unknown element is a mixture of isotopes ¹²⁰X and ¹²²X. The average atomic mass of X is 120.81 amu. What is the percent abundance of ¹²²X?

Answer 1

approximately 40 %.  Simple mass balance equation.  The presumption that isotope 120X has a mass of 120 AMU, and that 122X has a mass of 122 AMU, is, of course, likely untrue.  Only 12C has an actual mass of 12 AMU, and that is because we define AMU that way.

Answer 2

122*x + 120*(1-x) = 120.81 =>

2x = 0.81 =>

x = 0.405 = 40.5%