Answer :
Given:
The Coffee Counter charges $7.00 per pound for Kenyan French Roast coffee and $11.00 per pound for Sumatran coffee
Let the number of pounds from Kenyan French Roast coffee = x
And the number of pounds from Sumatran coffee = y
He wants to make a 24-pound blend that sells for $9.00 per pound
So, we have the following equations:
[tex]\begin{gathered} x+y=24\rightarrow(1) \\ 7x+11y=9\cdot24\rightarrow(2) \end{gathered}[/tex]From equation (1):
[tex]x=24-y\rightarrow(3)[/tex]substitute with (x) from equation (3) into equation (2) then solve for (y)
[tex]\begin{gathered} 7\cdot(24-y)+11y=9\cdot24 \\ 7\cdot24-7y+11y=9\cdot24 \\ 4y=9\cdot24-7\cdot24 \\ 4y=2\cdot24 \\ y=\frac{2\cdot24}{4}=12 \end{gathered}[/tex]substitute with (y) into equation (3) to find (x)
[tex]x=24-12=12[/tex]so, the answer will be:
The Coffee Counter should mix (12) pounds of Kenyan Roast coffee and (12) pounds of Sumatran coffee.