This is the remake of the original, so it is based on the original script by Donald E Westlake but uses a somewhat different one.
Still, the basic idea is the same: our villain goes from mother/child pair to mother/child pair, first behaving very nicely and then, when they don't measure up, killing them and moving on. The differences lie in the details of the plot.
In this version, he lives off the grid and pays cash for everything. This only makes the problem of how he finances his operation harder, as where he gets his cash is not really explored.
But that really doesn't matter; the film is not about how psycho killers finance themselves; it is about the tension the audience feels and, of course, the violence.
If you liked the original, you should like this one as well.
If you haven't seen any of them, but they sound attractive, you should like them.