39143

3 adults, 47 pensioners and 50 children
My solution was that there were 3 adults, 47 pensioners and 50 children. I mainly used trial and error, this is where you pick numbers from an educated guess and see if it works. If it doesn't you then would change your answers. I knew that there would be very few adults because their prices were too high at £3.50 and if 28 adults visited that would take the price to £98 meaning their would not be enough money remaining to get it to 100 people. So I started with the adults at two because that made a whole number(£6). I then had 50 pensioners and 48 children. That equaled 100 people but £97.80 which was too little. To take the price up I changed 2 adults to 3 and 50 pensioners to 49. This equaled £100.30 though, which was too much. I changed the 49 pensioners to 48 pensioners and 48 children to 49. It equaled £100.15 which was £0.15 too much but i had realized that the difference between pensioners and children was £0.15. Therefore I changed 48 pensioners to 47 and 49 children to 50 which saved £0.15 and then the number of people in the cinema was 100 and ticket sales equaled £100 meaning I had solved the problem. 3 adults, 47 pensioners and 50 children. 100 people, 100 pounds.