Question

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

Answer 1

Answer:

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:

$c+p=0.5$

Also, the price would be:

$5.5c+2.3p=(p+c)2.8$

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:

$5.5c+2.3p=(0.5)(2.8)$

Simplify:

$5.5c+2.3p=1.4$

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

$c+p=0.5$

Subtract p from both sides:

$c=0.5-p$

Now, substitute this into the equation earlier:

$5.5c+2.3p=1.4\\5.5(0.5-p)+2.3p=1.4$

Distribute:

$2.75-5.5p+2.3p=1.4$

Combine like terms:

$2.75-3.2p=1.4$

Subtract both sides by 2.75:

$-3.2p=-1.35$

Divide everything by -3.2:

$p=0.412875$

Now, find c:

$p+c=.5$

Substitute:

$c+0.421875=.5$

Subtract:

$c=0.078125$

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

Our answer is E.