How to Solve Maths Word Problems (Grade 12, Step by Step)

Steps

1. Read the question twice. First read for context, second read with a pen — underline numbers, units, and what you're asked to find.
2. Define your variables. Write 'Let x = …' for every unknown. Vague variables cause vague answers.
3. Translate each sentence into maths. Every English sentence becomes one equation or inequality. 'is' → =, 'more than' → +, 'product of' → ×, 'per' → /.
4. Solve the system. Use the simplest technique that works — substitution, factorising, or the quadratic formula.
5. Check the answer in the original wording. Reject negative ages, fractional people, or speeds above light. If the answer doesn't fit the story, you set up the wrong equation.

Worked example

The sum of two consecutive positive integers is 75 more than twice the smaller one. Find the integers.

1. Let x = the smaller integer, so the larger is x + 1.
2. Translate: x + (x + 1) = 2x + 75.
3. Simplify: 2x + 1 = 2x + 75 ⇒ 1 = 75, which is false — so re-read.
4. Correct reading: 'sum is 75 more than twice the smaller' ⇒ x + (x + 1) = 2x + 75 is wrong; it should be x + (x + 1) − 2x = 75 ⇒ 1 = 75. Still false, so the problem as stated has no solution — flag this in the exam and move on, or fix the wording.
5. Lesson: step 5 (check) is what saves you. If your equation collapses to a contradiction, your translation is off — re-underline the keywords.

Common mistakes

• Jumping to algebra without defining x.
• Translating 'more than' as − instead of +.
• Forgetting units (rands, km/h, hours).
• Accepting negative or non-integer answers when the context requires positive integers.

Exam tips

• Spend the first 60 seconds reading, not writing.
• Box your final answer with units.
• If you get stuck, snap the question into Snap&Learn for a step-by-step explanation that uses this exact 5-step method.
• Write a 'let' statement that defines the variable and its unit before you set up the equation.

Frequently asked questions

What is the best strategy for Matric maths word problems?

Use the 5-step method: read twice, define variables, translate sentence-by-sentence, solve, then sanity-check against the original wording.

Are word problems on Paper 1 or Paper 2?

Both — they're most common in algebra, finance and probability (Paper 1) and in trig 2D/3D and statistics (Paper 2).

How do I turn words into an equation?

Let a letter stand for the unknown, then translate phrase by phrase: 'more than' becomes +, 'of' usually becomes ×, and 'is' becomes =. For example, 'five more than twice a number is 17' becomes 2x + 5 = 17, so x = 6.