On the part “(0.8022 x 11.009) + (0.1978 x W) = 10.81 amu (natural atomic weight),” how do I know what to multiply 0.1978 by if W is unknown? How did they arrive at 10.81?

Hi youhaveabuttandamazinglgysodoI
They didn't 'arrive' at 10.81, 10.81 is a given, it was measured, presumably.
W is the unknown and is multiplied by its known ratio so as to put the equation that is then solved