**1. a)** John and Mary buy their fruit from the same shop. John bought 5 apples and 3 bananas for €4. On the same day, Mary bought 4 apples and 7 bananas for €6. How much does one apple cost? How much does one banana cost? Complete all of the following steps for maximum marks:

**(i)** Declare variables

**(ii)** Derive two equations that model the real-life situation described in the question.

**(iii)** By solving the 2 equations derived in part (ii), calculate (a) how much one apple costs, and (b) how much one banana costs.

**1. b)**

**(i)** Draw a diagram showing the stages involved in the mathematical modeling process.

**(ii)** Explain in your own words your understanding of the Validation stage of the mathematical modeling process. For maximum marks don’t just paraphrase my notes; show that you have a clear understanding of what might be involved in this stage of the process. Use your own example if it helps you explain better.