A coffee company wants a new flavor of Cajun coffee How many

A coffee company wants a new flavor of Cajun coffee. How many pounds of coffee worth $ 5 a pound should be added to 30 pounds of coffee worth $ 2 a pound to get a mixture worth $ 3 a pound?

Solution

Let x pounds of coffee worth $ 5 a pound be added to 30 pounds of coffee worth $ 2 a pound to get a mixture worth $ 3 a pound. The total weight of the blended coffee is x +30 pounds . The value of x pounds of coffee worth $ 5 a pound is $ 5x and the value of 30 pounds of coffee worth $ 2 a pound is $ 60. Then, the total value of blended coffee is $ (5x+60). Therefore, the worth per pound of the blended coffee is (5x+60)/(x+30). Now, since the worth per pound of the blended coffee is $ 3, we have (5x+60)/(x+30) = 3 or, 5x+60 = 3(x+30) or, 5x +60 = 3x + 90 or, 5x-3x = 90-60 or, 2x = 30 so that x = 30/2 = 15. Thus, 15 pounds of coffee worth $ 5 a pound should be added to 30 pounds of coffee worth $ 2 a pound to get a mixture worth $ 3 a pound.