Answer:   
<em>a.  The system of equations that models the situation is....</em>
<em>      </em>
</em>
<em>b.  The solution to the system:  x = 2 and y = 4 </em>
<em>The amount of 80/20 mixture is 2 pounds and the amount of 50/50              mixture is 4 pounds.</em>
Step-by-step explanation:
Suppose, the amount of 80/20 mixture is   pounds and the amount of 50/50 mixture is
 pounds and the amount of 50/50 mixture is   pounds.
 pounds. 
So, the amount of peanuts in 80/20 mixture  pound and the amount of almonds in 80/20 mixture
 pound and the amount of almonds in 80/20 mixture  pound.
 pound.
And the amount of peanuts in 50/50 mixture  pound and the amount of almonds in 50/50 mixture
 pound and the amount of almonds in 50/50 mixture  pound.
 pound.
Now, Sarah would like to make a 6 pounds nut mixture that is 60% peanuts and 40% almonds.
So, the amount of peanuts in that mixture  pounds
 pounds 
and the amount of almonds in that mixture  pounds.
 pounds.
So, the system of equations will be.........

Subtracting equation (2) from equation (1), we will get.....

Now, plugging this  into equation (1), we will get......
 into equation (1), we will get......

So, the amount of 80/20 mixture is 2 pounds and the amount of 50/50 mixture is 4 pounds.