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?

Answer 1

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.