Guide · For JSS 1 – SS 3 students · 6 min read
How to solve maths word problems, step by step
A simple six-step routine for any maths word problem, with a table for turning English into maths and three worked Nigerian examples: market prices, sharing in a ratio and ages.
By the MathPlug team, Reflex System · Published
Many students who can solve 4y + 500 = 9,300 in ten seconds freeze when the same question is written as a story about buying yams. The maths has not changed. What has changed is that you now have to decide what the maths is.
That decision is a skill, and like any skill it can be learnt with a routine. This guide gives you a six-step routine that works on almost every word problem, from JSS 1 market questions to WASSCE Paper 2. Then it walks through three Nigerian examples, each a little harder than the last.
Why word problems feel hard
A word problem asks you to do two jobs. First you translate the story into maths. Then you solve the maths. Most students only practise the second job, so the first job feels like a wall.
The other trap is rushing. Students often grab the numbers in the question and start calculating before they know what is being asked. A minute spent understanding the story saves five minutes of wrong working.
The six-step routine
Use these steps every time, even on easy questions, so that they are automatic when a hard one comes:
- Read it twice. The first time, get the story. The second time, pencil in hand, underline the numbers and circle the question.
- List what is given and what is asked. Write "Given:" and "Find:" and fill them in, with units.
- Draw a picture or a table. A quick sketch or a small table often shows the connection between the facts.
- Choose a letter and write an equation. Say clearly what the letter stands for, for example "Let x = the price of one tuber in naira".
- Solve. Work one step per line.
- Check against the story. Put your answer back into the words of the question, not just into your equation. Does it make sense?
💡 Tip: Step 6 is the one most students skip, and it is the one that catches a wrong equation. Our study tip on checking your answer shows quick ways to do it.
Turning words into maths
Certain words appear again and again. Learn what they usually mean:
| Words in the question | Maths | Example |
|---|---|---|
| sum, more than, increased by, total | + | 5 more than x → x + 5 |
| difference, less than, reduced by | − | 5 less than x → x − 5 |
| times, product, of, twice | × | twice x → 2x |
| per, each, shared equally, quotient | ÷ | ₦600 shared by 3 → 600 ÷ 3 |
| is, was, gives, will be | = | x increased by 4 is 10 → x + 4 = 10 |
Watch the order with "less than": "5 less than x" is x − 5, not 5 − x. Our study tip on learning the language of maths covers more of these words.
Example 1: market prices
Ngozi buys 4 tubers of yam, all at the same price, and pays ₦500 for transport home. She spends ₦9,300 altogether. How much does one tuber cost?
- Given: 4 tubers, same price; transport ₦500; total ₦9,300. Find: the price of one tuber.
- Let y = the price of one tuber in naira.
- Cost of yams + transport = total, so 4y + 500 = 9,300
- Subtract 500 from both sides: 4y = 8,800
- Divide both sides by 4: y = 2,200
- Answer: one tuber costs ₦2,200.
- Check against the story: 4 tubers at ₦2,200 cost ₦8,800. Add ₦500 transport: ₦9,300. Correct.
Example 2: sharing in a ratio
Emeka and Bisi share some money in the ratio 3 : 5. Bisi receives ₦6,000 more than Emeka. How much money was shared, and how much does each get?
- Given: ratio 3 : 5; Bisi gets ₦6,000 more. Find: the total, and each share.
- Think in parts. Emeka has 3 parts and Bisi has 5 parts.
- Bisi has 5 − 3 = 2 parts more than Emeka, and that difference is ₦6,000.
- So 2 parts = ₦6,000, which means 1 part = ₦3,000.
- Total = 3 + 5 = 8 parts = 8 × ₦3,000 = ₦24,000
- Emeka gets 3 × ₦3,000 = ₦9,000. Bisi gets 5 × ₦3,000 = ₦15,000.
- Check against the story: ₦15,000 − ₦9,000 = ₦6,000. And 9,000 : 15,000 simplifies (divide by 3,000) to 3 : 5. Correct.
💡 Tip: A common mistake here is to divide ₦6,000 by 8. The ₦6,000 is the difference between the shares, so it matches the difference in parts (2), not the total parts (8). Drawing the parts as boxes makes this clear.
Example 3: ages
Age questions confuse many students because two times are involved: now and later. A table keeps them apart.
| Person | Age now | Age in 5 years |
|---|---|---|
| Daughter (Bisi) | x | x + 5 |
| Father (Musa) | 4x | 4x + 5 |
Musa is 4 times as old as his daughter Bisi. In 5 years' time, he will be 3 times as old as she will be. How old are they now?
- Given: now, Musa = 4 × Bisi; in 5 years, Musa = 3 × Bisi. Find: both ages now.
- Let x = Bisi's age now in years. Then Musa is 4x now (see the table).
- In 5 years: Musa's age = 3 × Bisi's age, so 4x + 5 = 3(x + 5)
- Expand the bracket: 4x + 5 = 3x + 15
- Subtract 3x from both sides: x + 5 = 15
- Subtract 5 from both sides: x = 10
- Answer: Bisi is 10 years old and Musa is 4 × 10 = 40 years old.
- Check against the story: now, 40 = 4 × 10. In 5 years they will be 45 and 15, and 45 = 3 × 15. Correct.
Notice that the 5 years is added to both ages. Adding it to only one person is the most common slip in age questions.
When you are stuck
- Try a guess. Pick a number for the unknown and test it against the story. Even a wrong guess shows you how the facts connect, and that usually reveals the equation.
- Use smaller numbers. Replace ₦9,300 with ₦30 and ask how you would solve the easier version. Then use the same steps with the real numbers.
- Reread the last sentence. It tells you exactly what to find. Many answers are correct maths that answers the wrong question.
- Write units in your answer. "₦2,200" or "10 years", not just "2,200" or "10".
Practise a few word problems every week rather than many at once. Our lesson on word problems with equations is a good place to start.
Questions students ask
- What is the best strategy for solving maths word problems?
- Use the same routine every time: read the question twice, list what is given and what you must find, draw a picture or table, write an equation with a clearly defined letter, solve it, and check the answer against the original story.
- How do I turn a word problem into an equation?
- Choose a letter for the unknown quantity, then translate each phrase into maths: "more than" means add, "less than" means subtract, "of" and "times" mean multiply, "per" means divide, and "is" means equals.
- How do you solve age word problems?
- Make a table with each person's age now and at the other time in the question. Add or subtract the same number of years for every person, then write an equation from the relationship the question gives.
MathPlug is not affiliated with WAEC, NECO or any state examination board. Exam details here come from published syllabuses and exam schemes; always check the instructions on your own question paper and your school's timetable. Spotted something to correct? Tell us.