Answer:
11.25 kg of coffee worth $9.40/kg must be mixed with 0.75 kg of coffee worth $11/kg to give 12 kg of coffee worth $9.50/kg.
Explanation:
Let x be the amount of coffee worth $9.40/kg that needs to be mixed with coffee worth $11/kg to get 12 kg of coffee worth $9.50/kg.
We can start by setting up a system of linear equations based on the information given:
Equation 1: x + y = 12 (the total amount of coffee is 12 kg)
Equation 2: (9.4x + 11y)/12 = 9.5 (the average price of the mixed coffee is $9.50/kg)
Simplifying equation 2, we get:
9.4x + 11y = 114
We can now use substitution to solve for x. Solving equation 1 for y, we get:
y = 12 - x
Substituting this into equation 2, we get:
9.4x + 11(12 - x) = 114
Simplifying and solving for x, we get:
9.4x + 132 - 11x = 114
-1.6*x = -18
x = 11.25
Therefore, 11.25 kg of coffee worth $9.40/kg must be mixed with 0.75 kg of coffee worth $11/kg to give 12 kg of coffee worth $9.50/kg.