Many GCSE questions give a situation in words and ask you to form and solve an equation. The skill is translating the words into algebra before doing any calculation.
Process:
- Assign a letter to the unknown — write "Let $x = ...$" explicitly
- Write an expression for every relevant quantity in terms of $x$
- Use the condition in the question to form an equation (usually two expressions that are equal, or that sum to a given total)
- Solve the equation and interpret the answer in context
Example: The perimeter of a rectangle is 40 cm. The length is three more than twice the width. Find the dimensions.
Let width $= x$, length $= 2x + 3$. $$2(x + 2x + 3) = 40 \implies 2(3x + 3) = 40 \implies 6x + 6 = 40 \implies x = \frac{34}{6} \approx 5.67\text{ cm}$$
Common error: writing an expression but never forming the equation — you must equate two things before you can solve.