Question

A coffee distributor needs to mix a(n) Gazebo coffee blend that normally sells for $10.20 per pound with a Kona coffee blend that normally sells for $12.20 per pound to create 70 pounds of a coffee that can sell for $10.91 per pound. How many pounds of each kind of coffee should they mix

Answer 1

Let x represent pounds of Gazebo coffee and y represent pounds of Kona coffee.  

We are told that a coffee distributor wants 70 pounds of coffee. We can represent this information in an equation as:

$x+y=70...(1)$

$y=70-x...(1)$

We have been given that Gazebo coffee blend sells for $10.20 per pound, so cost of x pounds of Gazebo coffee would be $10.20x$.

Kona coffee blend sells for $12.20 per pound, so cost of y pounds of Kona coffee would be $12.20y$.

Cost of 70 pounds of a coffee that can sell for $10.91 per pound would be $70(10.91)$.

$10.20x+12.20y=70(10.91)...(2)$

Upon substituting equation (1) in equation (2), we will get:

$10.20x+12.20(70-x)=70(10.91)$  

$10.20x+854-12.20x=763.7$

$-2x+854=763.7$

$-2x+854-854=763.7-854$

$-2x=-90.3$

$\frac{-2x}{-2}=\frac{-90.3}{-2}$

$x=45.15$

Therefore, distributor should use 45.15 pounds of Gazebo coffee.

Upon substituting $x=45.15$ in equation (1), we will get:

$y=70-14.15=24.85$

Therefore, distributor should use 24.85 pounds of Kona coffee.