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
[tex]x[/tex]
Let the number of cups of flour and number of cups of butter for one batch of chocolate chip cookies be
[tex]y[/tex]
Then the given information can be represented in equation form as,
[tex]\begin{gathered} 2x+3y=26 \\ \frac{3}{4}x+y=9 \\ \end{gathered}[/tex]
Multiplying second equation by 4 on both sides, we get,
[tex]\begin{gathered} 2x+3y=26 \\ 3x+4y=36 \end{gathered}[/tex]
Multiplying first equation by 3 and second by 2 on both sides , we get,
[tex]\begin{gathered} 6x+8y=72 \\ 6x+9y=78 \end{gathered}[/tex]
Solving these two simultaneous equations, we get,
[tex]x=4,y=6[/tex]
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.
