1 Some jars need to be packed into small crates.
There are 17 small jars, 7 medium jars and 3 large jars to be packed.

• A medium jar takes up the same space as four small jars.
• A large jar takes up the same space as nine small jars.

Each crate can hold:

• at most 12 small jars,
• or at most 3 medium jars,
• or at most 1 large jar (and 3 small jars),
• or a mixture of jars of different sizes.
  1. One strategy is to fill as many crates as possible with small jars first, then continue using the medium jars and finally the large jars.

Show that this method will use seven crates. The jars can be packed using fewer than seven crates.

The jars are to be packed in the minimum number of crates possible.

• Describe how the jars can be packed in the minimum number of crates.
• Explain how you know that this is the minimum number of crates.

Some other numbers of the small, medium and large jars need to be packed into boxes.
The number of jars that a box can hold is the same as for a crate, except that

• a box cannot hold 3 medium jars.
• Describe a packing strategy that will minimise the number of boxes needed.