How do i dtrmn the % abundance of 3 isotopesof Si, w/ only the atomic mass of each & the avg atomic mass of Si

Question

Silicon has 3 common isotopes 28 Si, 29 Si and 30 Si. the number is the atomic mass. the average atomic mass of Si is 28.0855. determine the percent abundance for each isotope w/o looking it up.

i dont need the answer, just the method of determining it
i was planning on a system, w/ the equations being:
28x+29y+30z=28.085
x+y+z=1 The variables are percent abundance

However, i dont think this will work b/c i need a third equation.
if anyone knows how to do this, please answer with how and i will greatly appreciate it.

Answer 1

Your analysis is perfect. Without some additional information that would yield a third equation, the problem cannot be solved.

Answer 2

that's right, with more than two isotopes, you'd need more information. you can't solve for 3 variables with only 2 equations. trick question, good catch.