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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 phút đọcCập nhật 2 tháng 11, 2026Bởi Sumzo teamDuyệt bởi Sumzo team

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 → ==

Ví dụ giải mẫu

Easy: “three times as many”

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

Xem lời giải
  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 ✓.

Đáp án: Ana has 12 marbles.

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Ví dụ giải mẫu

Medium: consecutive integers

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

Xem lời giải
  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 ✓.

Đáp án: 23, 24 and 25.

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Ví dụ giải mẫu

Medium: a discount, worked backwards

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

Xem lời giải
  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 ✓.

Đáp án: The original price was $80.

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Ví dụ giải mẫu

Hard: two unknowns

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

Xem lời giải
  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 ✓.

Đáp án: 15 adult tickets (and 15 child tickets).

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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.

Câu hỏi thường gặp

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.

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