Floor Sums

Algebra Level 5

x+11100+x+12100++x+90100=331, \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 xx is a real number satisfying the equation above, what is 100x \left \lfloor 100 x \right \rfloor ?

Details and assumptions

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

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