How to calculate concentrations when dissolving two salts?

Some solid silver bromate was dissolved together with solid silver acetate what would be the highest achievable pH? \begin{align} K_\mathrm{sp}(\ce{AgBrO3}) &= 5.38 \times 10^{-5}\\ K_\mathrm{sp}(\ce{AgCH3COO}) &= 1.94 \times 10^{-3}\\ \mathrm{p}K_\mathrm{a}(\ce{CH3COOH}) &= 4.76 \end{align}

Now I know this is just a question about the common ion effect. I know how to do the question if silver ions are already present in the solution then silver acetate is added. Also given the concentration of acetate ions, I can easily calculate the pH.

The real problem with this question is that you are dissolving 2 salts which are both in equilibrium. I don't know how to calculate the concentration of acetate ions in this scenario.

This is what I did:

$$5.38 \times 10^{-5} = [\ce{Ag+}][\ce{BrO3-}] = x^2$$ $$x = \ce{[Ag+]} = 7.33 \times 10^{-3}$$ $$1.94 \times 10^{-3} = [\ce{Ag+}][\ce{CH3COO}] = (7.33 \times 10^{-3} + y)(y)$$ I then used quadratic formula to find y.

I am pretty sure that this method is wrong because wouldn't the dissolution of silver acetate cause the equilibrium of silver bromate to shift backwards, causing the value of x to decrease. Or can we assume that this shift is negligible.

Also, by highest achievable pH doesn't that imply that the final pH of solution is variable. However, shouldn't it have the same pH every single time, making the words highest achievable pH redundant? Or am I missing something?

• Different amounts of silver bromate and silver acetate would have different pH values. So "highest achievable pH" means to find the amounts of silver bromate and silver acetate which would give the highest pH. – MaxW Dec 19 '15 at 22:58
• Here you can find my answer to a similar question chemistry.stackexchange.com/a/40433/15235 :) – Hexacoordinate-C Dec 20 '15 at 23:49