

3 cups of flour and 1 cup of butter needed to make one batch of chocolate chip cookies.

Required:

Number of batches of each type of cookies can be made from 26 cups of flour and 9 cups of butter.

Answer:

Let the number of cups of flour and number of cups of butter for one batch of peanut butter cookies be

`x`

Let the number of cups of flour and number of cups of butter for one batch of chocolate chip cookies be

`y`

Then the given information can be represented in equation form as,

`\begin{gathered} 2x+3y=26 \\ (3)/(4)x+y=9 \\ \end{gathered}`

Multiplying second equation by 4 on both sides, we get,

`\begin{gathered} 2x+3y=26 \\ 3x+4y=36 \end{gathered}`

Multiplying first equation by 3 and second by 2 on both sides , we get,

`\begin{gathered} 6x+8y=72 \\ 6x+9y=78 \end{gathered}`

Solving these two simultaneous equations, we get,

`x=4,y=6`

Final Answer:

4 batches of peanut butter cookies and 6 batches of chocolate chip cookies can be made from 26 cups of flour and 9 cups of butter.