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:
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.
