Understand the question
Read the problem twice. The first time, read for the story. The second time, underline every number and every phrase that describes a relationship, such as “three times as many” or “decreased by”.
Then answer one question in writing: what exactly am I being asked to find?
Define your variables
Assign a letter to each unknown quantity and write down what it represents, including the unit. For example: let t be the time in hours. Clear definitions prevent most errors later in the solution.
Translate into equations
Convert each relationship in the text into mathematics, one sentence at a time.
- “is”, “equals” or “results in” usually means =
- “more than” or “increased by” usually means +
- “of” with fractions or percentages usually means multiply
- “per” usually indicates a rate or a division
Solve and check
Solve the equations, then substitute your answer back into the original wording, not only into your equation. Ask whether the result is realistic. A negative number of people or a car travelling at 900 km/h is a sign that something went wrong in the translation step.
Finish by writing a full sentence answer with the correct unit.