Word Problems in WASSCE Mathematics: Questions and Answers, Step by Step

📚 Part of the Algebra Clinic: every lesson on this topic, in one place.

In many Ghanaian classrooms, you can hear this statement almost every term:

That statement tells us something important. The learner is not always blank. Sometimes, the formula is in the head, but the question has not entered the mind properly.

This is why many students struggle with word problems in WASSCE Maths. They do not fail because they cannot press calculator buttons. They fail because they cannot translate the English sentence into mathematics.

At The Maths Clinic, we treat word problems like a reading-and-reasoning issue before we treat them as a calculation issue. A learner must first understand what is happening in the question before choosing any formula.

This post will help you learn seven practical ways to read, understand, and solve word problems in WASSCE Mathematics without panic.

Why are word problems hard in WASSCE Mathematics?

The main learner’s problem is this:

This is where the marks begin to leak. In WASSCE Maths, word problems are not only testing formulas. They are also testing reading, interpretation, translation, reasoning, and clear presentation.

A learner may know the formula for simple interest:

I = \dfrac{P \times R \times T}{100}

But when the question says, “Ama invested GH₵2,400 at 8% per annum for 3 years,” the learner must know that

• GH₵2,400 is the principal, P.
• 8% is the rate, R.
• 3 years is the time, T.
• “Per annum” means per year.
• The question may ask for interest only or the total amount. These are not the same.

So the real challenge is not only the formula. The real challenge is knowing what each part of the sentence means mathematically.

Why students get word problems wrong: 5 hidden gaps

The mistake usually happens because the learner has one or more hidden gaps. These gaps are small, but they can destroy a whole solution.

Hidden Gap 1: Poor Question Reading

Some learners read the first line and stop thinking. They do not read the full question. In WASSCE, one word can change the whole method. Words like “total,” “difference,” “remaining,” “per annum,” “at least,” “more than,” “less than,” and “nearest whole number” must not be ignored.

Hidden Gap 2: Weak Translation from English to Mathematics

A word problem is like a story. The learner must convert the story into mathematical statements. If the learner cannot translate the words, the formula alone will not save the answer.

Hidden Gap 3: Picking Numbers Without Understanding Their Roles

Many students see numbers and start using them anyhow. But every number in a word problem has a job. One number may be the cost price, another may be the selling price, and another may be the profit. If the roles are mixed up, the answer will also be wrong.

Hidden Gap 4: Memorising Formulas Without Meaning

A learner may memorise ten formulas and still fail if he or she does not know when each formula should be used. WAEC questions often test whether the learner understands the condition behind the formula.

Hidden Gap 5: Fear When the Question Looks Unfamiliar

Some learners panic immediately when a question looks longer than usual. Once fear enters, they stop thinking carefully. They guess the method, copy numbers wrongly, or leave the question blank.

What WAEC Chief Examiners say about word problems

WAEC-style Mathematics questions often require more than direct substitution. A learner must read carefully, identify the known values, decide what is being asked, and present the solution in a clear order.

The curriculum direction also supports problem-solving, application, reasoning, and communication. This means students must not only know how to calculate; they must be able to explain mathematical ideas through real-life situations.

Word problems appear in many Mathematics areas, including:

• Percentages, profit, loss, and discount
• Simple interest and compound interest
• Ratio and proportion
• Linear equations and simultaneous equations
• Mensuration and geometry
• Statistics and probability
• Variation
• Rates, speed, distance, and time
• Bearings and scale drawing

This means word problems are not a small topic. They are a skill that runs through many WASSCE Mathematics topics.

What a word problem is really asking you to do

A word problem is a mathematical question written in normal language. Your work is to change the normal language into mathematical language.

Think of it this way:

Before solving any word problem, ask three simple questions:

1. What is happening in the question?
2. What values have I been given?
3. What exactly am I being asked to find?

If you cannot answer these three questions, do not start calculating yet. You may be walking into a WAEC trap.

