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# Cinema Problem

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### Consecutive Numbers

### Adding All Nine

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Age 11 to 14

Challenge Level

*Cinema Problem printable sheet*

**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.

**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*

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

Make a set of numbers that use all the digits from 1 to 9, once and once only. Add them up. The result is divisible by 9. Add each of the digits in the new number. What is their sum? Now try some other possibilities for yourself!