A set of free notebooks was shared equally among the students in a class. Each student received a number of notebooks equal to one-eighth of the total number of students. If the number of students had been reduced to half, each student would have obtained 16 notebooks. What is the total number of notebooks distributed?

Explanation

Let the total number of students be x. Each student receives x/8 notebooks, so total notebooks = x * (x/8) = x^2 / 8. If the number of students is halved to x/2, each gets 16 notebooks, so total notebooks remain the same: (x/2) * 16 = 8x. Equate total notebooks: x^2 / 8 = 8x, which simplifies to x^2 = 64x, or x = 64 (ignoring zero). Total notebooks = 64^2 / 8 = 512.