IGCSE Maths / Algebraic equations

Setting up an equation from a problem revision notes

Edexcel International GCSE Maths (4MA1), chapter 5: Algebraic equations, specification point 2.4b-f. Free lesson.

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To set up an equation from a word problem, choose a simple quantity to call x and express the other quantities in terms of it. Use the statement that gives equal amounts to form the equation, then make sure you answer the question that was asked.

Choose what x stands for

The hardest part is often writing the first line. Choose the smallest or simplest quantity for x, then state clearly what x means. This usually keeps the other expressions tidy and makes sign errors less likely. Write every other quantity in terms of x. Any consistent choice can work, but a different choice may make the algebra longer.

Use the equality in the problem

Look for the sentence that says two amounts are equal, such as a total or a perimeter. Turn that information into an equation and write it clearly before solving. A correct equation can earn marks even if a later solving step goes wrong.

Set up and solve the age problem

Sam is 3 years older than Ben, so Ben is the simpler age to call x. Sam's age is therefore x + 3. Their ages add to 27, which supplies the equals sign.

Use the perimeter of a rectangle

The width is the simpler side, so call it x. The length is twice the width, which is 2x. A rectangle has two widths and two lengths, so its perimeter equation includes both pairs of sides.

Give the quantity the question asks for

The value of x is not always the answer. In the age problem, x means Ben's age, but the question asks for Sam's age. Use the definition of x to find the requested quantity. Ben is 12, so Sam is x + 3 = 15. For the rectangle, the width is 5 cm and the length is 10 cm. For the quick check, call the number x: 2x + 7 = 31, so x = 12.