My solution is done by trial and error. Everybody might not get the same answer because there are various ways to solve it.
We know that the total figure for the cost of the children's admission must end in 0.5 pounds or whole pounds. Therefore, the number of children must in multiples of ten. Using the children's figure in multiples of ten, I experimented using the largest number possible which is ninety children to work out a total cost of admission using the remaining numbers of adults and pensioners in different combinations.
Adult (£3.50) Pensioners (£1) Children (£0.85) Total Cost
5 (£17.5) 5 (£5) 90 (£76.5) £99
4 (£14) 16 (£16) 80 (£68) £98
5 (£ 17.5) 25 (£25) 70 (£59.5) £102
5 (£17.5) 45 (£45) 50 (£42.5) £105
3 (£10.5) 47 (£47) 50 (£42.5) £100
Through trial and error, I found the answer to be 3 adults, 47 pensioners and 50 children to fit the maximum amount of cinema goers for exactly one hundred pounds.