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When it comes to these problems, it helps to look at the direction of heat transfer from each of the objects/systems involved! When heat is being released by an object, q is negative with respect to that object, whereas when heat is being absorbed by another object, q is positive.
I think Sfinal - Sinitial works in general because that is the definition of delta S. In this case, I think it can be explained by the concept above; because the 800. K reservoir is losing heat, so its entropy when you calculate overall entropy change should be negative.
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