Choose the unknown and write the equation

The steps involved in setting up an equation

Setting up an equation for a problem always follows the same four-step method:

1. Read the problem several times to fully understand the situation.
2. Choose an unknown and label it clearly (for example, x = Lea’s age in years).
3. Translate each piece of information from the problem into an algebraic expression.
4. Link these expressions with an equals sign to form the equation.

Step-by-step example

Problem: “Sarah is 3 years older than her brother. The sum of their ages is 27 years. How old is her brother?”

Step 1: We understand that there are two ages related to one another.

Step 2: We choose the simplest unknown. Here, we let x = the brother’s age.

Step 3: Sarah’s age is then expressed as x + 3 (3 years older).

Step 4: The sum of the two ages is 27, so:

x + (x + 3) = 27

Which simplifies to 2x + 3 = 27.

Choosing the right unknown

You should always choose the simplest quantity as the unknown – the one in terms of which the others can be easily expressed. Here, expressing Sarah’s age in terms of her brother’s is simpler than the other way round.

A common pitfall to avoid

Never mix two different unknowns (x and y) if the question asks for just one thing: this unnecessarily complicates the solution at secondary school level. Also check that your equation accurately reflects ALL the information in the text, not just part of it. Finally, always specify the unit of your unknown (years, euros, cm, etc.) so you don’t get lost along the way.