How to solve word problems in Mathematics: 7 steps

Way 1: Read the Question Twice Before Touching the Calculator

The first reading gives you the story. The second reading gives you the mathematics. Many learners lose marks because they start calculating after reading only half of the question.

Classroom fix: After the first reading, ask: “What is the question talking about?” After the second reading, underline the important values and instruction words.

Way 2: Circle the Values and Write Their Meaning

Do not just copy numbers. Write what each number represents. A number without meaning can mislead you.

Classroom fix: For example, in profit and loss, GH₵80 may be the cost price while GH₵100 may be the selling price. If you confuse them, the percentage profit will be wrong.

Way 3: Identify the Topic Hidden Inside the Story

A word problem may not mention the topic directly. It may not say “use percentages” or “use simultaneous equations.” You must detect the topic from the situation.

Classroom fix: If two unknown items are being compared, it may lead to simultaneous equations. If money grows with time at a rate, it may be simple interest or compound interest.

Way 4: Write Down What the Question Is Asking For

Many learners solve for the wrong thing. The question may ask for profit, but the learner finds the selling price. It may ask for the total amount, but the learner finds interest only in it.

Classroom fix: Before calculation, write: Required = ________. This small habit keeps your mind focused.

Way 5: Change Key Words into Mathematical Operations

Word problems use language. You must know how to translate common words into operations.

Classroom fix: Words like “total” may suggest addition. “Difference” may suggest subtraction. “Of” in percentage problems may suggest multiplication. “Shared equally” may suggest division.

Way 6: Draw a Small Table, Diagram, or List

Some word problems become easier when you organise the information. A table is helpful for age problems, mixture problems, simple interest problems, and comparison questions.

Classroom fix: Do not be ashamed to draw. In mathematics, a simple diagram can rescue a confused mind.

Way 7: Check Whether Your Answer Makes Sense

After solving, compare your answer to the story. If a discount is bigger than the original price, something is wrong. If a time answer is negative in a normal real-life question, something is wrong.

Classroom fix: A sensible check can help you catch errors before you lose marks.

Worked example: a WASSCE-style word problem solved step by step

Example: Turning a Story into Mathematics

A trader bought 15 exercise books at GH₵8 each. He sold all the books for GH₵150. Find his percentage profit.

Step 1: Read and Identify the Story

The question is about buying and selling exercise books. So this is a profit and percentage profit problem.

Step 2: Write the Given Values with Their Meaning

• \text{Number of exercise books} = 15
• \text{Cost of one exercise book} = \text{GH₵}8
• \text{Total selling price} = \text{GH₵}150

Step 3: Find the Total Cost Price

Total Cost Price = Number of books × Cost of one book

\text{Total Cost Price} = 15 \times 8

\text{Total Cost Price} = \text{GH₵}120

Step 4: Find the Profit

Profit = Selling Price – Cost Price

\text{Profit} = 150 - 120

\text{Profit} = \text{GH₵}30

Step 5: Find the Percentage Profit

Percentage Profit = (Profit / Cost Price) × 100%

\text{Percentage Profit} = (\dfrac{30}{120}) \times 100\%

\text{Percentage Profit} = 25\%

Final Answer:

\text{Percentage Profit} = 25\%

The common wrong approach, and why it loses marks

A common wrong approach is to use GH₵150 as the cost price because it is the bigger amount in the question.

\text{Wrong Percentage Profit} = (\dfrac{30}{150}) \times 100\% = 20\%

This is wrong because the percentage profit must be based on the cost price, not the selling price.

Another wrong approach is to ignore the 15 books and treat GH₵8 as the total cost price. That also gives a wrong solution because GH₵8 is the cost of only one book, not the total cost of all the books.

The correct method in one routine

The correct method is to slow down and translate the question before calculating.

Correct Word Problem Method

• Read the question twice.
• Identify the topic hidden in the story.
• List the given values with their meanings.
• Write what the question is asking for.
• Choose the correct formula or operation.
• Substitute the values carefully.
• Check whether the answer makes sense.

