An algebra problem by Vatsalya Tandon

Algebra Level 4

x10+x20+x30=11x60 \large\left \lfloor \dfrac x{10} \right \rfloor + \left \lfloor \dfrac x{20} \right \rfloor + \left \lfloor \dfrac x{30} \right \rfloor = \dfrac{11x}{60}

Find the number of solutions of xx in the interval 0<x<10000<x<1000 satisfying the equation above.

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

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