# Floor Sums

Algebra Level 5

$\left \lfloor x +\frac {11}{100} \right \rfloor + \left \lfloor x + \frac {12}{100} \right \rfloor + \ldots + \left \lfloor x + \frac {90} {100} \right \rfloor = 331,$ Given that $$x$$ is a real number satisfying the equation above, what is $$\left \lfloor 100 x \right \rfloor$$?

Details and assumptions

$$\lfloor x \rfloor$$ denotes the greatest integer smaller than or equal to $$x$$. For example $$\lfloor 2.3 \rfloor = 2$$, $$\lfloor 100 \pi \rfloor = 314$$, $$\lfloor -0.5 \rfloor = -1$$.

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