Isotope Problems?

Question

Element X has 2 main isotopes, the wighted avg. mass of element X is found to be 26.73 amu. Isotopes A is found to have a mass of 23.4 amu and isotopes B is =27.9 amu. What are the precentage of the isotopes?

My Calculations:
23.4A+27.9B=26.73
A+B=1 A= 1-B
23.4(1-B)+27.9B=26.73
23.4+23.4B +27.9B=26.73
4.5B/4.5=3.3/4.5

B= 0.73 = 73%
A=1-B
A=1-0.73 = 0.27 = 27%

I copied this from the board, I understand it but my only problem is how I would figure that A=1-B? Also is there sites were I would find similar problems?

Answer 1

If A represents the percentage of the atoms that are isotope A, and B represents the same thing for isotope B, and if A and B are the only isotopes, then A+B has to equal 100%, which is 1.
So:
A+B=1
A=1-B (and B=1-A)

Answer 2

a= 1-b
because a+b=1

In percentages, a+b=100. If you do a sum of the abundances of both isotopes (a+b) it should be 100% or 1.

The reasoning is OK. I did not check the calculations.