A coffee company wants a new flavor of cajun coffee. how many pounds of coffee worth $10 a pound should be added to 20 pounds of coffee worth $4 a pound to get a mixture worth $5 a pound?
x = lbs of cheaper coffee
10x = value of cheaper coffee
4 = lbs of better coffee
4 * 20 = 80 = value of better coffee
20 + x = lbs of mixture
5(20 + x) = value of mixture
10x + 80 = 5(20 + x)
Solve for x
To solve this problem, we need to use the concept of weighted averages. Weighted averages consider the quantity or weight of each ingredient used in creating a mixture.
Let's break down the given information:
Let x be the number of pounds of coffee worth $10 a pound.
The price of the new coffee flavor is $10 per pound.
The price of the existing coffee is $4 per pound.
The resulting mixture should be worth $5 per pound.
The initial quantity of the existing coffee is 20 pounds.
To find the amount of the new coffee flavor needed, we'll set up an equation based on the weighted average formula:
(weight of new coffee flavor * price per pound) + (weight of existing coffee * price per pound) = (total weight of mixture * desired price per pound)
Using the given information, the equation becomes:
(x * $10) + (20 * $4) = (x + 20) * $5
Now, let's solve this equation:
10x + 80 = 5(x + 20)
10x + 80 = 5x + 100
10x - 5x = 100 - 80
5x = 20
x = 20 / 5
x = 4
Therefore, 4 pounds of coffee worth $10 per pound should be added to 20 pounds of coffee worth $4 per pound to obtain a mixture worth $5 per pound.