Forming Equations from Word Problems
An equation is a mathematical sentence with an equal sign (=). Forming equations means translating a word problem into a mathematical statement using numbers, operations, and a variable (unknown).
In Class 5, you will learn to read a word problem, identify the unknown quantity, assign a letter (like x) to it, and write an equation that represents the relationship described in the problem. You will then solve the equation to find the answer.
This skill bridges arithmetic and algebra. It teaches you to think logically and express real-life situations mathematically.
What is Forming Equations from Word Problems - Class 5 Maths (Patterns and Algebra)?
An equation is a statement that two expressions are equal. It always has an = sign.
- Variable: A letter (like x, n, or y) that represents an unknown number.
- Forming an equation: Translating words into a mathematical sentence.
Common word-to-symbol translations:
| Words | Symbol |
|---|---|
| more than, increased by, added to | + |
| less than, decreased by, taken away | − |
| times, product of, multiplied by | × |
| divided by, shared equally | ÷ |
| is, equals, gives, results in | = |
Types and Properties
Types of equations you will form:
- Addition equations: x + 5 = 12 (a number plus 5 equals 12).
- Subtraction equations: x − 8 = 15 (a number minus 8 equals 15).
- Multiplication equations: 4 × x = 36 (4 times a number equals 36).
- Division equations: x ÷ 3 = 7 (a number divided by 3 equals 7).
- Two-step equations: 2x + 3 = 11 (twice a number plus 3 equals 11).
Solved Examples
Example 1: Example 1: Addition Equation
Problem: Ria has some mangoes. She gets 5 more and now has 13. How many did she have?
Solution:
Step 1: Let the unknown number of mangoes = x
Step 2: She gets 5 more: x + 5
Step 3: Now she has 13: x + 5 = 13
Step 4: Solve: x = 13 − 5 = 8
Answer: Ria had 8 mangoes. Equation: x + 5 = 13.
Example 2: Example 2: Subtraction Equation
Problem: Arjun had some stickers. He gave 7 to his friend and was left with 15. How many did he have?
Solution:
Step 1: Let the original number = x
Step 2: He gave away 7: x − 7
Step 3: Left with 15: x − 7 = 15
Step 4: x = 15 + 7 = 22
Answer: Arjun had 22 stickers. Equation: x − 7 = 15.
Example 3: Example 3: Multiplication Equation
Problem: A packet has some biscuits. 6 such packets contain 48 biscuits in total. How many biscuits are in each packet?
Solution:
Step 1: Let biscuits in one packet = x
Step 2: 6 packets: 6 × x = 48
Step 3: x = 48 ÷ 6 = 8
Answer: Each packet has 8 biscuits. Equation: 6x = 48.
Example 4: Example 4: Division Equation
Problem: Aditi divides her marbles equally among 4 friends. Each friend gets 9 marbles. How many marbles did she have?
Solution:
Step 1: Let total marbles = x
Step 2: Divided among 4: x ÷ 4 = 9
Step 3: x = 9 × 4 = 36
Answer: Aditi had 36 marbles. Equation: x ÷ 4 = 9.
Example 5: Example 5: Two-Step Equation
Problem: Dev thinks of a number, doubles it, and adds 3. The result is 17. What is the number?
Solution:
Step 1: Let the number = x
Step 2: Doubles it: 2x. Adds 3: 2x + 3
Step 3: Result is 17: 2x + 3 = 17
Step 4: 2x = 17 − 3 = 14
Step 5: x = 14 ÷ 2 = 7
Answer: The number is 7. Equation: 2x + 3 = 17.
Example 6: Example 6: Age Problem
Problem: Meera is 3 years older than Priya. Meera is 11 years old. How old is Priya?
Solution:
Step 1: Let Priya’s age = x
Step 2: Meera is 3 years older: x + 3 = 11
Step 3: x = 11 − 3 = 8
Answer: Priya is 8 years old. Equation: x + 3 = 11.
Example 7: Example 7: Money Problem
Problem: Rahul buys 5 pens and pays ₹75. What is the cost of one pen?