For the worked example, the important translation is this:

Word problems practice questions

Every question below needs you to form an equation, which is the skill WAEC reports most often as missing. For each one: write “let x = …” in words, turn each fact into maths, solve, then check your answer in the story.

Question 1: Two numbers

The sum of two numbers is 45. One number is 9 more than the other. Find the two numbers.

Question 2: Ages

Kofi is 4 times as old as his sister Esi. In 6 years’ time, Kofi will be twice as old as Esi. Find their present ages.

Question 3: Money

Ama paid GH₵84 for 3 notebooks and 4 pens. A notebook costs GH₵7 more than a pen. Find the cost of one pen and one notebook.

Question 4: Speed

A trotro travels from a town to a village at 60 km/h and returns along the same road at 40 km/h. The whole journey takes 5 hours. How far is the village from the town?

Question 5: Reverse percentage

A trader sold a radio for GH₵690 and made a profit of 15%. Find the cost price of the radio.

Question 6: Two-digit number

The units digit of a two-digit number is 1 less than the tens digit. If the number is increased by 8 and then divided by the sum of its digits, the result is 8. Find the number. (Based on WASSCE 2021 Core, Question 8(b).)

Question 7: Two unknowns

At a canteen, 2 plates of rice and 3 bottles of water cost GH₵54. 3 plates of rice and 1 bottle of water cost GH₵60. Find the cost of one plate of rice and one bottle of water.

Question 8: Missing value in a mean

The numbers (x − 2), 4, (x + 2), (2x + 1) and 9 are arranged in order of size. If the median is equal to the mean, find the value of x. (Based on WASSCE 2021 Core, Question 10(b).)

Word problems questions and answers: full solutions

Solution 1

Let the smaller number be x. The bigger number is x + 9.
Equation: x + (x + 9) = 45
2x + 9 = 45, so 2x = 36 and x = 18.
Answer: 18 and 27.
Check: 18 + 27 = 45, and 27 is 9 more than 18.

Solution 2

Let Esi’s age now be x years. Kofi’s age now is 4x.
In 6 years: Esi is x + 6, Kofi is 4x + 6.
Equation: 4x + 6 = 2(x + 6)
4x + 6 = 2x + 12, so 2x = 6 and x = 3.
Answer: Esi is 3 years old and Kofi is 12.
Check: in 6 years they are 9 and 18, and 18 = 2 × 9.
Trap: adding 6 to Esi’s age but forgetting to add 6 to Kofi’s. Both people get older.

Solution 3

Let the cost of one pen be GH₵x. One notebook costs GH₵(x + 7).
Equation: 3(x + 7) + 4x = 84
3x + 21 + 4x = 84, so 7x = 63 and x = 9.
Answer: a pen costs GH₵9 and a notebook costs GH₵16.
Check: 3 × 16 + 4 × 9 = 48 + 36 = 84.

Solution 4

Let the distance be d km. Time = distance ÷ speed.
Time going: \dfrac{d}{60} hours. Time returning: \dfrac{d}{40} hours.
Equation: \dfrac{d}{60} + \dfrac{d}{40} = 5
Multiply every term by the LCM, 120: 2d + 3d = 600
5d = 600, so d = 120.
Answer: 120 km.
Check: 120 ÷ 60 = 2 hours, 120 ÷ 40 = 3 hours, total 5 hours.
Trap: using the “average speed” of 50 km/h. The trotro spends longer at the slower speed, so that is wrong.

Solution 5

Let the cost price be GH₵x. A 15% profit means the selling price is 115% of x.
Equation: \dfrac{115}{100} \times x = 690
x = 690 \times \dfrac{100}{115} = 600
Answer: GH₵600.
Check: 15% of 600 is 90, and 600 + 90 = 690.
Trap: taking 15% of GH₵690. The percentage is of the cost price, which we do not know yet.

