Algebraic Word Problem Modelling

Key idea

Build equations from real situations.

In depth

Modelling turns a story into algebra: name unknowns, translate each fact into an equation or inequality, solve, then interpret the answer with units and sanity checks.

Worked example

Two numbers sum to 20 and differ by 4: x + y = 20, x − y = 4 → x = 12, y = 8.

Real-world uses

• Turning a real situation such as a gym membership deal into an equation and choosing the best option

Common mistake

Not defining what each variable stands for before writing equations.

How to learn this

1. Read the key idea and say it in your own words.
2. Work through the worked example, then try a similar problem.
3. Use the interactive lesson’s visual and mini-quiz to check the pattern.

Frequently asked questions

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Related intermediate topics in Algebra

• Multi-Step Equations – Distribute, combine like terms, move variables to one side.
• Variables on Both Sides – Collect variable terms on one side first.
• Literal Equations – Rearrange formulas to solve for a chosen variable.
• Identity and No-Solution Equations – Some equations are always true or never true.
• Linear Inequalities – Solve like equations but reverse the sign when multiplying by a negative.
• Compound Inequalities – Combine two inequalities using “and” or “or”.