The idea here is that each isotope will contribute to the average of the element proportionally to their respective abundance.
Now, the key to this problem lies in how you can write the abundances of the two .
Let's assume that the decimal abundance, which is simply the percent abundance divided by
Since you only have two isotopes, it follows that their decimal abundances must add up to give
The average atomic mass of the element can be calculated using
$color(blue)("avg. atomic mass" = sum_i("isotope"_i xx "abundance"_i))$
In your case, you would have
$"110.352 u" = "111.624 u" xx (1-x) + "109.75 u" xx x$
This is equivalent to
$110.352 = 111.624 - 111.624 * x + 109.75 * x$
$1.874 * x = 1.272 implies x = 1.272/1.874 = 0.67876$
The percent abundances of the two isotopes will be
$"111.624 u " -> " 32.124%$ $"109.75 u " -> " 67.876%$