A room contains 96 people. A man leaves and is replaced by a women, leaving three times as many women as men in the room. How many men and how many women are there originally?

Let the number of men and women in the room be represented by an arbitrary constant, x and y respectively.

x + y = 96

y = 96 - x

When one man leaves, we get: x - 1

When one woman replaces the man, we get: y + 1

So, y + 1 = 3 (x - 1)

Substituting y = 96 - x, we get:

96 - x + 1 = 3x - 3

97 + 3 = 4x

100 = 4x

x = 25

Thus, there were 25 men and 41 women in the room originally.