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This problem introduces inequalities in the context of car parking charges which we hope will be familiar to students. After working on this problem, perhaps students could go on and explore Which is Bigger?, which explores the same mathematics in a more abstract and algebraic way.
The tasks can be tackled using informal numerical approaches but offer a great opportunity to show students the power of algebraic and graphical representations for making sense of real world situations involving comparisons. By switching between different representations, students can persevere and solve problems which would otherwise be out of reach to them.
Introduce the first part of the problem:
In car park A, it costs 80p to park for the first hour, and an extra 50p for each hour after that.
Is there a length of time for which the charges at both car parks would be the same?
Encourage students to draw tables to represent costs for 1 hour, 2 hours, 3 hours...
Which Is Bigger? offers some challenging follow-up questions.