Writing Equations from Word Problems

What you will learn

• Name the unknown.
• Write an equation from the words.
• Solve and check in the story.

Before you start: you should be able to solve one- and two-step equations. See Solving Equations.

The idea

A word problem is an equation told as a story. Your job is to turn the words into algebra, solve it and then say the answer in words.

Four steps

1. Name the unknown: “let $x$ be the cost of one pen”.
2. Write the equation from the story.
3. Solve it with inverse operations.
4. Check the answer in the story and give it units.

Checking

Put your answer back in the story. If pens cost £3, four pens cost £12, plus £3 is £15. ✓

Worked examples

Example 1: Number puzzle

I think of a number, double it and add $5$. The answer is $17$.

1. Let the number be $x$: $2x + 5 = 17$.
2. $2x = 12$, so $x = 6$.

Answer: $6$

Example 2: Money

Four pens and £3 postage cost £15. Find the price of a pen.

1. $4x + 3 = 15$.
2. $4x = 12$, so $x = 3$.

Answer: £3 each

Example 3: Ages

Ben is $x$ years old and Ana is $4$ years older. Together they are $30$.

1. $x + (x + 4) = 30$, so $2x + 4 = 30$.
2. $2x = 26$, so $x = 13$.

Answer: Ben is $13$ and Ana is $17$.

Tip: always write “let $x$ be …” first. It stops you mixing up what the letter means.

Why it matters

Almost every real problem, from budgets to travel plans, is an equation in disguise. Writing it down turns guessing into a method. Next, inequalities and graphs build on the same skills.