Respuesta :
Answer:
20 pounds of Kenya beans and 10 pounds of Columbia beans.
Step-by-step explanation:
Let x represent pounds of Kenya beans and y represent pounds of Columbia beans.
We have been given that Amy wants to create 30 pounds of blend. We can represent this information in an equation as:
[tex]x+y=30...(1)[/tex]
We are also told that Amy is mixing Kenya beans that cost $9.00 per pound with Colombia beans that cost $7.50 per pound to create a 30 pound blend that sells for $8.50 per pound. We can represent this information in an equation as:
[tex]9x+7.5y=30(8.50)...(2)[/tex]
From equation (1), we will get:
[tex]x=30-y[/tex]
Substituting this value in equation (2), we will get:
[tex]9(30-y)+7.5y=30(8.50)[/tex]
[tex]270-9y+7.5y=255[/tex]
[tex]270-1.5y=255[/tex]
[tex]270-270-1.5y=255-270[/tex]
[tex]-1.5y=-15[/tex]
[tex]\frac{-1.5y}{-1.5}=\frac{-15}{-1.5}\\\\y=10[/tex]
Therefore, Amy needs 10 pounds of Columbia beans to create her blend.
Now, we will substitute [tex]y=10[/tex] in equation (1) as:
[tex]x+10=30\\\\x+10-10=30-10\\\\x=20[/tex]
Therefore, Amy needs 20 pounds of Kenya beans to create her blend.
