Peanuts cost $3 per pound, almonds $4 per pound, and cashews $8 per pound. How many pounds of each should be mixed to produce 140 pounds of a nut assortment that cost $6 per pound, in which there are twice as many peanuts as almonds?

Added info: I know that I need a system of three equations to solve for my three unknowns, I just can't figure out those equations. I really need help!

p: lbs of peanuts

a: lbs of almonds
c: lbs of cashews

work with the weights:
p+a+c = 140
p = 2a

now, work with the values:
3p+4a+8c = 6*140

Now go for it

I must be doing something wrong because I keep coming out to big fractions with variables left over. I need another hint here. Am I supposed to have fractions in my answers?

Wait, I think I figured it out. Does p=40 a=20 c=80 sound right?

To solve this problem, let's assign variables to represent the amount of each type of nut we need.

Let:
x = pounds of almonds
2x = pounds of peanuts (since there are twice as many peanuts as almonds)
140 - (x + 2x) = 140 - 3x = pounds of cashews (since the total weight is 140 pounds)

Now, let's establish the cost equation based on the given information. The cost of the mixture should be $6 per pound.
The cost of almonds is $4 per pound, peanuts is $3 per pound, and cashews is $8 per pound.

The cost of almonds = 4 * x
The cost of peanuts = 3 * 2x (twice the number of almonds)
The cost of cashews = 8 * (140 - 3x)

Since the cost per pound is $6, we can create the equation:

4x + 3(2x) + 8(140 - 3x) = 6 * 140

Simplifying the equation:

4x + 6x + 1120 - 24x = 840

Combine like terms:

-14x + 1120 = 840

Subtract 1120 from both sides:

-14x = 840 - 1120
-14x = -280

Divide both sides by -14:

x = -280 / -14
x = 20

Now that we have the value of x (the pounds of almonds), if we substitute it back into our variables:

x = 20 (pounds of almonds)
2x = 2 * 20 = 40 (pounds of peanuts)
140 - 3x = 140 - 3 * 20 = 140 - 60 = 80 (pounds of cashews)

Therefore, you should mix 20 pounds of almonds, 40 pounds of peanuts, and 80 pounds of cashews to produce a 140-pound nut assortment that costs $6 per pound, with twice as many peanuts as almonds.