Sheet № 207 · Foundation + Higher · AQA · Edexcel · OCR
Solving Simultaneous Equations from Context –
Solving simultaneous equations from context is a common GCSE Maths skill where you translate a real-world situation into two equations and then solve them. These questions test both your ability to form equations and your algebraic solving skills.
§Key definitions
Question:
2 sandwiches and 3 drinks cost £9.50. 4 sandwiches and 1 drink cost £11.50. Find the cost of one sandwich and one drink.
Answer:
A sandwich costs £2.50 and a drink costs £1.50.
Q1 (Foundation):
3 pens and 2 rulers cost £3.80. 1 pen and 2 rulers cost £2.20. Find the cost of a pen and a ruler.
Q2 (Foundation):
4 apples and 3 bananas cost £2.50. 2 apples and 5 bananas cost £2.30. Find the cost of each fruit.
Q3 (Higher):
The perimeter of a rectangle is 34 cm. The length is 5 cm more than the width. Find the dimensions.
§Formulas to memorise
Define variables clearly, e.g. let t = cost of one tea, c = cost of one coffee
Write one equation per piece of information, then solve by elimination or substitution
Worked example
2 sandwiches and 3 drinks cost £9.50. 4 sandwiches and 1 drink cost £11.50. Find the cost of one sandwich and one drink.
Working:
⚠ Common mistakes
- ✗Using the same letter for both unknowns. Choose two different letters and define them clearly at the start.
- ✗Setting up the wrong equations. Read each sentence carefully. "3 teas and 2 coffees cost £8.50" means 3t + 2c = 8.50, not 3t × 2c.
- ✗Forgetting to check the answer in context. A negative price or a child older than a parent should alert you to an error.
✦ Exam tips
- →Always start by writing "let x = ... and y = ..." — this earns a mark and keeps your work organised.
- →Label each equation (e.g. Equation 1, Equation 2) so the examiner can follow your working.
- →After solving, substitute back into both original equations to verify your answer.