38925

Going to the Cinema

Obviously, we will have more children than Pensioners and Adults due to the fact that with 100 people and £100, the average will be £1 per person. Take 50 children for instance.

50 children x £0.85 = £42.50

Now we have to look at the other 50 people. Take 40 pensioners. This cannot work, as the 10 other people would be adults. The cost would be £117.50 pounds, and this is far more than Alison makes. Now use 45 pensioners. 50 + 45 = 95 people and the total cost (including the adults) comes out as £105.

The next odd number is 47. £42.50 + £47 = £89.50, and the remained 3 people must be adults. £3.50 x 3 = £10.50, and £89.50 + £10.50 = £100.

So:

50 children
47 pensioners
3 adults