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Cinema Problem

Stage: 3 and 4 Challenge Level: Challenge Level:1

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?
     
This problem is based on Cinema Problem from SIGMA 1 by David Kent and Keith Hedger
The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice. More information on many of our other activities can be found here.
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