x = amount of 21% alloy
y = amount of 50% alloy
The metallurgist wants a combination weighing a total of 44 lb, so
x + y = 44
Each pound of either alloy contributes either 0.21 or 0.5 pound of titanium. The final product needs to be comprised of 37% titanium; weighing at 44 lb, this means it should contain 0.37 * 44 = 16.28 lb. So
0.21x + 0.5y = 16.28
From the first equation,
x + y = 44 ==> y = 44 - x
Substitute this into the second equation and solve for x:
0.21x + 0.5(44 - x) = 16.28
-0.29x = -5.72 ==> x = 19.72
Substitute this into the first equation to solve for y:
19.72 + y = 44 ==> y = 24.28
