Need help with atomic relative mass question?

Question

The relative atomic mass of iridium is 192.2

irdium occurs naturally as a mixture of irdium 191 and irdium 193. work out the percentage of each isotope in naturally occuring irrdium.

Answer 1

You know that the two isotopes must have an average mass of 192.2

So set up equation which can solve for this like

Let decimal fraction of 191 isotope be x

So decimal fraction of 193 isotope is 1- x

And 191x + 193 (1-x) = 192.2

       191x + 193 - 193x = 192.2

Gives   2x = 0,8

           x = 0.4

Ask is it reasonable? Yes it is

40% 191  60% 193

Answer 2

There is a proportion, x, of all Iridium that is 191.  The remainder (1-x) is 193.  The total, x*191+(1-x)*193 = 192.2.  You need to solve this for x, i.e. 191x-193x+193=192.2

-2x=-0.8

x=0.4

so 40% of all iridium is 191 (60% is 193).