7 roses, 3 lilies and 2 tulips can be inserted in each bundle.

* * * There are 22 roses, 16 lilies and 10 tulips.

So roses can be inserted: 22/3=3 bunches 1.

Lily can be inserted: 16/3=5 bundles, 1 branch.

Tulips can be inserted: 10/2=5 bundles.

Therefore, you can insert 3 packages.