How to Solve Word Problems

Word problems feel hard because you must do two jobs at once: translate and calculate. Separate them with a five-step method and each job becomes manageable.

The five steps

  1. Read the whole problem and note what is asked.
  2. Define the unknown with a letter and units, such as “let w be the width in metres”.
  3. Build an equation from the relationship in the story.
  4. Solve the equation.
  5. Check the answer in the story, not just the equation.

Translating phrases into math

Words Math
sum, total, more than +
difference, less than −
of, times, product ×
per, quotient, shared equally ÷
is, was, gives, equals =

Watch for reversed order: “5 less than x” is x − 5, not 5 − x.

Draw and label

A quick sketch of a rectangle, number line or timeline often reveals the equation. Once the setup is written, solve it with the linear equation solver, or try the word problem solver to see a full worked solution. If you have two unknowns, move on to systems of equations.

Worked examples

Example 1: The sum of two consecutive numbers is 47. Find them.

  1. Let the first number be n, so the next is n + 1.
  2. Equation: n + (n + 1) = 47, so 2n + 1 = 47.
  3. Solve: 2n = 46, so n = 23. The numbers are 23 and 24.
  4. Check: 23 + 24 = 47 ✓

Final answer: 23 and 24

Example 2: A rectangle’s length is 3 m more than its width. Its perimeter is 54 m. Find the sides.

  1. Let the width be w, so the length is w + 3.
  2. Perimeter: 2(w + w + 3) = 54, so 4w + 6 = 54.
  3. Solve: 4w = 48, so w = 12 and the length is 15.
  4. Check: 2(12 + 15) = 54 ✓

Final answer: Width 12 m, length 15 m

Example 3: Ali is twice as old as Sara. In 5 years their ages add to 40. How old are they now?

  1. Let Sara’s age be s, so Ali’s is 2s.
  2. In 5 years: (2s + 5) + (s + 5) = 40, so 3s + 10 = 40.
  3. Solve: 3s = 30, so s = 10 and Ali is 20.

Final answer: Sara 10, Ali 20

Example 4: Two cars start 280 km apart and drive towards each other at 60 km/h and 80 km/h. When do they meet?

  1. Their gap closes at 60 + 80 = 140 km/h.
  2. Time = 280 ÷ 140 = 2.

Final answer: 2 hours

Common mistakes to avoid

  • Jumping straight to numbers without defining the unknown.
  • Choosing the wrong order for “less than”.
  • Forgetting to give units in the answer.
  • Solving for x but answering a different question.
  • Skipping the check against the story.

Frequently asked questions

How do I start a word problem?

Read it fully, then write down what you know and what you must find.

What if there are two unknowns?

Write two equations and solve them together, using substitution or elimination.

How can I get faster at word problems?

Practise by type: numbers, ages, money, speed, geometry. Patterns repeat.

Can an AI solver help me learn word problems?

Yes, if you try first and use the solver to compare your setup and equation.

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AI-generated solutions are for learning purposes. Always verify important answers.