Solving Simultaneous Equations for Fruit Costs
This page presents a hard simultaneous equations question and answer focused on calculating the cost of apples and pears. The problem is typical of GCSE exam practice higher tier questions in mathematics.
The question states:
The total cost of 3 apples and 4 pears is £1.84
The total cost of 5 apples and 2 pears is £1.76
Work out the cost of one apple and the cost of one pear.
Example: This problem can be represented by two equations:
3a + 4p = 1.84
5a + 2p = 1.76
Where 'a' represents the cost of one apple and 'p' represents the cost of one pear.
The solution process is then outlined step-by-step, demonstrating how to manipulate these equations to find the values of 'a' and 'p'.
Highlight: The key steps in solving this problem involve multiplying one equation to eliminate a variable when the equations are subtracted, and then using substitution to find the other variable.
The working shown includes:
- Multiplying the first equation by 5 and the second by 3
- Subtracting the resulting equations to eliminate 'a'
- Solving for 'p' (the cost of a pear)
- Substituting this value back into one of the original equations to solve for 'a' (the cost of an apple)
Vocabulary: Simultaneous equations are a set of equations with multiple unknowns that are solved together to find the values that satisfy all equations simultaneously.
The final answer, worth a total of 4 marks, is clearly presented:
Cost of one apple: £0.24
Cost of one pear: £0.28
This question exemplifies the type of simultaneous equations GCSE questions and answers that students might encounter, particularly those involving practical applications like cost calculations. It's an excellent example for students practicing for their GCSE maths higher tier exams, demonstrating the application of algebraic skills to real-world problems.
Definition: In GCSE maths, higher tier questions often involve more complex problem-solving and multi-step calculations, as demonstrated in this simultaneous equations problem.
This type of question could easily appear in a simultaneous equations worksheet and answers PDF or on websites like Maths Genie simultaneous equations answers or Corbettmaths simultaneous equations. It's particularly useful for students looking for GCSE maths higher simultaneous equations practice questions and answers.
