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Alison's cinema has 100 seats.
One day, Alison notices that her cinema is full,
and she has taken exactly £100.
The prices were as follows:
She knows that not everyone in the audience was a pensioner!
Is it possible to work out how many adults, pensioners and children were present?
You may want to start by trying different ways of filling all 100 seats.
e.g. 5 adults, 20 pensioners and 75 children
Does this earn you £100?
Too much? Too little?
Can you tweak the numbers to get closer to £100?
You may find this spreadsheet useful.
What other interesting mathematical questions can you think of to explore next?
We have thought of some possibilities:
Is there only one possible combination of adults, pensioners and children that add to 100 with takings of exactly £100?
Can there be 100 people and takings of exactly £100 if the prices are:
Can you find alternative sets of prices that also offer many solutions? What about exactly one solution?
If I can find one solution, can I use it to help me find other solutions?
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?
Going to the Cinema
This resource is part of "Freedom and Constraints"
Alison's cinema has 100 seats.One day, Alison notices that her cinema is full,
and she has taken exactly £100.
The prices were as follows:
| Adults | £3.50 |
| Pensioners | £1.00 |
| Children | £0.85 |
She knows that not everyone in the audience was a pensioner!
Is it possible to work out how many adults, pensioners and children were present?
You may want to start by trying different ways of filling all 100 seats.
e.g. 5 adults, 20 pensioners and 75 children
Does this earn you £100?
Too much? Too little?
Can you tweak the numbers to get closer to £100?
You may find this spreadsheet useful.
What other interesting mathematical questions can you think of to explore next?
We have thought of some possibilities:
Is there only one possible combination of adults, pensioners and children that add to 100 with takings of exactly £100?
Can there be 100 people and takings of exactly £100 if the prices are:
| Adults | £4.00 | Adults | £5.00 | |
| Pensioners | £1.00 | or | Pensioners | £2.50 |
| Children | £0.50 | Children | £0.50 |
Can you find alternative sets of prices that also offer many solutions? What about exactly one solution?
If I can find one solution, can I use it to help me find other solutions?
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?
We'd love you to share the questions you've come up with. Tell us also how you got started and any conclusions you have arrived at.
Send us your thoughts; we'll be publishing a selection.
Send us your thoughts; we'll be publishing a selection.
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