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15 October, 15:06

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?

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  1. 15 October, 15:12
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    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.
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