Word Problems on Simple Equations
The real power of equations is in solving real-life problems. When you read a word problem, you translate the words into a mathematical equation, solve it, and find the answer.
In Class 7 NCERT Maths, you will solve word problems about ages, numbers, perimeter, coins, and everyday situations by forming and solving simple equations.
The key skill is turning English sentences into mathematical statements using a variable for the unknown quantity.
What is Word Problems on Simple Equations - Grade 7 Maths (Simple Equations)?
Steps to solve word problems:
- Read the problem carefully.
- Identify the unknown — what are you asked to find?
- Let the unknown be x (or any variable).
- Form an equation using the information given.
- Solve the equation using the balance method or transposition.
- Check the answer against the original problem.
- Write the answer in words (with units if needed).
Word Problems on Simple Equations Formula
Common translations from words to maths:
- "Sum of" or "added to" → +
- "Difference" or "less than" or "subtracted from" → −
- "Product of" or "times" → ×
- "Quotient" or "divided by" → ÷
- "Is" or "equals" or "gives" → =
- "Twice a number" → 2x
- "Thrice a number" → 3x
- "A number increased by 5" → x + 5
- "7 less than a number" → x − 7
- "One-third of a number" → x/3
Types and Properties
Common types of word problems:
- Number problems: Finding a number when clues about it are given.
- Age problems: Finding someone's age using relationships like "5 years older" or "twice as old."
- Perimeter problems: Finding dimensions of shapes when the perimeter is given.
- Coin/money problems: Finding the number of coins or cost of items.
- Consecutive number problems: Finding consecutive numbers whose sum is given.
Solved Examples
Example 1: Number Problem
Problem: A number added to 15 gives 42. Find the number.
Solution:
Let the number be x.
Equation: x + 15 = 42
Transpose: x = 42 − 15 = 27
Check: 27 + 15 = 42. Correct!
Answer: The number is 27.
Example 2: Twice a Number
Problem: Twice a number decreased by 7 is 19. Find the number.
Solution:
Let the number be x.
Equation: 2x − 7 = 19
Transpose −7: 2x = 19 + 7 = 26
Transpose ×2: x = 26 / 2 = 13
Check: 2(13) − 7 = 26 − 7 = 19. Correct!
Answer: The number is 13.
Example 3: Age Problem
Problem: Ravi is 5 years older than Sita. The sum of their ages is 31. Find their ages.
Solution:
Let Sita's age = x. Then Ravi's age = x + 5.
Equation: x + (x + 5) = 31
Simplify: 2x + 5 = 31
Transpose: 2x = 31 − 5 = 26
x = 26 / 2 = 13
So Sita is 13 years old and Ravi is 13 + 5 = 18 years old.
Check: 13 + 18 = 31. Correct!
Answer: Sita is 13 years old and Ravi is 18 years old.
Example 4: Perimeter Problem
Problem: The perimeter of a rectangle is 54 cm. Its length is 3 cm more than its breadth. Find the length and breadth.
Solution:
Let breadth = x cm. Then length = (x + 3) cm.
Perimeter of rectangle = 2(length + breadth)
Equation: 2(x + 3 + x) = 54
Simplify: 2(2x + 3) = 54
4x + 6 = 54
4x = 54 − 6 = 48
x = 48 / 4 = 12
Breadth = 12 cm, Length = 12 + 3 = 15 cm.
Check: 2(15 + 12) = 2(27) = 54. Correct!
Answer: Length = 15 cm, Breadth = 12 cm.
Example 5: Consecutive Numbers
Problem: The sum of three consecutive numbers is 72. Find the numbers.
Solution:
Let the numbers be x, x + 1, x + 2.
Equation: x + (x + 1) + (x + 2) = 72
Simplify: 3x + 3 = 72
3x = 72 − 3 = 69
x = 69 / 3 = 23
The numbers are 23, 24, 25.
Check: 23 + 24 + 25 = 72. Correct!
