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)](https://tex.z-dn.net/?f=x%2By%3D70...%281%29)
![y=70-x...(1)](https://tex.z-dn.net/?f=y%3D70-x...%281%29)
We have been given that Gazebo coffee blend sells for $10.20 per pound, so cost of x pounds of Gazebo coffee would be
.
Kona coffee blend sells for $12.20 per pound, so cost of y pounds of Kona coffee would be
.
Cost of 70 pounds of a coffee that can sell for $10.91 per pound would be
.
![10.20x+12.20y=70(10.91)...(2)](https://tex.z-dn.net/?f=10.20x%2B12.20y%3D70%2810.91%29...%282%29)
Upon substituting equation (1) in equation (2), we will get:
![10.20x+854-12.20x=763.7](https://tex.z-dn.net/?f=10.20x%2B854-12.20x%3D763.7)
![-2x+854=763.7](https://tex.z-dn.net/?f=-2x%2B854%3D763.7)
![-2x+854-854=763.7-854](https://tex.z-dn.net/?f=-2x%2B854-854%3D763.7-854)
![-2x=-90.3](https://tex.z-dn.net/?f=-2x%3D-90.3)
![\frac{-2x}{-2}=\frac{-90.3}{-2}](https://tex.z-dn.net/?f=%5Cfrac%7B-2x%7D%7B-2%7D%3D%5Cfrac%7B-90.3%7D%7B-2%7D)
![x=45.15](https://tex.z-dn.net/?f=x%3D45.15)
Therefore, distributor should use 45.15 pounds of Gazebo coffee.
Upon substituting
in equation (1), we will get:
![y=70-14.15=24.85](https://tex.z-dn.net/?f=y%3D70-14.15%3D24.85)
Therefore, distributor should use 24.85 pounds of Kona coffee.