Three towns - Ambridge, Bordertown, and Capeside are each connected by a network of roads. There are 82 ways to get from Ambridge to Bordertown, including those routes that pass through Capeside. There are 62 ways to get from Bordertown to Capeside, including those routes that pass through Ambridge. The number of ways to get from Ambridge to Capeside, including those ways passing through Bordertown, is less than 300.

How many ways are there to get from Ambridge to Capeside, including those routes that pass through Bordertown?

(In reply to One answer by Larry)

One answer (by Larry):
   If the roads from A to B are equal to x
and the roads from B to C are equal to y
and the roads from A to C are equal to z,

then x + y*z = 82     eq1
       y + x*z = 62      eq2

Larry, no need  to try and err!

JUST  SUBTRACT EQ2 FROM EQ1: 

(X-Y)*(1-Z)=20    

or
(y-x)*( z-1 )=20

z= (2,3,5,6,11,21)

Only one z ( i.e.11)  yields

  z + x*y = "less than 300"        since       x =5   y=7 

 

we get 

x + y*z = 82                                 5+77
  y + x*z = 62                                7+55
z + x*y = 46                                  11+35

Posted by Ady TZIDON on 2009-01-25 01:07:47