How is zakat paid on saved money that has reached the nisab and on which a full year has passed, but it has commingled with other money, and the zakatable amount cannot be precisely determined?

If you do not know with certainty when the hawl (one year) has passed on your nisab (minimum amount subject to zakat), then exert your effort and act upon what you predominantly believe to be the date of the hawl's completion. The hawl for zakat is determined by lunar months, not Gregorian, based on Allah's saying: "They ask you about the new moons. Say: They are fixed times for people and for the pilgrimage."