Question

The coffee counter charges ?"$11.00" per pound for kenyan french roast coffee and ?"$13.00" per pound for sumatra coffee. How much of each type should be used to make a 26 pound blend that sells for ?$12.00 per? pound

Answer 1

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

$x+y=26,~~~~~~~~~~~~~~~~~~~~~~(A)\\\\11x+13y=12\times 26.~~~~~~~~~~(B)$

Multiplying equation (A) by 11 and subtracting from equation (B), we have

$13y-11y=12\times26-11\times26\\\\\Rightarrow 2y=26\\\\\Rightarrow y=13,$

and from equation (A),

$x=26-13=13.$

Thus, 13 pounds of each type of coffee should be used.