Adding Up A Lot Of Floors

Algebra Level 5

x+1100+x+2100++x+223100=521 \left \lfloor x +\frac {1}{100} \right \rfloor + \left \lfloor x + \frac {2}{100} \right \rfloor + \cdots + \left \lfloor x + \frac {223} {100} \right \rfloor = 521

If xx is a real number satisfying the equation above, find 100x\lfloor 100x\rfloor .

Notation: x\lfloor x \rfloor denotes the floor function.


Inspiration.

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