Translate a story into an equation
“I am thinking of a number. When I double it and add five, I get nineteen.” This is not a riddle — it is an equation in disguise: 2x + 5 = 19.
Word problems scare half the class. Yet they have a solid method that always works:
1. Mark. What is being looked for? That is x. Write a sentence: “x = number of pieces” or “x = price of a ticket”.
2. Translate. Go through the text sentence by sentence and write the relationships mathematically. “5 more” = +5. “Twice as many” = 2x. “Altogether” = add.
3. Build the equality. Find in the text what equals what — that is where the equals sign belongs.
4. Solve the equation, you already can.
5. Answer in a full sentence and check against the text, not only against the equation.
You can solve an equation. Today’s lesson trains translation — and that is the whole secret of word problems.
Adam and Jonáš are brothers. “Altogether we have 420 Kč,” says Adam, “and I have twice as much as you.” Jonáš calculates by guessing for a while: 100 and 200? That is 300, too little. 150 and 300? 450, too much… Ema is listening and writes: x = Jonáš’s money, Adam has 2x, altogether x + 2x = 420. “Three x is 420, so x = 140. Jonáš has 140, Adam 280.” Check: 140 + 280 = 420 and 280 is twice 140. Both conditions fit. Guessing lost by three rounds.
Mark as x the smaller or basic thing — the one the others are built from. “Adam has twice as much as Jonáš”: give x to Jonáš, Adam is then 2x. The other way you would struggle with fractions.
A translation dictionary and the method
English–maths dictionary:
- “7 more” → +7, “7 less” → −7
- “twice as many”, “double” → 2x
- “half” → x/2, “a third” → x/3
- “altogether”, “in total” → add
- “is”, “will be”, “costs”, “measures” → equals sign
Method on an example: An adult ticket costs 80 Kč more than a child ticket. Two adults and three children paid 560 Kč. How much does a child ticket cost?
- Mark: x = price of a child ticket. An adult is then x + 80.
- Translate: two adults = 2(x + 80), three children = 3x.
- Equality: 2(x + 80) + 3x = 560.
- Solve: 2x + 160 + 3x = 560 → 5x = 400 → x = 80.
- Answer: A child ticket costs 80 Kč. Check against the text: adult 160, two adults 320, three children 240, total 560. It fits.
A check against the TEXT is more important than an equation check — it also catches a wrong translation that the equation itself would not notice.
Example 1: a thought-of number
I am thinking of a number. When I multiply it by three and subtract four, I get 17. What number am I thinking of?
I mark: x = the thought-of number.
I translate: “multiply by three” → 3x, “subtract four” → 3x − 4, “I get” → equals sign.
Equation: 3x − 4 = 17.
I solve: 3x = 21 → x = 7.
Answer: The thought-of number is 7. Check with the text: 3 · 7 − 4 = 17. It fits.
Example 2: age in a few years
Tereza is 13, mum is 41. In how many years will mum be exactly twice as old as Tereza?
I mark: x = the number of years that will pass.
In x years: Tereza 13 + x, mum 41 + x. “Twice as old” → mum = 2 · Tereza:
41 + x = 2(13 + x).
I solve: 41 + x = 26 + 2x → 41 − 26 = 2x − x → x = 15.
Answer: In 15 years. Check: Tereza will be 28, mum 56 — and 56 is twice 28. It fits.
Example 3: sharing money
Three friends shared 720 Kč from a part-time job. Filip got 60 Kč more than Ema and Sofie twice as much as Ema. How much did Ema get?
I mark: x = Ema’s share. Filip = x + 60, Sofie = 2x.
Altogether: x + (x + 60) + 2x = 720.
I collect: 4x + 60 = 720 → 4x = 660 → x = 165.
Answer: Ema got 165 Kč. Check: Filip 225, Sofie 330; sum 165 + 225 + 330 = 720. It fits.
Do not forget to write what x is. A task “I got 15” without the sentence “x = number of years” is a half answer — on a test it often gets half marks. And write the answer in a full sentence with the unit: “A child ticket costs 80 Kč.”
Practice: now you do it 🎲
Now try it for real. You will see all the questions at once, like on paper. Bắt đầu with ten. When it goes well, add more.
Solve the equation and write only x. Picture with each one what story could be hiding behind it.
On paper
Five steps with every problem: mark, translate, build, solve, answer in a sentence.
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I am thinking of a number. When I double it and add 9, I get 31. Build the equation and solve.
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A book and a notebook together cost 260 Kč. The book is 180 Kč more expensive than the notebook. How much does the notebook cost?
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Jonáš has three times as many cards as Filip. Altogether they have 96. How many does each have?
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Invent your own word problem that leads to the equation 2x + 50 = 250, and solve it.
Now you 💪
- I always start with the sentence “x = …”.
- I can translate “more”, “twice as many” and “altogether” into maths.
- I check the result against the text of the problem, not only against the equation.
Done when: You have four translated and solved problems with answers in a full sentence and a run of five correct in practice.
What to take from this lesson
- A word problem = translation: mark x, translate the sentences, build the equality.
- “5 more” = +5, “twice as many” = 2x, “is/costs/measures” = equals sign.
- Give x to the basic thing the others are built from.
- Check against the text — it also catches a wrong translation.
- Write the answer in a full sentence with the unit.
© 2026 Ing. Martin Polak / AlgoRhino · Điều khoản sử dụng nội dung