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Stage: 3 Challenge Level: 
Alison's cinema has 100 seats.
One day, Alison notices that her cinema is full, and she has taken exactly £100.
The prices were:
Adults £3.50
Pensioners £1.00
Children £0.85
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:
Adults £4.00
Pensioners £1.00
Children £0.50
What if the prices are:
Adults £5.00
Pensioners £2.50
Children £0.50
Here are some questions you might like to consider:
- 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?
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NRICH is part of the family of activities in the Millennium Mathematics Project.
NRICH is part of the family of activities in the Millennium Mathematics Project.