Mr. Wilson and one man got on a streetcar. At the secong stop three people got on. At the third stop, three people got on and one got off. At the fourth stop, three got off. At the fifth stop, six people got off. At the sixth stop, one-half of the passengers got off and Mr. Wilson was the only passenger left on the the streetcar. How many passengers were on the streetcar when Mr. Wilson got on?
first stop: x+2
2nd stop: x+5
3rd stop: x+7
4th stop: x+4
5th stop: x-2
6the stop: (x-2) - (1/2)(x-2) = 1
which solves to
x = 4
shutup
To solve this problem, let's analyze the information step by step:
1. Mr. Wilson and one man got on the streetcar: From the given information, we know that initially there were at least two passengers on the streetcar.
2. At the second stop, three people got on: This means that after the second stop, the number of passengers increased by three.
3. At the third stop, three people got on and one got off: From this, we can conclude that the net change in the number of passengers at the third stop is two (3 got on minus 1 got off).
4. At the fourth stop, three got off: Similarly, at this stop, the number of passengers decreased by three.
5. At the fifth stop, six people got off: Here, the number of passengers decreased further by six.
6. At the sixth stop, one-half of the passengers got off and only Mr. Wilson was left: This implies that after the sixth stop, the number of passengers reduced to one (as Mr. Wilson was the only passenger left).
Now, to find out how many passengers were on the streetcar when Mr. Wilson got on, we need to reverse the sequence of events and calculate:
1. At the sixth stop, when there was only one passenger left, we know that half of the passengers got off. So, if 1 represents half the original number of passengers, then the original number of passengers would be 1 multiplied by 2, which equals 2.
2. At the fifth stop, six people got off. Since there were two passengers on the streetcar before that, this means that the total number of passengers after the fifth stop would be two plus six, which equals eight.
3. At the fourth stop, three people got off. Therefore, the number of passengers before the fourth stop would be eight plus three, which equals eleven.
4. At the third stop, three people got on and one got off. If the number of passengers before this stop was eleven, and the net increase was two, then the number of passengers after this stop would be eleven plus two, which equals thirteen.
5. At the second stop, three people got on. This means that before the second stop, there were thirteen minus three passengers, which equals ten.
Finally, we conclude that there were ten passengers on the streetcar when Mr. Wilson initially got on.