How to calculate the remaining mass in the mother solution after multiple extractions?
In old lecture notes of mine I found this formula

$ g_i = g\left(\frac{V_1}{V_1 + V_2K_2}\right)^n$

where $g_i$ is the remnant mass of a product initially dissolved in volume $V_1$, to be $n$-times extracted by volume $V_2$ with a given Nernst dissipation coefficient $K = \frac{a_2}{a_1}$.  Here, $g$ refers to the mass of the product initially dissolved in $V_1$.

Applied to your case, assuming a molar mass of 180 g/mol, this would read like 0.54 g initially dissolved in you 150 mL solution 1 (3 mmol).  After a single extraction with 50 mL of 2, only 90 mg were remaining (0.5 mmol) in $V_1$, after the third time 2.5 mg (about 14 umol).

I speculate a textbook like P. W. Atkins' Physical Chemistry may contain an example to confirm such a calculation.