SOLUTION: Hi, I setted up the equation, but when I solved it. It wouldn't work when I plugged it in to the story. Question goes as.. One morning a certain number of passengers got on an

Question 776405: Hi, I setted up the equation, but when I solved it. It wouldn't work when I plugged it in to the story.
Question goes as..
One morning a certain number of passengers got on an elevator at the main floor of an office building. Four got off at the second floor, 2/5 of the reaminder at the third floor, 75% of the remainder at the fourth floor, and 3 on th fifth floor. If the elevator was empty at this point, how many got on the elevator at the main floor?
Here's my work, I know the answer is 24. But when I solved my equation I end up with 18.
Let X= Amount of people that go on from the main floor.
.75(2/5(x-4))-3= x
3/4(2/5x-8/5)-3= x
30x/20-120/20-3= x
30x/20-6/1-3/1
30x/20-9/1= x (Multiply both sides by 20)
30x-180=20x
10x=180
[x=18]
Did I do this correctly? I'm positive I didn't. The answer should be 24, but my teacher wants me to solve it with equations.
Again! I would really appreciate it if anyone could help me! Thanks!

Answer by htmentor(1343) (Show Source): You can put this solution on YOUR website!
x = the number that got on at the main floor
At the 2nd floor 4 got off so there are x-4 remaining
At the 3rd floor 2/5 of the remainder got off or 2/5(x-4). So there are 3/5(x-4) remaining
At the 4th floor 75% or 3/4 of the remainder got off, which is (3/4)(3/5)(x-4).
That means there are (1/4)(3/5)(x-4) left.
At the 5th floor 3 get off and there are none left:
(1/4)(3/5)(x-4) - 3 = 0
Solve for x:
(3/20)(x-4) - 3 = 0
Multiply through by 20/3:
x - 4 - 20 = 0
x = 24
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