Answer: 3 pounds.
Explanation:
We have two metals:
One that contains 20% nickel, let's call it metal A.
One that contains 80% nickel, let's call it metal B.
We have 6 pounds of metal B, in those 6 punds we have:
0.80*6lb = 4.8lb of nickel.
Now, if we add X pounds of metal A, then we will have:
X + 6lb in total weight.
4.8lb + 0.2*X of nickel.
And we want to have exactly 60% of nickel, so we must have that the quotient between the amount of nickel and the total weight is equal to 0.6
(4.8lb + 0.2*X)/(6lb + X) = 0.6
now we solve it for X:
(4.8lb + 0.2*X) = 0.6*(6lb + X) = 3.6lb + 0.6*X
4.8lb - 3.6lb = 0.6*X - 0.2*X
1.2lb = 0.4*X
1.2lb/0.4 = 3lb = X
We should use 3 pounds of the metal with 20% of nickel.