Which of the following barium salts should dissolve in a strong acid such as HCl: Ba(OH)₂, BaSO₄, or BaCO₃?
I thought they all would be that can't be the answer, can you explain how you know?

The cations Ba ²⁺ and Sr ²⁺ can be precipitated as very insoluble sulfates.
a) If you add sodium sulfate to a solution containing these metal cations, each with a concentration of 0.10 M, which is precipitated first, BaSO₄, or SrSO₄?
I got this part right it is BaSO4 (Ksp = 1.1x 10^-10). It is less soluble than SrSO4 (Ksp 3.4 x 10_-7)
b) What will be the concentration for the first ion that precipitates when the second, more soluble salt begins to precipitate?
I don't know how you do these but the answer key says 1.8 x 10^-7 M. Can you explain this to me?

Yeah I got 3.4 x 10-6 M needed to start the precipitation of SrSO4. But when I plug that concentration for BaSO4 to find the conc. of Ba +2, I get some crazy number. 1.1 x 10-10 = (x)(3.4x10-6)
x = 3.24 x 10-5...This isn't the right answer in the back of the book...
And how about the other one?

Seems to me like your answer is the correct one.

For dissolution you will need to protonate SO₄^2- to HSO₄^-. With pKa1=-3 that's not an easy task.