The coffee counter charges $10 per pound for kenyan french roast coffee and $9 per pound for sumatran coffee.
how much of each type should be used to make a 20 pound blend that sells for $ 9.50 per pound?

      10 pounds of each type of coffee should be mixed to make a 20 pound blend that sells for $9.50 per pound.

 Charges for Kenyan French Roast coffee = $10 per pound

 Charges for Sumatran coffee = $9 per pound

Let the amount of Kenyan French Roast used = K pound

And the amount of Sumatran coffee used = S pound

If the total amount of the mixture = 20 pounds

Equation for the total amount will be,

K + S = 20 (1)

If the cost of this mixture = $9.50

Equation for the cost of the mixture will be,

10K + 9S = 20×9.50

10k + 9S = 190 (2)

Multiply equation (1) by 9 and subtract this equation from equation (2),

(10k + 9S) - (9K + 9S) = 190 - 180

K = 10 pounds

Substitute the value of K in equation (1),

10 + S = 20

S = 10 pounds

     Therefore, 10 pounds of each blend of coffee should be mixed.

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10 pounds of each

Step-by-step explanation:

If K is the amount of Kenyan French Roast coffee, and S is the amount of Sumatran coffee, then the total amount is:

K + S = 20

And the total cost is:

10K + 9S = 9.5×20

10K + 9S = 190

Solving the system of equations, let's substitute:

10K + 9(20 − K) = 190

10K + 180 − 9K = 190

K = 10

S = 20 − K

S = 10

10 pounds of Kenyan French Roast and 10 pounds of Sumatran coffee should be used to make a 20 pound blend worth $9.50 per pound.