17. The owner of an organic fruit stand also sells nuts. She wants to mix cashews worth $5.50 per pound with peanuts worth $2.30 per pound to get a 1/2 pound mixture that is worth $2.80 per pound. How much of each kind of nut should she include in the mixed bag?

Answer 1

Let the amount of cashews be x and the amount of peanuts be y.

We know that the total weight of the mixture is 1/2 pound, so:

x + y = 1/2

We also know that the mixture is worth $2.80 per pound, so the total cost of the mixture is:

0.5 * $2.80 = $1.40

The cost of the cashews is $5.50 per pound, so the cost of x pounds of cashews is:

$5.50x

Similarly, the cost of y pounds of peanuts is:

$2.30y

Since we want the total cost of the mixture to be $1.40, we can set up the following equation:

$5.50x + $2.30y = $1.40

Now we have two equations with two variables:

x + y = 1/2

$5.50x + $2.30y = $1.40

We can solve for one variable in terms of the other from the first equation:

y = 1/2 - x

Substituting this into the second equation, we get:

$5.50x + $2.30(1/2 - x) = $1.40

Simplifying, we get:

$5.50x + $1.15 - $2.30x = $1.40

Combining like terms, we get:

$3.20x = $0.25

Dividing both sides by $3.20, we get:

x ≈ 0.078

Substituting this value back into the equation y = 1/2 - x, we get:

y ≈ 0.422

Therefore, the owner should mix approximately 0.078 pounds of cashews with 0.422 pounds of peanuts to get a 1/2 pound mixture that is worth $2.80 per pound.