# 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: Math Assignment, UCD, Ireland

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.

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