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How to solve a word problem: 5 steps that work

A five-step method for solving word problems, the key words that turn into maths, and worked examples — ages, consecutive numbers, discounts and tickets.

2 min readUpdated 2 November 2026By Sumzo team (AI-assisted)Reviewed by Sumzo AI (owner-delegated review)

A word problem describes a situation in words and asks you to find a number. The maths is usually simple once it is written down — the skill is turning the words into an equation. This method works for almost every word problem you will meet in school.

Solving word problems in 5 steps

  1. Read the whole problem and underline the question: what exactly must you find?
  2. Name the unknown with a letter, e.g. “let xx be Ana’s marbles”.
  3. Write an equation that says the same thing as the words.
  4. Solve the equation.
  5. Check the answer in the original words, not just in your equation — and include units.

Key words and what they mean

  • sum, total, more than, increased by → ++
  • difference, less than, decreased by → −- (careful: “5 less than xx” is x−5x - 5)
  • product, times, of, twice → ×\times
  • quotient, per, shared equally → ÷\div
  • is, equals, gives, will be → ==

Worked example

Easy: “three times as many”

Sam has three times as many marbles as Ana. Together they have 48. How many marbles does Ana have?

Show the working
  1. Let xx be Ana’s marbles, so Sam has 3x3x.
  2. Together they have 48.
    x+3x=48x + 3x = 48
  3. Solve.
    4x=48⇒x=124x = 48 \Rightarrow x = 12
  4. Check in the words: Sam has 36, and 12+36=4812 + 36 = 48 ✓.

Answer: Ana has 12 marbles.

Checked by Sumzo’s math engine

Worked example

Medium: consecutive integers

The sum of three consecutive integers is 72. Find them.

Show the working
  1. Let the smallest be nn; the others are n+1n + 1 and n+2n + 2.
  2. Write the equation.
    n+(n+1)+(n+2)=72n + (n + 1) + (n + 2) = 72
  3. Solve.
    3n+3=72⇒3n=69⇒n=233n + 3 = 72 \Rightarrow 3n = 69 \Rightarrow n = 23
  4. Check: 23+24+25=7223 + 24 + 25 = 72 ✓.

Answer: 23, 24 and 25.

Checked by Sumzo’s math engine

Worked example

Medium: a discount, worked backwards

A jacket costs $68 after a 15% discount. What was the original price?

Show the working
  1. After 15% off you pay 85% of the original price pp.
    0.85p=680.85p = 68
  2. Divide by 0.85.
    p=680.85=80p = \frac{68}{0.85} = 80
  3. Check: 15% of $80 is $12, and 80−12=6880 - 12 = 68 ✓.

Answer: The original price was $80.

Checked by Sumzo’s math engine

Worked example

Hard: two unknowns

Adult tickets cost $12 and child tickets $8. A school sold 30 tickets for $300. How many adult tickets were sold?

Show the working
  1. Let aa be adult tickets and cc child tickets.
    a+c=30,12a+8c=300a + c = 30, \quad 12a + 8c = 300
  2. Substitute c=30−ac = 30 - a into the second equation.
    12a+8(30−a)=300⇒4a+240=30012a + 8(30 - a) = 300 \Rightarrow 4a + 240 = 300
  3. Solve.
    4a=60⇒a=15,  c=154a = 60 \Rightarrow a = 15, \; c = 15
  4. Check: 15×12+15×8=180+120=30015 \times 12 + 15 \times 8 = 180 + 120 = 300 ✓.

Answer: 15 adult tickets (and 15 child tickets).

Checked by Sumzo’s math engine

Common mistakes

  • Answering a different question: the problem asks for Ana’s marbles, not Sam’s.
  • Translating “less than” backwards: “5 less than xx” is x−5x - 5, not 5−x5 - x.
  • Mixing units, such as minutes and hours, in one equation.
  • Skipping the check — a negative number of tickets means something went wrong.

Frequently asked questions

What is a word problem in math?

A maths question written as a short story or real-life situation instead of an equation. You turn the words into an equation, solve it, and answer in words.

What is the first step in solving word problems?

Find the question — what you must work out — and give that unknown a letter. Everything else in the problem is information to build the equation.

Can Sumzo solve a word problem for me?

Yes. Type or photograph it in the Sumzo word problem solver: it writes the equation, solves it and explains each step, so you can learn the method too.

Calculators

Practice

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