The purpose of this multi-level task is to engage students in using their knowledge of linear relationships to solve a problem.

This background knowledge and skills that need to be established before and/or during this task are outlined in the diagram below:

This task may be carried out with numerical exploration, and/or by generalising with rules that have been established earlier. The approach should be chosen in sympathy with their skills and depth of understanding.

Task: A car rental business has two rental schemes, red and blue for rentals up to ten days. These schemes are advertised in their brochures with this graph.

Use the following information to work out how many days of rental would carry the same total cost on either the blue or the red scheme.

- The area under the graph gives the total cost of renting.
- The schemes each follow a linear pattern, cutting the vertical axis at 120 and 170.
- Both blue and red schemes cost $110 on the 4th day of rental.

### The arithmetic approach (show more)

- The student is able to interpret the graphical information given and to use a tool such as a table, to solve the problem.

### The procedural algebraic approach (show more)

- The student is able use algebraic techniques to solve the problem.

### The conceptual algebraic approach (show more)

- The student is able devise an original approach, using mathematical techniques to solve the problem.