Question

Joseph would like to make sixteen pounds of a coffee blend at a cost of $6 per pound. He blends Ground Chicory at $5 a pound with Jamaican Blue Mountain at $9 per pound. How many pounds of each type of coffee should he use?

Answer 1

Answer: Let's call the amount of Ground Chicory that Joseph uses "x" and the amount of Jamaican Blue Mountain that he uses "y".

Since he wants to make 16 pounds of coffee blend, we know that:

x + y = 16

We also know that he wants to make the blend at a cost of $6 per pound, so the total cost of the blend will be:

6 * 16 = $96

The cost of the blend is determined by the cost of the two types of coffee that Joseph is using. We can set up another equation based on the cost:

5x + 9y = 96

Now we have two equations with two variables. We can use any method to solve for x and y, but one common method is to use substitution.

Solve the first equation for x in terms of y:

x = 16 - y

Now substitute this expression for x in the second equation:

5(16 - y) + 9y = 96

Simplify and solve for y:

80 - 5y + 9y = 96

4y = 16

y = 4

So Joseph should use 4 pounds of Jamaican Blue Mountain coffee.

To find out how much Ground Chicory to use, we can go back to the first equation:

x + y = 16

Substitute y = 4 and solve for x:

x + 4 = 16

x = 12

So Joseph should use 12 pounds of Ground Chicory.

Therefore, Joseph should use 12 pounds of Ground Chicory and 4 pounds of Jamaican Blue Mountain coffee to make 16 pounds of coffee blend at a cost of $6 per pound.

Explanation: