Alison's cinema has 100 seats.
One day, Alison notices that her cinema is full, and she has taken exactly £100.
The prices were:
She knows that not everyone in the audience was a pensioner.
How many adults, pensioners and children were present?
Can there be 100 people and takings of exactly £100 if the prices are:
What if the prices are:
Here are some questions you might like to consider:
This problem is based on Cinema Problem from SIGMA 1 by David Kent and Keith Hedger
- How many solutions are there for each set of prices?
- If I can find one solution, can I use it to help me find all the other solutions?
- Can you find alternative sets of prices that offer many solutions?
- What about exactly one solution?
- If a children's film has an audience of 3 children for every adult (no pensioners), how could the prices be set to take exactly £100 when all the seats are sold?
- What about a family film where adults, children and pensioners come along in the ratio 2:2:1?