John is making his own trail mix. He has bought two kinds of trail mix from the store, one that is 65% peanuts and one that is 30% peanuts. If he wants to have 10 lbs of trail mix that is 40% peanuts, how much of each will he need to use?

x + y = 10

.65 x + .30 y = .40 * 10

To determine how much of each trail mix John needs to use, we can set up a system of equations based on the given percentages.

Let's assume that John needs x pounds of the trail mix that is 65% peanuts, and y pounds of the trail mix that is 30% peanuts.

The first equation we can form is based on the total weight of the trail mix:
x + y = 10

The second equation is based on the desired percentage of peanuts in the final mixture:
(0.65x + 0.30y) / 10 = 0.40

Now we have a system of equations that can be solved to find the values of x and y.

To solve the system, we can use the method of substitution. Rearrange the first equation to solve for y:
y = 10 - x

Substitute this value of y into the second equation:
(0.65x + 0.30(10 - x)) / 10 = 0.40

Now simplify and solve for x:
(0.65x + 3 - 0.30x) / 10 = 0.40
0.35x + 3 = 4
0.35x = 1
x = 1 / 0.35
x ≈ 2.86

So, John needs approximately 2.86 pounds of the trail mix that is 65% peanuts. To find the amount of the 30% peanuts trail mix, substitute the value of x into the first equation:
2.86 + y = 10
y = 10 - 2.86
y ≈ 7.14

Therefore, John needs approximately 2.86 pounds of the trail mix that is 65% peanuts and 7.14 pounds of the trail mix that is 30% peanuts to make 10 pounds of trail mix that is 40% peanuts.