Question

The Coffee Counter charges $9.00 per pound for Kenyan French Roast coffee and $8.00 per pound for Sumatran coffee. How much of each type should be used to make a 20-lb blend that sells for $8.40 per pound?

Answer 1

To make a 20-lb blend selling for $8.40 per pound, use 12 pounds of Kenyan French Roast and 8 pounds of Sumatran coffee.

Step-by-step explanation:

To solve this problem, we can set up a system of equations. Let x represent the pounds of Kenyan French Roast and y ) represent the pounds of Sumatran coffee. The total pounds of the blend is 20, so ( x + y = 20 ).

The cost per pound for the Kenyan coffee is $9.00, and for the Sumatran coffee, it's $8.00. The blend sells for $8.40 per pound, so the average cost is
`\( 8.40 * 20 = $168.00 \)`0 = $168.00. The cost equation is 9x + 8y = 168.

Now, we can solve these equations simultaneously. First, solve for x + y = 20 ) to find ( x = 20 - y ). Substitute this into the cost equation:

9(20 - y) + 8y = 168

Simplify the equation:

180 - 9y + 8y = 168

Combine like terms:

-y = -12

Solve for y :

y = 12

Now that we know y , substitute it back into the equation x + y = 20 to find x :

x + 12 = 20

x = 8

So, the solution is x = 8 and y = 12 , meaning 8 pounds of Kenyan French Roast and 12 pounds of Sumatran coffee should be used to make the 20-lb blend. This combination yields the desired average price of $8.40 per pound.