bonanova Posted July 31, 2008 Report Share Posted July 31, 2008 Every station on the commuter line sells tickets to every other station on the line. Last week some new stations were added, and 46 additional sets of tickets had to be printed. How many stations were there before last week? How many stations were added? No bickering now ... at no time does the number of stations go to infinity. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted July 31, 2008 Report Share Posted July 31, 2008 Every station on the commuter line sells tickets to every other station on the line. Last week some new stations were added, and 46 additional sets of tickets had to be printed. How many stations were there before last week? How many stations were added? No bickering now ... at no time does the number of stations go to infinity. 11 stations were there last week and 2 stations have been added Quote Link to comment Share on other sites More sharing options...
0 Guest Posted July 31, 2008 Report Share Posted July 31, 2008 Ben Law got it. n stations need n(n-1) sets of tickets. Suppose x new stations have been added. Then we need (n+x)(n+x-1) sets of tickets now. That means we need x(x+2n-1) sets of new tickets. x(x+2n-1) = 46 = 2*23 Considering x and n are positive integers we get x = 2 and n = 11. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted July 31, 2008 Report Share Posted July 31, 2008 A) from 11 stations added to become 13 stations - 110 tickets to 156 tickets B) from 23 stations added to become 24 stations - 506 tickets to 552 tickets My calculation is based on number of print out ticket = n(n-1), where n = number of stations. correct? Quote Link to comment Share on other sites More sharing options...
0 Guest Posted July 31, 2008 Report Share Posted July 31, 2008 n stations need n(n-1) sets of tickets. Suppose x new stations have been added. Then we need (n+x)(n+x-1) sets of tickets now. That means we need x(x+2n-1) sets of new tickets. x(x+2n-1) = 46 = 2*23 Considering x and n are positive integers we get x = 2 and n = 11. Its an addition to my previous answer. Two sets of answers. Initially 23 stations and 1 station added. Initially 11 stations and 2 stations added. Quote Link to comment Share on other sites More sharing options...
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bonanova
Every station on the commuter line sells tickets to every other station on the line.
Last week some new stations were added, and 46 additional sets of tickets had to be printed.
How many stations were there before last week?
How many stations were added?
No bickering now ... at no time does the number of stations go to infinity.
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