Writing Equations from Context Examples in Math

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Writing Equations from Context.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Math.

Concept Recap

Translating real-world situations and word problems into algebraic equations by identifying the unknown, choosing a variable, and expressing relationships mathematically.

Word problems are stories in disguise. Your job is to find the main character (the unknown—call it x), figure out what's happening to it (the operations), and write down the punchline (the equation). 'Five more than twice a number is 17' becomes 2x + 5 = 17.

Read the full concept explanation →

How to Use These Examples

  • Read the first worked example with the solution open so the structure is clear.
  • Try the practice problems before revealing each solution.
  • Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: Identify what is unknown (assign a variable), identify the relationships and constraints (write expressions), and connect them with an equals sign. Key translations: 'is' means =, 'more than' means +, 'less than' means -, 'of' often means \times.

Common stuck point: Knowing where to start. Always ask: (1) What am I trying to find? That's x. (2) What information do I have? Those become the numbers and operations. (3) What relationship ties them together? That's the equation.

Sense of Study hint: Start by writing 'Let x = [what you are finding]' and then re-read each sentence to build the equation piece by piece.

Worked Examples

Example 1

easy
Write an equation: 'Three times a number decreased by 4 is 17.'

Solution

  1. 1
    Let n = the unknown number.
  2. 2
    'Three times a number' = 3n.
  3. 3
    'Decreased by 4' = 3n - 4.
  4. 4
    'Is 17' = = 17. Equation: 3n - 4 = 17.
  5. 5
    Solve: 3n = 21, n = 7.

Answer

3n - 4 = 17; \quad n = 7
Translating word problems: assign a variable, convert each phrase to math, and connect with an equals sign.

Example 2

medium
A plumber charges \50 for a visit plus \30 per hour. If the bill was \$170, how many hours did the job take?

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

easy
Write an equation: 'Half of a number plus 6 equals 10.'

Example 2

hard
The perimeter of a rectangle is 34 cm. The length is 5 cm more than the width. Find the dimensions.
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Background Knowledge

These ideas may be useful before you work through the harder examples.

equationsvariablesexpressions