How is the problem in the story "The Cold Equations" resolved?

The problem is solved by ejecting the girl, Marilyn, into
space and to her death.

The problem is that Marilyn stowed
away on a space transport, headed for a planet where her brother is a colonist. She has
not seen him in ten years. The planet's human colonists experience an epidemic, and the
ship is launched to take them medicines; without them, the colonists will die. The ship
has *exactly* enough fuel to complete its mission, and no more. Marilyn does not realize
this. She thinks she will get in some trouble, have to pay a fine, but it will be worth
it to see her brother. The ship's captain tries to figure out some way to save both
Marilyn and the colonists, but there is no way around the numbers--the ship does not
have enough fuel to transport her, and she is sacrificed to save the
colony.