Problem of the Week 6

A book has n consecutive pages* torn out.  Suppose A is the last numbered page before the torn-out section and B is the first numbered page following the torn-out section.  Find a formula for n in terms of A and B.

*Each paper in a book has two sides.  Each side is one page.

 

Alternate Problem 6

At some stops, a certain bus picks up 5 people.  At other stops, it picks up 2 and, at the same time, lets off 5.  There are no other stops but these.  The bus starts its run empty and picks up 5 people.  At the end, it has 11 people aboard.  If the number of stops is greater than 17, what is the least number of stops the bus makes?

 

Extension Problem 6

At some stops, a certain bus picks up 5 people.  At other stops, it picks up 2 and, at the same time, lets off 5.  There are no other stops but these.  The bus starts its run empty and picks up 5 people.  At the end, it has 11 people aboard.

a.  If the number of stops is greater than 75, what is the least number of stops the bus makes?

b.  If the number of stops is greater than 703, what is the least number of stops the bus makes?

c.  For part a, how many of the stops must be where the total gain in passengers is 5?  For part b?