Expert: Steve Holleran - 4/12/2008

Question
at some stops, a certain bus picks up 5 people. at other stops it picks up 2 people and at the same time drops off 5 people. there are no other stops but these. the bus starts its run empty and at the end of its run the bus has 11 people left. if the number of stops is greater the 17 what is the least number of stops the bus makes?

Answer
Hi Kate,

I don't know that there's a graphical method of doing this--I tried linear programming, but it didn't  work out.  I eventually just tried a listing.

Let x = # stops where 5 people get on

   y = # stops where 2 get on, and 5 get off : net -3

Then you want 5x - 3y = 11 and x + y > 17

    x         y            5x - 3y = 11

    9         8                21

    10        8                24

    10        9                23

    10        12               14

    10        13               11     So I would say 23 stops

Hope this is ok.

Steve