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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