Question

Amy operates a coffee kiosk and is blending her special house coffee. She 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. How many pounds of Kenya beans and how many

pounds of Colombia beans does Amy need to use to create her blend?

Answer 1

20 pounds of Kenya beans and 10 pounds of Columbia beans.

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:

`x+y=30...(1)`

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:

`9x+7.5y=30(8.50)...(2)`

From equation (1), we will get:

`x=30-y`

Substituting this value in equation (2), we will get:

`9(30-y)+7.5y=30(8.50)`

`270-9y+7.5y=255`

`270-1.5y=255`

`270-270-1.5y=255-270`

`-1.5y=-15`

`(-1.5y)/(-1.5)=(-15)/(-1.5)\\\\y=10`

Therefore, Amy needs 10 pounds of Columbia beans to create her blend.

Now, we will substitute
`y=10` in equation (1) as:

`x+10=30\\\\x+10-10=30-10\\\\x=20`

Therefore, Amy needs 20 pounds of Kenya beans to create her blend.