Answer:
We should use 4 pounds of $6 coffee and 2 pounds of $3 coffee for the blend.
Step-by-step explanation:
The blend should,
Cost = $5
Weigh = 6 pounds.
Lets take the weight of $6 coffee as [tex]x[/tex] pounds
And lets take the weight of $3 coffee as [tex]y[/tex] pounds.
Lets write an equation for the weight of the blend,
[tex]x+y=6[/tex] <---------- 1st equation.
[tex]\frac{6x+3y}{x+y} =5[/tex]
=[tex]6x+3y=5x+5y[/tex]
=[tex]x=2y[/tex] <---------- 2nd equation
We can substitute to x in 1st equation from 2nd equation,
⇒[tex]2y+y=6[/tex]
=[tex]2y+y=6[/tex]
=[tex]3y=6[/tex]
=[tex]y=2[/tex]
We can substitute y value to 2nd equation to find x,
⇒[tex]x=2y[/tex]
=[tex]x=2*2[/tex]=[tex]x=4[/tex]
Therefore, we should use 4 pounds of $6 coffee and 2 pounds of $3 coffee for the blend.
