Linear equation word problems: Class 8 practice
Turn the words into one equation in one unknown, solve it and check the answer makes sense. Read the method, follow the three worked examples, then try the six questions.
What you should know first
- Solving linear equations
The idea behind linear equation word problems
Turn the words into one equation in one unknown, solve it and check the answer makes sense. Age and number problems are common: write today's ages, then ages after or before n years.
Step-by-step method
- Choose the unknown (e.g. x = son's age now).
- Express other quantities in x.
- Write and solve the equation.
- Check against the question.
Worked example 1 (Basic)
One number is 9 more than another, and their sum is 37. Find the numbers.
- x + (x + 9) = 37
- x = 14
- Answer: 14 and 23
Worked example 2 (Standard)
A father is 5 times as old as his son. In 5 years the sum of their ages will be 64. Find their present ages.
- Son x, father 5x
- (x + 5) + (5x + 5) = 64
- 6x = 54 → x = 9
- Answer: Son 9, father 45
Worked example 3 (Challenge)
A father is 3 times as old as his son. In 7 years the sum of their ages will be 42. Find their present ages.
- Son x, father 3x
- (x + 7) + (3x + 7) = 42
- 4x = 28 → x = 7
- Answer: Son 7, father 21
Common mistakes and misconceptions
- Adding years to only one person
- Answering with x when another quantity is asked
Practice questions
- (Basic) One number is 9 more than another, and their sum is 55. Find the numbers.
- (Basic) One number is 2 more than another, and their sum is 16. Find the numbers.
- (Standard) A father is 4 times as old as his son. In 6 years the sum of their ages will be 52. Find their present ages.
- (Standard) A father is 5 times as old as his son. In 10 years the sum of their ages will be 92. Find their present ages.
- (Challenge) A father is 3 times as old as his son. In 8 years the sum of their ages will be 52. Find their present ages.
- (Challenge) A father is 4 times as old as his son. In 10 years the sum of their ages will be 50. Find their present ages.
Answer key with full working
- Q1: x + (x + 9) = 55 → x = 23 → Answer: 23 and 32
- Q2: x + (x + 2) = 16 → x = 7 → Answer: 7 and 9
- Q3: Son x, father 4x → (x + 6) + (4x + 6) = 52 → 5x = 40 → x = 8 → Answer: Son 8, father 32
- Q4: Son x, father 5x → (x + 10) + (5x + 10) = 92 → 6x = 72 → x = 12 → Answer: Son 12, father 60
- Q5: Son x, father 3x → (x + 8) + (3x + 8) = 52 → 4x = 36 → x = 9 → Answer: Son 9, father 27
- Q6: Son x, father 4x → (x + 10) + (4x + 10) = 50 → 5x = 30 → x = 6 → Answer: Son 6, father 24
Syllabus note
This skill is listed under "Linear Equations in One Variable" for Class 8 in the NCERT/CBSE books. ICSE, IGCSE, IB and state boards may teach it in a different chapter or year.
Answers on this page are generated and automatically re-checked by a second, independent calculation. They have not been reviewed by a teacher — if you spot a problem, tell us on WhatsApp.
Related practice and notes
Frequently asked questions
Which chapter is linear equation word problems in?
"Linear Equations in One Variable", Class 8 Maths (NCERT/CBSE). Other boards may place it differently.
How were the answers checked?
Answers on this page are generated and automatically re-checked by a second, independent calculation. They have not been reviewed by a teacher — if you spot a problem, tell us on WhatsApp.