A coffee shop mixes French roast coffee worth $9 per pound with Kona coffee worth $4 per pound. How much of each type of coffee was used in order to obtain 20 pounds of a mixture worth $5 per pound.

To solve this problem, let's use a system of equations:

Let's assume that x pounds of French roast coffee and y pounds of Kona coffee were used.

Since the total mixture weighs 20 pounds, we have the equation:

x + y = 20 ----(1)

The cost of French roast coffee is $9 per pound, and the cost of Kona coffee is $4 per pound. The total value of the mixture should be $5 per pound.

To find the equation for the mixture value, we'll multiply the price per pound by the number of pounds for each type of coffee. The equation is as follows:

9x + 4y = 5(20) ----(2)

Now we have a system of equations consisting of equations (1) and (2). We can solve this system using substitution, elimination, or another method.

Let's use the substitution method. Rearrange equation (1) to solve for x:

x = 20 - y

Substitute this value of x into equation (2):

9(20 - y) + 4y = 100

Distribute and simplify:

180 - 9y + 4y = 100
-5y = -80
y = 16

Now substitute the value of y back into equation (1) to solve for x:

x + 16 = 20
x = 20 - 16
x = 4

Therefore, 4 pounds of French roast coffee and 16 pounds of Kona coffee were used to obtain the desired mixture.