A small business, “GreenGrocer”, sells organic fruits and vegetables. They are trying to optimise their pricing strategy for apples and bananas. Let $x$ represent the price of apples per kilogram and $y$ represent the price of bananas per kilogram (both in dollars). Market research suggests that the weekly demand for apples and bananas is influenced by their prices according to the following relationships.
b. After further analysis, GreenGrocer refines their model to include a factor representing customer loyalty, resulting in a slightly different system of equations:
$$2x + y = 7$$
$$4x + 2y = 15$$
Explain the nature of the solutions to this new system. What does this imply about the demand for apples and bananas at these prices?
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Create Free Account Log inThis is a free VCE Units 3 & 4 Mathematical Methods practice question worth 2 marks, testing your understanding of Simultaneous Linear Equations. It falls under Algebra, number and structure in Unit 4: Mathematical Methods Unit 4. Submit your answer above to receive instant AI-powered marking and personalised feedback.
Continues the study of functions, algebra, calculus, and introduces probability and statistics.
Covers algebra of functions, inverse functions, and solutions of equations and systems of equations.
solution of simple systems of simultaneous linear equations, including consideration of cases where no solution or an infinite number of possible solutions exist (geometric interpretation only required for two equations in two variables).
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