Question 1 is a possibilities and constraints problem. Similar problems can be found in Algebra, Figure It Out, Levels 2–3. A variety of strategies could be used:
• trial and improvement
Two dinghies and two kayaks can hold 10 people in total. So try a kayak holding one person and a dinghy holding four people …
• using a table to organise the information

• using patterns

Question 2 builds on this answer and provides a more complex possibilities and constraints problem.  Similar strategies can be used, for example, trial and improvement using a table:

Answers to Activities

1. a. 2
b. If 2 dinghies and 2 kayaks hold 10 people, then 1 dinghy and 1 kayak must hold 5
people.
If the kayak holds 1 person and the dinghy 4, then 3 dinghies and 1 kayak would hold 3 x 4 + 1 = 13 people. So this can’t be correct. Another possibility is that the kayak holds 2 people and the dinghy holds 3. This means 3 dinghies and 1 kayak hold 3 x 3 + 2 = 11 people, which agrees with the information given.
2. 6 dinghies and 9 kayaks