Solution:
Step 1: Let cost of one pen = x
Step 2: 5 pens cost ₹75: 5x = 75
Step 3: x = 75 ÷ 5 = 15
Answer: One pen costs ₹15. Equation: 5x = 75.
Example 8: Example 8: Sum of Two Numbers
Problem: The sum of two numbers is 45. One number is 18. Find the other.
Solution:
Step 1: Let the other number = x
Step 2: x + 18 = 45
Step 3: x = 45 − 18 = 27
Answer: The other number is 27. Equation: x + 18 = 45.
Example 9: Example 9: Perimeter Problem
Problem: A rectangle has a perimeter of 30 cm. Its length is 9 cm. Find the breadth.
Solution:
Step 1: Let breadth = x
Step 2: Perimeter = 2(length + breadth) = 2(9 + x) = 30
Step 3: 9 + x = 15
Step 4: x = 15 − 9 = 6 cm
Answer: The breadth is 6 cm. Equation: 2(9 + x) = 30.
Example 10: Example 10: Think of a Number
Problem: Kavi thinks of a number, subtracts 4, and gets 19. What is the number?
Solution:
Step 1: Let the number = x
Step 2: x − 4 = 19
Step 3: x = 19 + 4 = 23
Answer: The number is 23. Equation: x − 4 = 19.
Key Points to Remember
- An equation has an equal sign (=) and shows that two sides are balanced.
- A variable (like x) represents the unknown quantity.
- Translate key words: “more than” = +, “less than” = −, “times” = ×, “divided by” = ÷.
- To form an equation: identify the unknown, assign a variable, write the relationship, and solve.
- Solving means finding the value of the variable that makes the equation true.
- Check your answer by substituting it back into the equation.
- Two-step equations involve two operations (e.g., 2x + 3 = 11).
Practice Problems
- Neha has some toffees. She gets 8 more and now has 20. Form an equation and solve for the original number.
- A number multiplied by 7 gives 63. Write the equation and find the number.
- Aman had some money. He spent ₹45 and has ₹30 left. Form an equation and find how much he had.
- The sum of two numbers is 50. One number is 23. Write an equation to find the other.
- Dev thinks of a number, triples it, and subtracts 5. The result is 22. Form the equation and solve.
- 48 students are divided equally into groups. Each group has 8 students. How many groups are there? Write the equation.
- A rectangle has a perimeter of 42 cm and length 13 cm. Form an equation to find the breadth.
- Priya is twice as old as Kavi. Priya is 14 years old. Write an equation and find Kavi’s age.
Frequently Asked Questions
Q1. What does forming an equation mean?
Forming an equation means translating a word problem into a mathematical statement using numbers, a variable (like x), and an equal sign. For example, “a number plus 5 equals 12” becomes x + 5 = 12.
Q2. What is a variable?
A variable is a letter (usually x, y, or n) that stands for an unknown number. You find its value by solving the equation.
Q3. How do I know which operation to use?
Look for clue words: “more than” or “added to” means addition; “less than” or “gave away” means subtraction; “times” or “each” means multiplication; “shared equally” means division.
Q4. How do I solve an equation?
Use inverse (opposite) operations. If x + 5 = 12, subtract 5 from both sides to get x = 7. If 3x = 18, divide both sides by 3 to get x = 6.
Q5. How do I check my answer?
Substitute the value of x back into the original equation. If both sides are equal, the answer is correct. For example, x + 5 = 12: if x = 7, then 7 + 5 = 12. Correct.
Q6. What is a two-step equation?
A two-step equation requires two operations to solve. For example, 2x + 3 = 11. First subtract 3 (2x = 8), then divide by 2 (x = 4).
Q7. Can a word problem have more than one equation?
At the Class 5 level, most problems lead to a single equation with one variable. More complex systems of equations are studied in higher classes.
Q8. Why is forming equations useful?
Equations let you express and solve problems systematically. Once you write the equation, you can use mathematical rules to find the exact answer instead of guessing.
Q9. Is this topic in the NCERT Class 5 syllabus?
Yes. Introduction to simple equations and forming equations from word problems is part of the Patterns and Algebra topics in NCERT/CBSE Class 5 Maths.
