Cinema Problem

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A cinema has $100$ seats. The ticket prices are:
$£10$ for adults
$50$p for pensioners

What is the minimum that the cinema's takings could be, if all $100$ tickets are sold?
What is the next smallest amount that the takings could be? And the next? And the next...?

The cinema took $£449$ one day. Work out how many adults and how many pensioners bought tickets, if all the seats were filled.

A cinema has $100$ seats. The ticket prices are:
$£10$ for adults
$10$p for children

What is the minimum that the cinema's takings could be, if all $100$ tickets are sold?
What is the next smallest amount that the takings could be? And the next? And the next...?

The cinema took $£208$ one day. Work out how many adults and how many children bought tickets, if all the seats were filled.

A cinema has $100$ seats.
The ticket prices are:
$50$p for pensioners
$10$p for children

What is the minimum that the cinema's takings could be, if all $100$ tickets are sold?
What is the next smallest amount that the takings could be? And the next? And the next...?

The cinema took $£20$ one day. Work out how many pensioners and how many children bought tickets, if all the seats were filled.

The ticket prices at a cinema are:
$£10$ for adults
$50$p for pensioners

How many different ways can you find of selling tickets so that the takings are exactly $£60$?

The cinema introduces a child ticket for $10$p. The cinema manager starts to list the different combinations of adults, children and pensioners that will earn him exactly $£60$. Part of his table is shown below:



Without listing all the combinations work out how many different ways there are to earn exactly $£60$.
What is special about the total number of tickets sold when exactly 4 adult tickets are sold (and the takings are exactly $£60$)? Explain why.

A cinema has $100$ seats.
Show how it is possible to sell exactly $100$ tickets and take exactly $£100$ if the prices are:
$£10$ for adults
$50\text{p}$ for pensioners
$10\text{p}$ for children

Is there only one solution?