SOLUTION: A train started is Journey from city hall interchange.At the first stop.2/5 of the passengers alighted and 22 boarded the train .At the second stop ,1/4 of the new total number of

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Question 995904: A train started is Journey from city hall interchange.At the first stop.2/5 of the passengers alighted and 22 boarded the train .At the second stop ,1/4 of the new total number of passenger alighted and 5 boarded the train .Now there are 80 passenger on board the train.
How many passenger were on the train at city hall interchange.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
A train started is Journey from city hall interchange.
At the first stop, 2/5 of the passengers alighted and 22 boarded the train.
At the second stop, 1/4 of the new total number of passenger alighted and 5 boarded the train.
Now there are 80 passenger on board the train.
How many passenger were on the train at city hall interchange.
:
let x = original number of passengers
:
"At the first stop, 2/5 of the passengers alighted and 22 boarded the train."
x - 2%2F5x + 22 = 3%2F5x + 22
we can write this expression as a decimal
.6x + 22 on the train when they left the 1st stop
:
"At the second stop, 1/4 of the new total number of passenger alighted and 5 boarded the train.
Now there are 80 passenger on board the train.
If 1/4 left, there are 3/4 on the train, so we have
3%2F4(.6x+22) + 5 = 80
3%2F4(.6x+22) = 80 - 5
3%2F4(.6x+22) = 75
multiply both sides by 4
3(.6x+22) = 4(75)
1.8x + 66 = 300
1.8x = 300 - 66
1.8x = 234
x = 234/1.8
x = 130 pass when the train left the interchange
:
:
We can confirm this answer
3/5 of 130 + 22 = 100 on the train when it left the 1st stop
then 1/4 got off
3/4 of 100 + 5 = 80 remain on the train