An algebra problem by Vatsalya Tandon

Algebra Level 4

$\large\left \lfloor \dfrac x{10} \right \rfloor + \left \lfloor \dfrac x{20} \right \rfloor + \left \lfloor \dfrac x{30} \right \rfloor = \dfrac{11x}{60}$

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

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

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