Oh Nuts! sells pistachio kernels for $6.50 per pound and almonds for $8.00 per pound. How much of each type should be used to make a 50lb mixture that sells for $7.40 per pound?

x = no. lbs of 6.50 nuts

6.50x = value of 6.50 nuts
50 - x = no. lbs of 8.00 nuts
8.00(50 - x) = value of 8.00 nuts
7.40(50) = value of mixture

6.50x + 8.00(50 - x) = 7.40(50)

Solve for x, lbs of 6.50 nuts
50 - x = lbs of 8.00 nuts

To solve this problem, we can use a system of equations. Let's use variables to represent the amounts of pistachio kernels and almonds in the mixture.

Let x represent the number of pounds of pistachio kernels.
Let y represent the number of pounds of almonds.

We can set up the following equations based on the information given:

Equation 1: x + y = 50
This equation represents the total weight of the mixture, which is 50 pounds.

Equation 2: (6.50x + 8.00y) / 50 = 7.40
This equation represents the average price per pound of the mixture, which is $7.40.

To solve this system of equations, we can first rewrite equation 2 to eliminate the fraction:

(6.50x + 8.00y) / 50 = 7.40
Multiply both sides of the equation by 50:

6.50x + 8.00y = 7.40 * 50
6.50x + 8.00y = 370

Now, we can solve the system of equations using any method, such as substitution or elimination. Let's use the substitution method:

From equation 1, we can express x in terms of y:
x = 50 - y

Now, substitute this value of x into equation 2:
6.50(50 - y) + 8.00y = 370
325 - 6.50y + 8.00y = 370
1.50y = 45
y = 30

So, the number of pounds of almonds, y, is 30.

Substitute this value of y into equation 1 to find x:
x + 30 = 50
x = 20

Therefore, the number of pounds of pistachio kernels, x, is 20.

To summarize, you would need 20 pounds of pistachio kernels and 30 pounds of almonds to make a 50-pound mixture that sells for $7.40 per pound.