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

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:

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

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:

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

$270-9y+7.5y=255$

$270-1.5y=255$

$270-270-1.5y=255-270$

$-1.5y=-15$

$\frac{-1.5y}{-1.5}=\frac{-15}{-1.5}\\\\y=10$

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.