Equation Word Problems (Grade 5)
Equation word problems require you to read a real-life situation, form an equation using a variable, and then solve it. This is a critical skill that connects algebra to everyday life.
In Class 5, these problems involve basic operations — addition, subtraction, multiplication, and division. The key step is translating the English sentence into a mathematical equation.
For example, "Ria has some stickers. She gives away 12 and has 25 left" becomes: x − 12 = 25, which gives x = 37.
What is Equation Word Problems - Class 5 Maths (Patterns and Algebra)?
An equation word problem presents a situation in words. You must:
- Read the problem carefully.
- Identify what is unknown — assign a variable.
- Form an equation based on the given information.
- Solve the equation using inverse operations.
- Check the answer and write it as a sentence.
Equation Word Problems (Grade 5) Formula
Common translations from words to equations:
| Words | Equation |
|---|---|
| A number increased by 8 is 20 | x + 8 = 20 |
| A number decreased by 5 is 12 | x − 5 = 12 |
| 3 times a number is 27 | 3x = 27 |
| A number divided by 4 is 6 | x ÷ 4 = 6 |
| Twice a number plus 5 is 19 | 2x + 5 = 19 |
Solved Examples
Example 1: Example 1: Stickers Problem
Problem: Ria has some stickers. She gives 18 to her friend and has 27 left. How many stickers did she have?
Solution:
Let original stickers = x
Equation: x − 18 = 27
x = 27 + 18 = 45
Check: 45 − 18 = 27 ✓
Answer: Ria had 45 stickers.
Example 2: Example 2: Money Problem
Problem: Aman has ₹250. After buying a book, he has ₹175 left. How much did the book cost?
Solution:
Let cost of book = ₹b
Equation: 250 − b = 175
b = 250 − 175 = 75
Answer: The book cost ₹75.
Example 3: Example 3: Equal Distribution
Problem: A teacher distributes 96 pencils equally among some students. Each student gets 8 pencils. How many students are there?
Solution:
Let number of students = s
Equation: 96 ÷ s = 8, which means 8 × s = 96
s = 96 ÷ 8 = 12
Answer: There are 12 students.
Example 4: Example 4: Age Problem
Problem: Priya is 4 years older than Kavi. If Priya is 13 years old, how old is Kavi?
Solution:
Let Kavi's age = k
Equation: k + 4 = 13
k = 13 − 4 = 9
Answer: Kavi is 9 years old.
Example 5: Example 5: Fruit Purchase
Problem: Aditi buys 5 kg of mangoes. The total cost is ₹400. What is the price per kg?
Solution:
Let price per kg = ₹p
Equation: 5p = 400
p = 400 ÷ 5 = 80
Answer: Mangoes cost ₹80 per kg.
Example 6: Example 6: Two-Step Problem
Problem: Dev thinks of a number. He doubles it and adds 9. The result is 35. Find the number.
Solution:
Let the number = n
Equation: 2n + 9 = 35
Step 1: 2n = 35 − 9 = 26
Step 2: n = 26 ÷ 2 = 13
Check: 2(13) + 9 = 26 + 9 = 35 ✓
Answer: The number is 13.
Example 7: Example 7: Classroom Problem
Problem: A class has 45 students. There are 7 more girls than boys. How many boys are there?
Solution:
Let number of boys = b
Number of girls = b + 7
Equation: b + (b + 7) = 45
2b + 7 = 45
2b = 38
b = 19
Check: Boys = 19, Girls = 26, Total = 45 ✓
Answer: There are 19 boys.
Example 8: Example 8: Distance Problem
Problem: Meera walks to school and back. The total distance is 3 km. How far is her school from home?
Solution:
Let distance to school = d km
Equation: 2d = 3 (going and coming back)
d = 3 ÷ 2 = 1.5
Answer: Her school is 1.5 km from home.
Example 9: Example 9: Sharing Problem
Problem: Neha and Rahul share ₹180. Rahul gets ₹30 more than Neha. How much does each get?
Solution:
Let Neha's share = ₹n
Rahul's share = ₹(n + 30)
Equation: n + (n + 30) = 180
2n + 30 = 180
2n = 150
n = 75
Answer: Neha gets ₹75, Rahul gets ₹105.
Example 10: Example 10: Weight Problem
Problem: A bag of rice weighs 3 times as much as a bag of sugar. The rice bag weighs 15 kg. Find the weight of the sugar bag.
Solution:
Let weight of sugar = s kg
Equation: 3s = 15
s = 15 ÷ 3 = 5
Answer: The sugar bag weighs 5 kg.
Key Points to Remember
- Read the problem carefully to understand what is unknown.
- Assign a variable (letter) to the unknown quantity.
- Translate the words into an equation using operations.
- Solve the equation using inverse operations.
- Always check your answer by substituting it back into the original problem.
- Write the answer as a complete sentence with proper units.
Practice Problems
- Arjun has some chocolates. He gives 15 to his sister and has 22 left. How many did he have?
- A number multiplied by 7 gives 91. Find the number.
- Ria is 3 years younger than her brother. Her brother is 14. How old is Ria?
- The cost of 6 identical pens is ₹90. Find the cost of one pen.
- A number is divided by 8 to get 12. What is the number?
- Priya thinks of a number. She triples it and subtracts 4 to get 20. Find the number.
- There are 52 apples in two baskets. One basket has 8 more apples than the other. How many apples are in each basket?
- Dev's age is twice Kavi's age. If Dev is 18 years old, find Kavi's age.
Frequently Asked Questions
Q1. How do you form an equation from a word problem?
Identify the unknown quantity and assign a variable to it. Then translate the relationships described in the problem into a mathematical equation using +, −, ×, or ÷.
Q2. What does 'increased by' mean in a word problem?
'Increased by' means addition. 'A number increased by 5' translates to x + 5.
Q3. What does 'decreased by' mean?
'Decreased by' means subtraction. 'A number decreased by 8' translates to x − 8.
Q4. What does 'times' or 'product' mean?
'Times' and 'product' mean multiplication. '4 times a number' translates to 4x.
Q5. How do you check your answer?
Substitute your answer back into the original word problem. If the condition is satisfied, your answer is correct.
Q6. What if the problem involves two unknowns?
Express one unknown in terms of the other. For example, if 'Ria has 5 more than Aman,' and Aman has x, then Ria has x + 5. Use their relationship to form one equation.
Q7. What is the most common mistake in equation word problems?
The most common mistake is setting up the equation incorrectly — confusing addition with subtraction or mixing up who has more. Always re-read the problem before writing the equation.
Q8. Do I always need to write a variable?
Using a variable makes the solution clear and systematic. While you can sometimes solve simple problems mentally, using variables is essential for complex problems and is good practice for algebra.
