I don't believe you can solve the problem by treating each equilibrium as isolated from the other, because the two equilibria are interconnected. E.g., at equilibrium, the concentration of CaO and CO_{2} are not identical, because CO_{2} is consumed in the second reaction. Therefore you cannot solve for x in the first table as though these two species have the same concentration.

I would set up two ICE tables with different variables x and y for changes. The change in CO_{2} would then be x-y (gained in first equilibrium and lost in second). Then you can solve for x because you know y = 0.15 mol. A quick solve gives me moles of CaCO_{3}, CaO and CO_{2} at equilibrium equal to 0.721, 0.279, and 0.129, respectively. This does return the equilibrium constant for the first reaction of 0.05, so at least that checks out.