A coffee distributor wants to mix an amount of House coffee that sells for 13.40 a pound with some Mexican Shade Grown coffee that sells for 11.20 a pound to create 55 pounds of a new coffee blend that will be priced at 12.28 per pound. How many pounds of each kind of coffee should they blend together? Round your answers to the nearest whole number of pounds. Enter your answer \( \begin{array}{ll}\sqrt{x} & \text { pounds of the House coffee } \\ \text { Enter your answer } & \text { I } \\ \sqrt{x} & \text { pounds of the Mexican Shade Grown coffee. }\end{array} \)

To find out how many pounds of each type of coffee should be mixed, we can set up a system of equations based on the total weight of the blend and the price per pound. Let's denote: - \( x \) = pounds of House coffee - \( y \) = pounds of Mexican Shade Grown coffee We know: 1. The total weight of the coffee blend is 55 pounds: \( x + y = 55 \) 2. The total cost of the blend must equal the price for the blend at $12.28 per pound: \( 13.40x + 11.20y = 12.28(55) \) \( 13.40x + 11.20y = 674.40 \) Now we can solve these equations. From the first equation, we can express \( y \) in terms of \( x \): \( y = 55 - x \) We substitute this into the second equation: \( 13.40x + 11.20(55 - x) = 674.40 \) \( 13.40x + 616 - 11.20x = 674.40 \) Combine like terms: \( (13.40 - 11.20)x + 616 = 674.40 \) \( 2.20x + 616 = 674.40 \) Subtract 616 from both sides: \( 2.20x = 58.40 \) Now divide by 2.20: \( x = \frac{58.40}{2.20} \approx 26.55 \) Rounding to the nearest whole number, we find \( x \approx 27 \) pounds of House coffee. Now, substitute back to find \( y \): \( y = 55 - 27 = 28 \) pounds of Mexican Shade Grown coffee. So, the final answer is: 27 pounds of House coffee 28 pounds of Mexican Shade Grown coffee