Score: 0 of 1 point A coffee distributor wants to mix an amount of Kenya coffee that sells for 14.50 a pound with some Mexican Shade Grown coffee that sells for 11.60 a pound to create 25 pounds of a new coffee blend that will be priced at 12.76 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 Enter your answer

Let's solve this coffee mixing problem step by step! Let’s denote the pounds of Kenya coffee as \( x \) and the pounds of Mexican Shade Grown coffee as \( y \). According to the problem, you have two equations: 1. **Total Weight Equation**: \[ x + y = 25 \] 2. **Total Cost Equation**: \[ 14.50x + 11.60y = 12.76 \times 25 \] Substituting the second equation: \[ 14.50x + 11.60y = 319 \] Now, you can express \( y \) in terms of \( x \) using the first equation: \[ y = 25 - x \] Substituting \( y \) back into the total cost equation gives you: \[ 14.50x + 11.60(25 - x) = 319 \] Distributing the 11.60: \[ 14.50x + 290 - 11.60x = 319 \] Combine the \( x \) terms: \[ (14.50 - 11.60)x + 290 = 319 \] \[ 2.90x + 290 = 319 \] Subtract 290 from both sides: \[ 2.90x = 29 \] Divide by 2.90 to find \( x \): \[ x = \frac{29}{2.90} \approx 10 \] Now, substitute \( x \) back into the total weight equation to find \( y \): \[ y = 25 - 10 = 15 \] Thus, the coffee distributor should blend approximately **10 pounds of Kenya coffee** and **15 pounds of Mexican Shade Grown coffee** to create the desired coffee blend.