The Coffee Counter charges \( \$ 10 \) per pound for Kenyan French Roast coffee and \( \$ 9 \) per pound for Sumatran coffee. How much of each type should be used to make a 20 pound blend that sells for \( \$ 9.65 \) per pound? The Coffee Counter should mix \( \square \) pounds of Kenyan Roast coffee and pounds of Sumatran coffee to make 20 pounds of a blend that sells for \( \$ 9.65 \) per pound.

Let \( x \) be the number of pounds of Kenyan French Roast coffee, and \( y \) be the number of pounds of Sumatran coffee. We have the following system of equations based on the problem: 1. The total weight of the blend: \[ x + y = 20 \] 2. The total cost of the blend: \[ 10x + 9y = 9.65 \times 20 \] Calculating the right side of the second equation: \[ 9.65 \times 20 = 193 \] So, the second equation becomes: \[ 10x + 9y = 193 \] Now we have the system of equations: 1. \( x + y = 20 \) 2. \( 10x + 9y = 193 \) We can solve this system using substitution or elimination. Let's use substitution. From the first equation, we can express \( y \) in terms of \( x \): \[ y = 20 - x \] Now, substitute \( y \) into the second equation: \[ 10x + 9(20 - x) = 193 \] Expanding this gives: \[ 10x + 180 - 9x = 193 \] Combining like terms: \[ x + 180 = 193 \] Subtracting 180 from both sides: \[ x = 13 \] Now, substitute \( x = 13 \) back into the equation for \( y \): \[ y = 20 - 13 = 7 \] Thus, the Coffee Counter should mix: - \( 13 \) pounds of Kenyan French Roast coffee - \( 7 \) pounds of Sumatran coffee In conclusion, the Coffee Counter should mix \( \boxed{13} \) pounds of Kenyan Roast coffee and \( 7 \) pounds of Sumatran coffee to make a 20-pound blend that sells for \( \$ 9.65 \) per pound.