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.
c. GreenGrocer further adjusts their model to account for seasonal variations, leading to the system:
$$2x + y = 7$$
$$4x + ay = 14$$
Determine the value of $a$ for which the price of apples and bananas can be uniquely determined using this model.
Marking your answer...
This may take a few seconds
Sign up for free to see your full marking breakdown and personalised study recommendations.
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).
All free, all instant AI marking.
A chemist is experimenting with two solutions, $A$ and $B$, each containing different concentrations of a particular solute. Let $x$ represe…
Consider the following system of linear equations: $x + ay + z = 1$ $x + 2y + z = b$ $2x + 4y + 2z = 2b$ where $a$ and $b$ are real numbers.…
The following system of equations is given: $x + y = 5$ $2x + 2y = k$ State the value of $k$ for which this system has infinitely many solut…
StudyPulse has thousands of VCE Mathematical Methods questions with full AI feedback, mark breakdowns, progress tracking, and study notes across every Key Knowledge point including Simultaneous Linear Equations.
