it takes $a$ algebra books (all the same thickness) and $h$ geometry books (all the same thickness, which is greater than that of an algebra book) to completely fill a certain shelf. also, $s$ of the algebra books and $m$ of the geometry books would fill the same shelf. finally, $e$ of the algebra books alone would fill this shelf. given that $a$, $h$, $s$, $m$, and $e$ are distinct positive integers, it follows that $e$ is