What is Writing an Equation From a Word Problem?

S1-SA5-1190

Grade Level:

Class 5

Maths, Computing, AI, NLP, Physics, Finance

Definition

What is it?

Writing an equation from a word problem means converting a story problem into a mathematical sentence using numbers, variables (like 'x' or 'y'), and mathematical operations (+, -, *, /). It helps us solve real-life puzzles using the power of maths.

Simple Example

Quick Example

Imagine your friend has some laddoos, and you give them 3 more. Now they have 8 laddoos. If 'L' is the number of laddoos your friend had to begin with, the equation would be: L + 3 = 8.

Worked Example

Step-by-Step

Let's try this: "A vendor sold 5 samosas. He has 12 samosas left. How many samosas did he have at the start?"

Step 1: Identify what we need to find. We need to find the total number of samosas the vendor had at the start. Let's call this 'S'.
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Step 2: Identify the known numbers. He sold 5 samosas. He has 12 samosas left.
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Step 3: Think about the relationship. If he started with 'S' samosas and sold 5, he would have (S - 5) left.
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Step 4: Form the equation. The number of samosas left (S - 5) is equal to 12. So, S - 5 = 12.
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Step 5: (Optional, but good to check) Solve the equation. To find S, we add 5 to both sides: S = 12 + 5. So, S = 17.
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Answer: The equation is S - 5 = 12. (He had 17 samosas at the start).

Why It Matters

Learning to write equations helps you solve problems not just in maths, but also in computing, science, and even managing your pocket money! Engineers use equations to design bridges, and data scientists use them to understand trends, helping make apps like Swiggy work better.

Common Mistakes

MISTAKE: Using the wrong operation (e.g., adding instead of subtracting) | CORRECTION: Read the problem carefully. Words like 'more than', 'increased by' usually mean addition (+). Words like 'less than', 'decreased by', 'taken away' usually mean subtraction (-). 'Times', 'product' mean multiplication (*). 'Divided by', 'shared equally' mean division (/).

MISTAKE: Not defining the variable (e.g., just writing 'x' without saying what 'x' represents) | CORRECTION: Always state what your variable stands for. For example, write: "Let 'C' be the cost of one cricket ball."

MISTAKE: Confusing the order of operations, especially with subtraction or division | CORRECTION: Pay close attention to what is happening TO what. If 'x' is reduced by 5, it's x - 5. If 5 is reduced by 'x', it's 5 - x.

Practice Questions

Try It Yourself

QUESTION: Riya has some stickers. Her brother gives her 7 more. Now Riya has 20 stickers. Write an equation to find out how many stickers Riya had initially. | ANSWER: S + 7 = 20 (where S is the initial number of stickers)

QUESTION: A bus conductor collected Rs. 150 from 10 passengers. If each ticket costs the same amount, write an equation to find the cost of one ticket. | ANSWER: 10 * T = 150 (where T is the cost of one ticket)

QUESTION: Your dad bought a pack of biscuits. You ate 3 biscuits, and your sister ate 2. There are 15 biscuits left in the pack. Write an equation to find out how many biscuits were in the pack initially. | ANSWER: B - 3 - 2 = 15 or B - 5 = 15 (where B is the initial number of biscuits)

MCQ

Quick Quiz

Which equation correctly represents this problem: "There are 4 friends, and they share 'X' amount of sweets equally. Each friend gets 6 sweets."

X + 4 = 6

X / 4 = 6

X * 4 = 6

X - 4 = 6

The Correct Answer Is:

The problem states that 'X' amount of sweets are shared equally among 4 friends, meaning division. Each friend getting 6 sweets means the result of the division is 6. So, X divided by 4 equals 6.

Real World Connection

In the Real World

When you use a food delivery app like Zomato, the app's system uses equations to calculate your total bill, including food cost, delivery charges, and discounts. Even ISRO scientists use complex equations to calculate rocket trajectories and satellite orbits!

Key Vocabulary

Key Terms

EQUATION: A mathematical statement showing two expressions are equal, usually with an '=' sign. | VARIABLE: A symbol (like x, y, a) that represents an unknown number or quantity. | EXPRESSION: A combination of numbers, variables, and operation signs, but without an '=' sign. | WORD PROBLEM: A mathematical problem presented in the form of a short story or sentence.

What's Next

What to Learn Next

Great job understanding how to write equations! Next, you should learn 'How to Solve One-Step Equations'. This will teach you the methods to find the value of the unknown variable in the equations you just learned to write. It's the next exciting step!