Here are the prices for 1st and 2nd class mail within the UK [in 2002].

Weight up to First Class Second Class
$60g$ $27p$ $19p$
$100g$ $41p$ $33p$
$150g$ $57p$ $44p$
$200g$ $72p$ $54p$
$250g$ $84p$ $66p$
$300g$ $96p$ $76p$
$350g$ $£1.09$ $87p$
$400g$ $£1.30$ $£1.05$
$450g$ $£1.48$ $£1.19$
$500g$ $£1.66$ $£1.35$
$600g$ $£2.00$ $£1.60$
$700g$ $£2.51$ $£1.83$
$750g$ $£2.69$ $£1.94$*
$800g$ $£2.91$
$900g$ $£3.20$
$1kg$ $£3.49$

Costs for First Class items over $1kg$ are $£3.49$ and then $85p$ for each extra $250g$.
*Items over $750g$ cannot be sent second class.

You have an unlimited number of each of these stamps:

 $4p$ $10p$ $19p$ $27p$ $37p$ $£1.00$

1/ Which stamps would you need to post a parcel weighing $825g$?

2/ I want to send a package 1st class which weighs $235g$. It is very small so I want to use as few stamps as possible. Which ones would I use?

3/ If I only had $3$ of each kind of stamp, which $2$nd class price could I not make?

4/ How many different combinations of stamps could be stuck on a letter weighing $140g$ if it goes 1st class?

5/ I use the following stamps to send two items, one 1st class and the other 2nd class:

What could their weights be?

Further extension to this activity can be carried out by considering the value of the stamps alone, as numbers $4$, $10$, $19$, $27$, $37$ & $100$. For example taking the $5$ lowest numbers [missing out the $100$] challenging the pupils to come up with the smallest number of ways you can get totals between $4$ and $50$. This could lead to questions about what totals can NOT be had, and checking to see if you've really got the smallest number of ways, each time.