All-mixed-up nut shop sells mix consisting of cashews and pistachios. how many pounds of cashews, which sell for $7 per pound , should be mixed with 4 pounds of pistachios which sell for $4 per pound to get a mix of $5 per pound?

7c + 4(4) = 5(c+4)

c = 2

To solve this problem, we need to set up an equation based on the given information.

Let's assume the number of pounds of cashews to be mixed is 'x', so the total weight of the mix is 'x + 4' pounds.

Now, let's calculate the cost of cashews and pistachios separately:

The cost of cashews = number of pounds of cashews * cost per pound of cashews = x * $7
The cost of pistachios = number of pounds of pistachios * cost per pound of pistachios = 4 * $4 = $16

The total cost of the mix = (cost of cashews + cost of pistachios) = ($7x + $16)

According to the given information, the average cost per pound of the mix should be $5. So we can set up the following equation:

Average cost per pound of the mix = total cost of the mix / total weight of the mix

$5 = ($7x + $16) / (x + 4)

To solve this equation for 'x', we can cross-multiply and simplify:

5(x + 4) = 7x + 16
5x + 20 = 7x + 16
5x - 7x = 16 - 20
-2x = -4
x = (-4) / (-2)
x = 2

Therefore, you should mix 2 pounds of cashews with 4 pounds of pistachios to get a mix that costs $5 per pound.

To solve this problem, let's break it down step-by-step:

1. Let's assume we need to mix x pounds of cashews with 4 pounds of pistachios.

2. Since we want to achieve a mix of $5 per pound, we can create the following equation for the total cost of the mixture:

(7 * x + 4 * 4) / (x + 4) = 5

Here, 7 * x represents the cost of the cashews (at $7 per pound) and 4 * 4 represents the cost of the pistachios (at $4 per pound). We divide this sum by the total weight of the mixture (x + 4) to get the average price.

3. Now, let's solve the equation to find the value of x:

(7 * x + 16) / (x + 4) = 5

Cross-multiply to eliminate the denominator:

7 * x + 16 = 5 * (x + 4)

Distribute the multiplication:

7 * x + 16 = 5 * x + 20

Simplify:

7 * x - 5 * x = 20 - 16

2 * x = 4

Divide both sides by 2:

x = 2

4. Therefore, you need to mix 2 pounds of cashews with 4 pounds of pistachios to get a mixture of $5 per pound.