Word Problems Examples in Math

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Word Problems.

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

Concept Recap

Word problems require translating a real-world scenario described in natural language into mathematical relationships, identifying the unknown quantity, setting up equations or expressions, and solving them to answer the question.

You are decoding a story into variables, equations, and constraints.

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: Model first, compute second: translate the words into a math structure, then apply operations to find the answer.

Common stuck point: Students start calculating before defining variables and relationships.

Sense of Study hint: Underline all quantities and keywords in the problem. Name the unknown with a variable (let x = ...). Then write one equation per relationship you find. Finally, solve the equation and check your answer back in the original words.

Worked Examples

Example 1

easy
Maria had 45 stickers. She gave 12 to her friend and then bought 20 more. How many stickers does she have now?

Solution

  1. 1
    Start with the initial amount: Maria has 45 stickers.
  2. 2
    After giving away 12, subtract: 45 - 12 = 33.
  3. 3
    After buying 20 more, add: 33 + 20 = 53.

Answer

53 \text{ stickers}
Translate each action in the story into a mathematical operation: 'gave away' means subtract, 'bought more' means add. Perform operations in chronological order.

Example 2

medium
A rectangular garden has a perimeter of 56 metres. If the length is 3 metres more than twice the width, find the dimensions.

Practice Problems

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

Example 1

easy
A baker makes 8 trays of muffins with 12 muffins per tray. He sells all but 15. How many muffins were sold?

Example 2

hard
Two trains leave the same station at the same time, travelling in opposite directions. One train travels at 65 km/h and the other at 85 km/h. After how many hours will they be 450 km apart?
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Background Knowledge

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

algebraic representationmodeling with equationsproportional reasoning