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Word problems with equations

This page was translated from German with AI. It has not been checked by a native speaker. Original page in German

A brother is 3 years older than his sister. Together they are 25 years old. How old is the sister? You learn how to turn a text into an equation.
📄 Open worksheet (PDF, German)

The video

In the video we always solve word problems in four steps.

Subtitles are available in ten languages. Choose them at the bottom right of the video.

Contents of the video

  1. 0:00 Introduction
  2. 0:21 Four steps
  3. 1:20 A number puzzle
  4. 1:52 Careful, mistake!
  5. 2:20 Try it yourself

The most important points

Four steps

1. Choose \(x\): what are we looking for? 2. Set up the equation. 3. Solve the equation. 4. Check and answer sentence (der Antwortsatz).

x + (x + 3) = 25, so x = 11. The sister is 11, the brother 14.
\(x + (x + 3) = 25\), so \(x = 11\). The sister is 11, the brother 14.
Number puzzle: 4x + 6 = 30, so x = 6.
Number puzzle: \(4x + 6 = 30\), so \(x = 6\).

Read the text carefully. “Together” means: sister plus brother. \(x + 3 = 25\) is wrong.

The sister is missing in the equation.
The sister is missing in the equation.

The worksheet

Here you can see the worksheet for the video (in German). First it explains everything again, then there are practice tasks at three levels. You can also open it as a PDF and print it.

📄 Open worksheet (PDF, German)

The worksheet – Page 1
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The worksheet – Page 2
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The worksheet – Page 3
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Show the worksheet solutions
The worksheet – Page 4
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Try it yourself

Task

Three numbers come directly one after another (like 4, 5, 6). Together they make 24. Which numbers are they?

Show solution

\(x + (x + 1) + (x + 2) = 24\), \(3x + 3 = 24\), \(x = 7\). The numbers are 7, 8 and 9.

Keep learning with a language model

Du bist meine Mathe-Lehrkraft. Ich lerne Deutsch als Zweitsprache. Unser Thema: Textaufgaben mit Gleichungen (x festlegen, Gleichung aufstellen, lösen, Probe, Antwortsatz). Stelle mir nacheinander fünf kurze Aufgaben. Warte immer auf meine Antwort. Sag mir dann, ob sie richtig ist, und erkläre kurz, warum. Benutze einfache deutsche Sätze.

How this was made: The idea, structure and examples of the series are mine. I made them with the help of AI: a language model (LLM) built the slides of the video following my instructions. The voice was generated with Qwen3-TTS, modelled on my own voice.

The subtitles, the translations, the worksheet and this page were also made with the help of AI. The translations have not been checked by native speakers.

The videos, worksheets, texts and prompts in this series are licensed under CC BY 4.0: you may use, change and share them if you name the source.