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Forming Equations

FoundationChallengeAQAEdexcelOCR

This free Foundation GCSE Maths worksheet on forming equations helps you revise forming and solving equations. Questions build from straightforward to exam standard, with full worked answers in the mark scheme — ideal for revision or homework. Suitable for AQA, Edexcel and OCR. Turn the words into algebra first, then solve the equation you've built.

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These worksheets and mark schemes are original, written for Virtus Academy and checked against the current AQA, Edexcel and OCR specifications. Every worksheet comes with a full mark scheme.

Foundation

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Challenge / Extension

Stretch yourself beyond the basics.

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Topic overview

Forming equations means turning a described situation into algebra, then solving it. It combines writing expressions with solving equations, and it is where algebra becomes genuinely useful.

Start by choosing a letter for the unknown and writing down clearly what it represents. Then translate the information into an equation, using the fact that something in the problem is equal to something else.

The final step is often forgotten: answer the question that was asked. If \(x\) represents the number of pencils and you find \(x = 7\), the answer is seven pencils, not simply the number seven.

Revision notes

Choosing and defining a letter

Pick a letter for the quantity you are asked to find, and state what it means.

If a question involves consecutive numbers, let the first be \(n\), so the next are \(n + 1\) and \(n + 2\). Defining the letter is worth a mark on its own in many questions.

Building the equation

Find the statement in the question that says two things are equal, and write it in symbols.

If three consecutive numbers add to \(48\), then \(n + (n+1) + (n+2) = 48\), which simplifies to \(3n + 3 = 48\).

Solving and interpreting

Solve as normal, then translate back into the context of the question.

Here \(3n = 45\), so \(n = 15\), and the three numbers are \(15\), \(16\) and \(17\). Giving only \(n = 15\) would not fully answer the question.

Key points

  • Define what the letter represents.
  • Find the statement of equality in the question.
  • Write the equation in symbols.
  • Simplify before solving.
  • Solve using the usual methods.
  • Answer the question that was actually asked.

Worked examples

Example 1

Three consecutive numbers add to \(72\). Find them.

Working

\[n + (n+1) + (n+2) = 72\]let the first number be n and form the equation
\[3n + 3 = 72 \Rightarrow 3n = 69\]simplify and solve
\[23, 24, 25\]n = 23, so state all three numbers

Example 2

A rectangle has length \(x + 4\) and width \(x\). Its perimeter is \(28\)cm. Find \(x\).

Working

\[2(x + 4) + 2x = 28\]perimeter is twice the length plus twice the width
\[4x + 8 = 28 \Rightarrow 4x = 20\]expand and simplify
\[x = 5\]solve for x

Example 3

Sam has \(n\) sweets. Ben has twice as many. Together they have \(36\). Find \(n\).

Working

\[n + 2n = 36\]form the equation from the total
\[3n = 36\]collect like terms
\[n = 12\]Sam has 12 sweets

Common mistakes

  • Not defining the letter.

    A full answer states what the letter represents before the equation appears.

  • Forming an expression rather than an equation.

    An equation needs an equals sign, connecting the expression to a known value.

  • Solving but not answering the question.

    If asked for three numbers, give all three, not just the value of n.

  • Misreading the relationship.

    Twice as many as n is 2n, not n + 2.

Exam tips

  • Write let n be… as your first line every time.
  • Look for the word is, totals or equals to find the equation.
  • Simplify the equation before solving it.
  • Finish by answering in the words of the question, with units where relevant.

Key terms

Form an equation
To translate a described situation into algebra.
Consecutive
Following one after another, such as n, n+1, n+2.
Perimeter
The total distance around the outside of a shape.
Unknown
The quantity represented by a letter.

Related topics

Written and reviewed against the current AQA, Edexcel and OCR specifications. Spotted an error? Let us know.