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Linear Equations (Word Problems) (F)

Crack GCSE Foundation word problems with linear equations. Turn stories into maths, define variables, build equations, and solve step by step to find sensible, unit-checked answers.

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Fascinating Fact:

At a market stall, 5 apples and one banana cost £4.40. A banana costs £0.20 more than an apple. Let a be apple. 5a + (a + 0.20) = 4.40, so 6a + 0.20 = 4.40, a = £0.70, banana = £0.90.

In GCSE Maths (Foundation), word problems become linear equations by translating language into algebra. Define variables, write the equation from the story, solve systematically, then interpret and check that your answer fits the context and units.

Key Terms

Variable: A letter representing an unknown quantity, such as x or a.
Linear equation: An equation where variables have power 1, e.g., 6a + 0.2 = 4.4.
Model: The algebraic statement built from the problem’s words, numbers, and units.

Frequently Asked Questions (Click to see answers)

How do I set up a linear equation from a word problem?

Define a variable for the unknown, translate each sentence into algebra (totals, differences, “more than”), combine into one equation, then solve and interpret the result.

What steps solve two-step equations in real contexts?

Undo operations in reverse order: subtract or add to isolate the term with the variable, then divide or multiply to find the variable. Finally, include correct units.

How do I check that my answer makes sense?

Substitute it back into the original wording and arithmetic, confirm units, and estimate roughly to see if the value is reasonable for the situation.