Thallium has two stable isotopes, 203tl and 205tl. knowing that the atomic weight of thallium is 204.4, which isotope is the more abundant of the two? explanation

You have to figure out a way to write the two unknown abundances in terms of one variable.

The total abundance is 1 (or 100%). So if you say the abundance for the first one is X then the abundance for the second one has to be 1-X (where X is the decimal of the percentage so say 0.8 for 80%).

203(X) + 205(1-X) = 204.4

Then you just solve for X to get the percentage for TI-203.
And then solve for 1-X to get the percentage for TI-205.

After that the higher percentage would be the most abundant.

203x + 205 - 205x = 204.4
-2x + 205 = 204.4
-2x = -0.6

x = 0.3
1-x = 0.7

Then the TI-205 would have the highest percentage and would be the most abundant.

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The answer to this is the 3rd choice!