Answer: The numbers are 23, 24, and 25.
Example 6: Coin Problem
Problem: Priya has some Rs. 5 coins and Rs. 2 coins. She has 15 coins in total worth Rs. 54. How many of each type does she have?
Solution:
Let the number of Rs. 5 coins = x. Then Rs. 2 coins = 15 − x.
Total value: 5x + 2(15 − x) = 54
5x + 30 − 2x = 54
3x + 30 = 54
3x = 54 − 30 = 24
x = 24 / 3 = 8
Rs. 5 coins = 8, Rs. 2 coins = 15 − 8 = 7.
Check: 8 × 5 + 7 × 2 = 40 + 14 = 54. Correct!
Answer: 8 coins of Rs. 5 and 7 coins of Rs. 2.
Example 7: Division Problem
Problem: If you divide a number by 4 and add 3, you get 10. Find the number.
Solution:
Let the number be x.
Equation: x/4 + 3 = 10
x/4 = 10 − 3 = 7
x = 7 × 4 = 28
Check: 28/4 + 3 = 7 + 3 = 10. Correct!
Answer: The number is 28.
Example 8: Distribution Problem
Problem: A teacher distributes 50 sweets equally among some students. Each student gets 5 sweets and 10 are left over. How many students are there?
Solution:
Let the number of students = x.
Equation: 5x + 10 = 50
5x = 50 − 10 = 40
x = 40 / 5 = 8
Check: 5(8) + 10 = 40 + 10 = 50. Correct!
Answer: There are 8 students.
Real-World Applications
Where word problems on equations are useful:
- Daily life: Calculating costs, splitting bills, figuring out quantities.
- Competitive exams: Number and age problems are common in olympiads and scholarship tests.
- Geometry: Finding dimensions of shapes when perimeter or area is given.
- Science: Applying formulas where one quantity is unknown.
- Budgeting: If you earn Rs. x per day and spend Rs. 200, your savings equation helps plan finances.
Key Points to Remember
- Read the problem carefully and identify the unknown.
- Let the unknown be x (or any letter).
- Translate words to maths: "sum" = +, "difference" = −, "times" = ×, "is" = =.
- Form an equation from the given information.
- Solve using transposition or the balance method.
- Always check the answer against the original problem.
- Write the answer with proper units.
- For age problems, express all ages in terms of one variable.
Practice Problems
- The sum of a number and 12 is 35. Find the number.
- Three times a number minus 8 equals 19. Find the number.
- Anita is twice as old as Bina. The sum of their ages is 36. Find their ages.
- The perimeter of a square is 60 cm. Find the side length.
- The sum of two consecutive even numbers is 46. Find them.
- A father is 30 years older than his son. In 5 years, the father will be 3 times as old as the son. Find their present ages.
Frequently Asked Questions
Q1. How do I start solving a word problem?
Read the problem carefully. Find what is unknown. Let the unknown be x. Use the given information to write an equation. Solve the equation and check the answer.
Q2. What does 'less than' mean in word problems?
'7 less than a number' means x − 7 (not 7 − x). The phrase 'less than' means you subtract from the number, not from the given value.
Q3. How do I solve age problems?
Express all ages using one variable. If Ravi is 5 years older than Sita, let Sita's age = x, so Ravi's age = x + 5. Then use the condition given (like sum of ages) to form an equation.
Q4. What are consecutive numbers?
Consecutive numbers come one after another. If the first number is x, the next three consecutive numbers are x + 1, x + 2, x + 3. For consecutive even numbers: x, x + 2, x + 4.
Q5. Can word problems have fractional answers?
Yes. Some problems may give fractional answers. For example, if 3 pens cost Rs. 50, one pen costs Rs. 50/3 which is approximately Rs. 16.67.
Q6. How do I check my answer?
Substitute your answer back into the original word problem (not just the equation). Check if all conditions in the problem are satisfied.
