Respuesta :
In the office building, 24 people got on the elevator on the main floor.
Given: In an office, a finite number of people entered an elevator on the main floor.
- 4 people got off at the 2nd floor
- 2/ 5 of the remainder got off at the third floor
- 75% of the remainder got off at the fourth floor
- 3 got off at the 5th floor
To find the total number of people who entered the elevator on the main floor.
Let's solve the problem.
We assume that the total number of people who entered the elevator on the main floor is x.
According to the question:
1. 4 got off on the first floor.
The number of people remaining in the elevator after 4 people got off on the 2nd floor is (x - 4)
2. 2 / 5 of the remainder got off at the 3rd floor.
The number of people left = (x - 4) - 2 / 5 (x - 4)
Taking (x - 4) common:
(x - 4) [ 1 - 2 / 5 ] = (x - 4) × [ (5 - 2) / 5 ]
= 3 / 5 (x - 4)
So the number of people left in the elevator after 2 / 5 of the people left on the 3rd floor is 3 / 5 (x - 4)
3. 75% of the remainder is on the 4th floor.
The number of people left on the 4th floor is 75% of 3 / 5 (x - 4)
= 75 / 100 × 3 / 5 (x - 4)
= 3 / 4 × 3 / 5 (x - 4)
The number of people left on the 4th floor was 3 / 4 × 3 / 5 (x - 4)
Therefore the number of people left in the elevator is:
3 / 5 (x - 4) - [ 3 / 4 × 3 / 5 (x - 4) ]
Taking 3 / 5 (x - 4) common:
= 3 / 5 (x - 4) [ 1 - 3 / 4 ]
= 3 / 5 (x - 4) [ (4 - 3) / 4 ]
= 3 / 5 (x - 4) × 1 / 4
= 3 / 20 (x - 4)
Number of people left in the elevator = 3 / 20 (x - 4)
4. 3 people left on the 5th floor
So number of people left in the elevator = 3 / 20 (x - 4) - 3
Now as per the question it is mentioned that the elevator becomes empty on the 5th floor.
so 3 / 20 (x - 4) - 3 = 0
Adding 3 on both sides:
3 / 20 (x - 4) - 3 Â + 3 = 0 + 3
= 3 / 20 (x - 4) Â = 3
Multiplying both sides by 20:
20 × 3 / 20 (x - 4) = 3 × 20
= 3 (x - 4) = 3 × 20
Dividing both sides by 3: Â
3 (x - 4) / 3 = 3 × 20 / 3
(x - 4) = 20
Adding 4 on both sides:
(x - 4) + 4 = 20 + 4
x = 24
Therefore there were 24 people on the elevator.
Hence in the office building, 24 people got on the elevator on the main floor.
Know more about "remainder problems" here: https://brainly.com/question/13802213
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Disclaimer: The given problem is incomplete. The complete problem is mentioned below:
One morning a certain number of passengers got on an elevator on the main floor of an office building. Four got off on the second floor, 2/5 of the remainder on the third floor, 75% of the remainder on the fourth floor, and 3 on the 5th floor. If the elevator was empty at this point, how many got on the elevator on the main floor?
