Question

After a certain number of people entered an empty room, 2/3 of the people who’d entered the room leave. After 2 more people leave, 1/4 of the original number of people who entered the room remain. What was the original number of people who entered the empty room?

Answer 1

24

Explanation:

Let x be the original number of people who entered the room

Since 2/3 of the people leave, 1/3 of the people remain = (1/3)x

If 2 more people leave, number of people remaining in the room = (1/3)x - 2

We know this to be 1/4 of the original number = (1/4)x

`\rm{So\;(1)/(3)x - 2 = (1)/(4)x\\\\`

Multiply throughout by 12 to get rid of the denominator

`\rm{So\;12 \left((1)/(3)x - 2\right) = 12\left((1)/(4)x\right)\\\\`

`4x - 24 = 3x\\\\\implies x = 24\\\\`

Original number of people who entered the empty room = 24