An algebra problem by Kshetrapal Dashottar

Algebra Level pending

Find the sum of all triples $$(x, y, z)$$ of real numbers satisfying the following three equations (where [r] and {r}) denote that greater integer r  and r – [r] respectively)

$$x + [y] + \{z\} = 200.2$$
$$\{x\} + y + [z] = 200.1$$
$$[x] + \{y\} + z = 200.0$$

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