Question

Community coffee company wants a new flavor of cajun coffee. how many pounds of coffee worth $7 a pound should be added to 20 pounds of coffee worth $2 a pound to get a mixture worth $5 a pound

Answer 1

To get a mixture of coffee worth $5 a pound, you should add 30 pounds of coffee worth $7 a pound to 20 pounds of coffee worth $2 a pound.

Step-by-step explanation:

To solve this problem, we can use the method of mixtures. Let's assume that x pounds of coffee worth $7 a pound is added to 20 pounds of coffee worth $2 a pound. The total weight of the mixture will be (x + 20) pounds. The total value of the mixture will be the sum of the values of the two types of coffee.

The value of the 20 pounds of coffee worth $2 a pound is 20 * 2 = $40. The value of the x pounds of coffee worth $7 a pound is 7x. So, the total value of the mixture will be $40 + 7x.

Since we want the mixture to be worth $5 a pound, we can set up the equation:

(40 + 7x) / (20 + x) = 5

To solve this equation, we can cross-multiply:

(40 + 7x) = 5(20 + x)

Expanding the right side of the equation, we get:

40 + 7x = 100 + 5x

Subtracting 5x from both sides, we get:

2x = 60

Dividing both sides by 2, we get:

x = 30

Therefore, 30 pounds of coffee worth $7 a pound should be added to 20 pounds of coffee worth $2 a pound to get a mixture worth $5 a pound.

Answer 2

Let us say that:

x = pounds of $7 coffee

So that:

7 x + 2 * 20 = 5 * (x + 20)

7x + 40 = 5x + 100

2x = 60

x = 30 pounds

Therefore 30 pounds should be added.