SOLUTION: A train can hold 78 passengers. The train starts out empty and picks up one passenger at the first stop,2 passengers at the second stop,3 passengers at the third stop,and so forth.

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Question 407183: A train can hold 78 passengers. The train starts out empty and picks up one passenger at the first stop,2 passengers at the second stop,3 passengers at the third stop,and so forth. After how many stops will the train be full.
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
Let s = the stop number where the train fills.
Then 1+2+3+...+s = 78, or
%28s%28s%2B1%29%29%2F2+=+78, or
s%5E2+%2B+s+=+156
s%5E2+%2B+s+-+156+=+0
(s+13)(s-12) = 0
==> s = 12.
Hence on the 12th stop the train is full.