Solution 6

Let the units digit be x. The tens digit is x + 1.
The number is 10(x + 1) + x = 11x + 10. The sum of the digits is 2x + 1.
Equation: \dfrac{11x + 10 + 8}{2x + 1} = 8
11x + 18 = 16x + 8, so 5x = 10 and x = 2.
Answer: 32.
Check: 32 + 8 = 40, the digits add to 5, and 40 ÷ 5 = 8.
Trap: writing the number as x + (x + 1). A two-digit number is 10 × tens digit + units digit. WAEC reported that most candidates “could not apply the place value concept” here.

Solution 7

Let one plate of rice cost GH₵r and one bottle of water cost GH₵w.
(1) 2r + 3w = 54
(2) 3r + w = 60
From (2): w = 60 – 3r. Substitute into (1):
2r + 3(60 – 3r) = 54
2r + 180 – 9r = 54, so -7r = -126 and r = 18.
Then w = 60 – 3(18) = 6.
Answer: rice costs GH₵18 a plate; water costs GH₵6 a bottle.
Check: 2(18) + 3(6) = 54, and 3(18) + 6 = 60.

Solution 8

The numbers are in order, so the median is the middle one: x + 2.
Sum = (x – 2) + 4 + (x + 2) + (2x + 1) + 9 = 4x + 14
Mean = \dfrac{4x + 14}{5}
Equation: \dfrac{4x + 14}{5} = x + 2
4x + 14 = 5x + 10, so x = 4.
Answer: x = 4.
Check: the numbers are 2, 4, 6, 9, 9. Median = 6, mean = 30 ÷ 5 = 6.

Common WAEC Word Problem Traps to Watch

• Using all the numbers in the question, even when one number is not needed.
• Finding the interest when the question asks for the total amount.
• Finding the discount but forgetting to subtract it from the marked price.
• Using the selling price as the denominator for percentage profit.
• Ignoring units such as cm, m, km, hours, minutes, years, and Ghana cedis.
• Writing the final answer without checking whether it matches the question.
• Leaving the answer in an unfinished form when the question needs a final value.

Word problems: frequently asked questions

Why do students fail word problems even when they know the formula?

Because knowing a formula is not the same as understanding the question. Many students fail because they cannot identify the values, translate the English sentence into mathematics, or decide what the question is asking for.

How can I improve in WASSCE word problems?

Start by reading the question twice, listing the given values with their meanings, identifying the topic, and writing what you are required to find before solving.

Are word problems a separate topic in Mathematics?

Not exactly. Word problems appear in many topics such as percentages, algebra, financial maths, mensuration, speed, ratio, probability, and statistics.

Should I memorise keywords for word problems?

Keywords can help, but do not depend on them alone. Always understand the full sentence because some words can change meaning depending on the question.

What should I do when I do not understand a word problem?

Break it into smaller parts. Write the known values, draw a simple diagram or table, and ask what the question wants you to find. Then choose the method.

Conclusion: Do Not Fight the Formula Before You Understand the Story

In WASSCE Maths, word problems are not meant to punish students. They are meant to test whether the learner can connect mathematics to real situations.

So when you see a word problem, do not rush. Read the story. Identify the topic. Give each number a meaning. Write what you are looking for. Then solve step by step.

The learner who understands the question has already solved half of the problem. The calculation only completes the work.

At The Maths Clinic, we believe many students can improve in Mathematics when the hidden gap is properly diagnosed and corrected. Word problems become easier when you stop guessing and start understanding.

Written by Dickson Sarpong

NTC-certified SHS Mathematics teacher in Ghana with WAEC marking experience, and author of The Bridge Series textbooks. Every lesson here is built around the mistakes WAEC examiners keep reporting.

About DicksonStuck? Ask a question

Want the whole topic, step by step? My textbooks, The Bridge to Mathematics and The Bridge to Additional Mathematics for SHS, follow the new curriculum and rebuild the basics as you go.

Read a free chapter →