Tessa wants to mix chocolates that cost four dollars per pound with nuts that cost six dollars per pound to make 6 pounds of a mixture that cost $31. How many pounds of each should she include in the mix?

Let's assume Tessa uses x pounds of chocolates and y pounds of nuts to make the mixture.

The cost of chocolates is $4 per pound, so the cost of x pounds of chocolates is 4x dollars.
The cost of nuts is $6 per pound, so the cost of y pounds of nuts is 6y dollars.

Since Tessa wants to make a 6-pound mixture that costs $31, we can set up the following equation:

4x + 6y = 31

To solve for x and y, we need another equation. The total weight of the mixture is 6 pounds, so we can set up the equation:

x + y = 6

Now we have a system of equations:

4x + 6y = 31 ...(1)
x + y = 6 ...(2)

To solve this system, we can use substitution or elimination method. Let's use the elimination method.

Multiply equation (2) by 4 to eliminate x:

4(x + y) = 4(6)
4x + 4y = 24 ...(3)

Now, subtract equation (3) from equation (1) to eliminate x:

(4x + 6y) - (4x + 4y) = 31 - 24
2y = 7
y = 7/2
y = 3.5

Substitute the value of y in equation (2) to solve for x:

x + 3.5 = 6
x = 6 - 3.5
x = 2.5

Therefore, Tessa should include 2.5 pounds of chocolates and 3.5 pounds of nuts in the mix.

\textbf{Answer:} She should include 2.5 pounds of chocolates and 3.5 pounds of nuts in the mix.