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?

Question

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?

ACashews: 0.10 lb.; peanuts: 0.40 1b.
BCashews: 0.42 lb.; peanuts: 0.08 1b.
CCashews: 0.40 lb.; peanuts: 0.10 1b
DCashews: 0.27 lb.; peanuts: 0.23 1b.
E Cashews: 0.23 lb.; peanuts: 0.27 1b.
F Cashews: 0.08 lb.; peanuts: 0.42 1b

Answer 1

To solve this problem, we can set up a system of equations based on the information given.

Let's use the variables C and P to represent the amount of cashews and peanuts, respectively, in pounds.

According to the problem, we want to mix cashews worth $5.50 per pound with peanuts worth $2.30 per pound to get a 1/2 pound mixture worth $2.80 per pound.

From this information, we can write the following equations:

1. The total weight equation:
C + P = 1/2

2. The value equation:
(5.50 * C + 2.30 * P) / (C + P) = 2.80

To solve the system of equations, we can use substitution or elimination.

Let's use substitution:

Rearrange the total weight equation to solve for C:
C = 1/2 - P

Substitute this value for C in the value equation:
(5.50 * (1/2 - P) + 2.30 * P) / ((1/2 - P) + P) = 2.80

Simplify and solve for P:

(2.75 - 5.50P + 2.30P) / (1/2 + 0.5P) = 2.80

(2.75 - 3.20P) / (1/2 + 0.5P) = 2.80

Cross-multiply:

2.75 - 3.20P = 2.80(1/2 + 0.5P)

2.75 - 3.20P = 1.40 + 1.40P

Combine like terms:

3.20P + 1.40P = 2.75 - 1.40

4.60P = 1.35

Divide by 4.60:

P = 1.35 / 4.60

P ≈ 0.2935

Now, substitute the value of P back into the total weight equation to find the value of C:

C + 0.2935 = 1/2

C ≈ 1/2 - 0.2935

C ≈ 0.2065

Therefore, the owner should include approximately 0.2065 pounds of cashews and 0.2935 pounds of peanuts in the mixed bag.

So, the correct answer is option D: Cashews: 0.27 lb.; peanuts: 0.23 lb.

Answer 2

Just as a guess, since cashews cost so much more, you'd need to use a lot less of them. So I'd choose A or F. To be sure, solve

p+c = 1/2
5.50c + 2.30p = 2.80 * 1/2