Adding Up A Lot Of Floors

Algebra Level 5

\[ \left \lfloor x +\frac {1}{100} \right \rfloor + \left \lfloor x + \frac {2}{100} \right \rfloor + \cdots + \left \lfloor x + \frac {223} {100} \right \rfloor = 521 \]

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

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


Inspiration.

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