Forming equations involves translating words or real-life situations into algebraic expressions. This is an important step in solving many GCSE Maths problems.
Forming an equation means taking information written in words and turning it into an algebraic equation.
This topic is important because many GCSE algebra questions begin with a word problem. Before solving it, you first need to form the correct equation.
A statement showing that two expressions are equal.
A letter used to represent an unknown value.
A mathematical phrase made with numbers, variables and operations.
Build or create the algebraic equation from the information given.
The value you are trying to find.
Change words into mathematical symbols and algebra.
For example, let \(x\) be the unknown number.
Do not rush straight to the final equation.
Words like “is” or “equals” usually show where the equals sign goes.
Make sure the algebra says exactly what the sentence says.
“A number plus 3 is 10”
“Twice a number is 18”
“One number is 4 more than another”
Use known formulas and relationships to build the equation.
Forming equations means translating a word problem into algebra. You turn words into mathematical expressions and connect them with an equals sign.
Start by deciding what the letter represents.
Break the sentence into parts and translate each phrase.
“more than”, “plus” → \(+\)
“less than”, “minus” → \(-\)
“times”, “twice”, “double” → \(\times\)
“is”, “gives”, “total” → \(=\)
Once the equation is formed, solve it if required.
Exam-style questions inspired by Edexcel GCSE Mathematics, focusing on translating words into algebraic equations and solving them.
Form an equation for: \( \text{A number increased by 5 is equal to 17} \).
Form an equation for: \( \text{Three times a number decreased by 2 is equal to 13} \).
Form an equation and solve: \( \text{A number divided by 4 is equal to 6} \).
The perimeter of a rectangle is 30 cm. Its length is \( x \) cm and its width is 5 cm. Form an equation.
The sum of two consecutive integers is 41. Form an equation to find the integers.
Exam-style questions based on the AQA GCSE Mathematics specification, focusing on algebraic modelling and solving real-life problems.
Ali is \( x \) years old. His sister is 4 years older. Their combined age is 24. Form an equation.
The cost of 3 pens and a notebook is £7. The notebook costs £2. Form an equation to find the cost of one pen.
The angles of a triangle are \( x \), \( x + 20 \), and \( x + 40 \). Form an equation.
A number is increased by 15% to give 69. Form an equation to find the original number.
The length of a rectangle is 3 cm longer than its width. The perimeter is 46 cm. Form an equation.
Exam-style questions aligned with OCR GCSE Mathematics, emphasising reasoning, multi-step problem-solving, and interpreting algebraic models.
A taxi charges a fixed fee of £3 plus £2 per mile. If the total fare is £15, form an equation to find the number of miles travelled.
The sum of three consecutive integers is 72. Form an equation to find the integers.
The area of a rectangle is 48 cm^2. Its length is \( x \) cm and its width is \( x - 2 \) cm. Form an equation.
A shop sells adult tickets for £8 and child tickets for £5. The total cost of 6 tickets is £39. Form an equation.
The sum of the interior angles of a quadrilateral is 360^\circ. The angles are \( x \), \( x + 10 \), \( x + 20 \), and \( x + 30 \). Form an equation.
Decide what the variable represents.
Translate the wording into algebra one phrase at a time.
Use the equals sign in the correct place.
Check that the equation really matches the words.
Turning a sentence into the wrong algebraic expression.
Especially in phrases like “less than” and “more than”.
Forgetting that an equation needs an equals sign.
Not using the information about totals, perimeter, ages or measurements properly.
These are common mistakes students make when forming equations from word problems in GCSE Maths.
A student uses a variable without explaining what it represents.
Always define your variable clearly at the start, for example: “Let x be the number of apples.” This avoids confusion later.
A student writes expressions incorrectly for phrases like “3 less than x”.
Pay close attention to wording. “3 less than x” means \(x - 3\), not \(3 - x\).
A student writes part of the relationship but does not form a full equation.
An equation must show two expressions equal to each other. Make sure you include the equals sign to complete the statement.
A student writes only one side of the relationship.
If the question asks for an equation, you must write both sides. An expression is not enough.
A student forms the correct equation but makes errors when solving it.
After forming the equation, solve it carefully using correct algebraic steps. Always check your solution in the original context.
Practise translating word problems into algebraic equations.
Translate simple sentences into equations.
A number x increased by 5 is equal to 12. Which equation is correct?
A number y decreased by 3 is equal to 10. Write an equation.
Twice a number x is equal to 14. Which equation represents this?
Three more than a number x is 20. Write an equation.
Five less than a number x is 8. Which equation is correct?
A number n multiplied by 4 is 28. Write an equation.
A number x divided by 3 is 7. Which equation is correct?
A student writes \(x - 5 = 10\) for "5 less than x is 10". Are they correct?
Ten more than a number x is 25. Write an equation.
Which equation represents: "A number x is 6 more than 12"?
Form equations from multi-step and real-life problems.
A number x plus 4 is equal to twice the number. Which equation is correct?
Three times a number x minus 5 is 16. Write an equation.
The perimeter of a rectangle is 30. Its length is x and width is 5. Which equation is correct?
The sum of a number x and its double is 21. Write an equation.
A student is 4 years older than their brother. Their age is x. Brother’s age is y. Which equation is correct?
A number x divided by 2 and then increased by 3 gives 11. Write an equation.
A student writes \(3x - 5 = 16\) for "three times a number plus 5 is 16". What is the mistake?
The total cost of x items at £4 each plus £3 delivery is £27. Write an equation.
A number x is 5 less than twice another number y. Which equation is correct?
The sum of three consecutive numbers starting from x is 45. Write an equation.
Practise this topic with interactive games.
Turning words into algebra.
Keywords like ‘sum’, ‘difference’ or ‘product’.
It links maths to real-life problems.