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](https://tex.z-dn.net/?f=c%2Bp%3D0.5)
Also, the price would be:
![5.5c+2.3p=(p+c)2.8](https://tex.z-dn.net/?f=5.5c%2B2.3p%3D%28p%2Bc%292.8)
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)](https://tex.z-dn.net/?f=5.5c%2B2.3p%3D%280.5%29%282.8%29)
Simplify:
![5.5c+2.3p=1.4](https://tex.z-dn.net/?f=5.5c%2B2.3p%3D1.4)
Now, we can solve the system of equations. Isolate a variable from the very first equation:
![c+p=0.5](https://tex.z-dn.net/?f=c%2Bp%3D0.5)
Subtract p from both sides:
![c=0.5-p](https://tex.z-dn.net/?f=c%3D0.5-p)
Now, substitute this into the equation earlier:
![5.5c+2.3p=1.4\\5.5(0.5-p)+2.3p=1.4](https://tex.z-dn.net/?f=5.5c%2B2.3p%3D1.4%5C%5C5.5%280.5-p%29%2B2.3p%3D1.4)
Distribute:
![2.75-5.5p+2.3p=1.4](https://tex.z-dn.net/?f=2.75-5.5p%2B2.3p%3D1.4)
Combine like terms:
![2.75-3.2p=1.4](https://tex.z-dn.net/?f=2.75-3.2p%3D1.4)
Subtract both sides by 2.75:
![-3.2p=-1.35](https://tex.z-dn.net/?f=-3.2p%3D-1.35)
Divide everything by -3.2:
![p=0.412875](https://tex.z-dn.net/?f=p%3D0.412875)
Now, find c:
![p+c=.5](https://tex.z-dn.net/?f=p%2Bc%3D.5)
Substitute:
![c+0.421875=.5](https://tex.z-dn.net/?f=c%2B0.421875%3D.5)
Subtract:
![c=0.078125](https://tex.z-dn.net/?f=c%3D0.078125)
Thus, the owner would need 0.08 pounds of cashews and 0.42 pounds of peanuts.
Our answer is E.