Answer:
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.
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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