To keep it simple, I'm going to refer to the element as element #X#. We know that element #X# has two possible isotopes, which I'm going to call #X_1# and #X_2#.
We know the average mass of element #X# is 141.8, the mass of #X_1# is 148.6, and that 41.11% of element #X# is found to be #X_1#. This also tells us that the other percentage of element X is #100 - 41.11 = 58.89%#.
Now knowing all of this information, we can set up a formula to solve for the mass of #X_2#, as the average mass of element #X# is 41.11% the mass of #X_1# and 58.99% the mass of #X_2#:
#"Average Mass" = .4111xxX_1 + .5899xxX_2#
#141.8 = .4111xx148.6 + .5899xxX_2#
Now all we do is solve for #X_2#, yielding
#X_2 = (141.8 - .4111xx148.6)/(.5899) = 136.8 " amu"#
We can double check our work by plugging in values for #X_1# and #X_2# and making sure that they average out to 141.8:
#.4111xx148.6 + .5899xx136.8 = 141.8" amu"#
