Answer: The answer is 13 ponds of each type should be used.
Step-by-step explanation: Given that the coffee counter charges $11.00 per pound for kenyan french roast coffee and $13.00 per pound for sumatra coffee. We are to find the quantity of each type that should be used to make a 26 pound blend that sells for $12.00 per pound.
Let 'x' pound and 'y' pound of kenyan french roast coffee and sumatra coffee be used in the mixture of 26 pound.
So, we have
[tex]x+y=26,~~~~~~~~~~~~~~~~~~~~~~(A)\\\\11x+13y=12\times 26.~~~~~~~~~~(B)[/tex]
Multiplying equation (A) by 11 and subtracting from equation (B), we have
[tex]13y-11y=12\times26-11\times26\\\\\Rightarrow 2y=26\\\\\Rightarrow y=13,[/tex]
and from equation (A),
[tex]x=26-13=13.[/tex]
Thus, 13 pounds of each type of coffee should be used.
