Question

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?

Answer 1

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.