Respuesta :
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:
[tex]x+y=70...(1)[/tex]
[tex]y=70-x...(1)[/tex]
We have been given that Gazebo coffee blend sells for $10.20 per pound, so cost of x pounds of Gazebo coffee would be [tex]10.20x[/tex].
Kona coffee blend sells for $12.20 per pound, so cost of y pounds of Kona coffee would be [tex]12.20y[/tex].
Cost of 70 pounds of a coffee that can sell for $10.91 per pound would be [tex]70(10.91)[/tex].
[tex]10.20x+12.20y=70(10.91)...(2)[/tex]
Upon substituting equation (1) in equation (2), we will get:
[tex]10.20x+12.20(70-x)=70(10.91)[/tex]
[tex]10.20x+854-12.20x=763.7[/tex]
[tex]-2x+854=763.7[/tex]
[tex]-2x+854-854=763.7-854[/tex]
[tex]-2x=-90.3[/tex]
[tex]\frac{-2x}{-2}=\frac{-90.3}{-2}[/tex]
[tex]x=45.15[/tex]
Therefore, distributor should use 45.15 pounds of Gazebo coffee.
Upon substituting [tex]x=45.15[/tex] in equation (1), we will get:
[tex]y=70-14.15=24.85[/tex]
Therefore, distributor should use 24.85 pounds of Kona coffee.
