Several preps were meeting in a room. After 45 of them left, the room was 5/8 as full as it was initially. How many preps were in the room at the start of the meeting?
Let's assume that the total number of preps in the room at the start of the meeting is x.
After 45 of them left, the room was 5/8 as full as it was initially, which means there were 5/8 * x preps in the room.
So, the equation becomes 5/8 * x = x - 45.
Multiplying both sides by 8 to get rid of the fraction, we get 5x = 8(x - 45).
Expanding the equation, we get 5x = 8x - 360.
Subtracting 8x from both sides, we get -3x = -360.
Dividing both sides by -3, we get x = -360 / -3 = 120.
Therefore, there were 120 preps in the room at the start of the meeting.