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?
A. Cashews: 0.10 lb.; peanuts: 0.40 1b.
B. Cashews: 0.42 lb.; peanuts: 0.08 1b.
C. Cashews: 0.40 lb.; peanuts: 0.10 1b
D. Cashews: 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

E

Step-by-step explanation:

Let's let c denote the amount of cashews and let's let p denote the amount of peanuts.

So, the owner 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.

In other words, the total pounds as an equation is:

Also, the price would be:

Since we mixed the peanuts and cashews, our sum would be 2.8(p+c).

And we already determined that p+c is 0.5. Thus, substitute:

Simplify:

Now, we can solve the system of equations. Isolate a variable from the very first equation:

Subtract p from both sides:

Now, substitute this into the equation earlier:

Distribute:

Combine like terms:

Subtract both sides by 2.75:

Divide everything by -3.2:

Now, find c:

Substitute:

Subtract:

Thus, the owner would need 0.08 pounds of cashews and 0.42 pounds of peanuts.

Our answer is E.

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