how many pounds of peanuts that sell for $2 a pound must be mixed with six pounds of cashew nuts that sell for$4 a pound to get a mixture that can sell for $2.50 a pound?

x pounds of peanuts + 6 pounds cash = (x+6) pounds mix

2 x + 4 * 6 = 2.5 (x+6)

2 x + 24 = 2.5 x + 15

.5 x = 9

x = 18

Why did the peanuts become friends with the cashew nuts? Because they heard they were a "nutty" bunch!

Now, let's crack this nutty problem. Let's assume we need "x" pounds of peanuts to mix with the cashew nuts.

The peanuts are selling at $2 per pound, so the total cost of peanuts would be $2 times "x" pounds, which equals to 2x dollars.

The cashew nuts weigh 6 pounds and sell for $4 per pound, so their total cost is 4 times 6 dollars, which equals to 24 dollars.

To get a mixture that sells for $2.50 per pound, the total cost of the mixture should be 2.50 times (x + 6) dollars.

Since the total cost of the mixture is equal to the sum of the costs of the peanuts and cashew nuts, we can set up the equation:

2x + 24 = 2.5(x + 6)

Let me crunch the numbers for you and solve it.

To determine the number of pounds of peanuts needed to create a mixture that can sell for $2.50 a pound, we can set up the following equation:

Let's assume x represents the number of pounds of peanuts.

The cost of peanuts = $2 per pound
The cost of cashew nuts = $4 per pound
The desired cost of the mixture = $2.50 per pound

The equation becomes:
(2 * x + 4 * 6) / (x + 6) = 2.50

To solve for x:

2x + 24 = 2.50(x + 6)
2x + 24 = 2.50x + 15
24 - 15 = 2.50x - 2x
9 = 0.50x
x = 9 / 0.50
x = 18

Therefore, you would need 18 pounds of peanuts to mix with the 6 pounds of cashew nuts to get a mixture that can sell for $2.50 a pound.

To find the number of pounds of peanuts needed to create the desired peanut and cashew nut mixture, we can use a basic algebraic approach.

Let's assume that the number of pounds of peanuts needed is represented by "x". Therefore, the cost of the peanuts would be 2x dollars.

According to the given information, the mixture should sell for $2.50 a pound. We can find the amount of cashew nuts in the mixture by subtracting the peanuts' weight. So the weight of the cashew nuts would be (6 - x) pounds, and their cost would be (6 - x) × 4 dollars.

The total weight of the mixture would be the sum of the weights of both peanuts and cashews, which is x + (6 - x) = 6 pounds.

To find the cost of the mixture, we can multiply the total weight by the desired selling price per pound, which is 6 × 2.50 = $15.

Since the cost of the mixture equals the sum of the cost of peanuts and cashews, we can form the equation:

2x + (6 - x) × 4 = 15

Simplifying the equation:

2x + 24 - 4x = 15
-2x = 15 - 24
-2x = -9

Dividing both sides by -2:

x = -9 / -2
x = 4.5

Based on this calculation, we find that 4.5 pounds of peanuts selling for $2 per pound should be mixed with 6 pounds of cashew nuts selling for $4 per pound to obtain a mixture that can sell for $2.50 per pound. However, note that you can't have 4.5 pounds of peanuts exactly, so you may need to adjust the quantities accordingly.