Clearly write a system of two linear equations with two unknowns and solve algebraically. Guess and check work is not allowed and will receive no credit, so make sure to set up your equations and solve the system.
In addition, make sure to specify what your variables stand for in your work. If your answers are reversed in the boxes below, you will not receive credit - be very careful in your answers!
A coffee distributor needs to mix a(n) Gazebo coffee blend that normally sells for $10.10 per pound with a Ethiopian coffee blend that normally sells for $14.90 per pound to create 70 pounds of a coffee that can sell for $11.20 per pound. How many pounds of each kind of coffee should they mix?
Let:
- Let x be the number of pounds of the Gazebo coffee blend
- Let y be the number of pounds of the Ethiopian coffee blend
We can set up the following system of equations based on the given information:
1) The total weight of the coffee blend is 70 pounds:
x + y = 70
2) The cost per pound of the coffee blend is $11.20:
(10.10x + 14.90y) / 70 = 11.20
To solve this system algebraically, we can use the method of substitution.
From equation 1), we can rewrite it as x = 70 - y.
Substituting x = 70 - y into equation 2), we get:
(10.10(70 - y) + 14.90y) / 70 = 11.20
(707 - 10.10y + 14.90y) / 70 = 11.20
(707 + 4.8y) / 70 = 11.20
707 + 4.8y = 784
4.8y = 77
y = 77 / 4.8
y ≈ 16.04
Substituting y = 16.04 into x = 70 - y, we get:
x = 70 - 16.04
x ≈ 53.96
Therefore, the coffee distributor should mix approximately 53.96 pounds of Gazebo coffee blend with approximately 16.04 pounds of Ethiopian coffee blend.