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.