From the question we know that everyone in the cinema hall is not a pensioner. If everyone is a child, the total cost will be too less because 100 x 0.85 = 85. If everyone is an adult, the total cost will be too high because 100 x 3.50 = 350. On an average, everybody's ticket costs 1 pound so if there are only pensioners and children, the total cost will be too less. If there are only pensioners and adults, the total cost will be too high. If there are adults and children, the equation is solvable but the answer is not a whole number. Therefore, there are adults, children and pensioners in the cinema hall. For every adult, the price is 2.50 pounds more than the average price. For every child, the price is 0.15 pounds less than the average price. The LCM of 2.50 and 0.15 is 7.50. 2.50 x 3 is 7.50 and 0.15 x 50 is 7.50. Therefore, for every 50 children, there are 3 adults.
We can conclude that there are 3 adults, 47 pensioners and 50 children.