What is Formation of Algebraic Equations? | Simple Explanation for Class 7

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What is the Formation of Algebraic Equations from Word Problems?

Grade Level:

Class 7

AI/ML, Data Science, Physics, Economics, Cryptography, Computer Science, Engineering

Definition

What is it?

Forming algebraic equations from word problems means translating a story or situation described in words into a mathematical statement using variables (like 'x' or 'y') and numbers. It helps us solve real-life puzzles by converting them into a language that algebra understands.

Simple Example

Quick Example

Imagine you bought 3 samosas and a cup of chai. If each samosa costs Rs. 10 and the total bill was Rs. 40, how much did the chai cost? We can let 'x' be the cost of chai. The equation would be: 3 * 10 + x = 40.

Worked Example

Step-by-Step

PROBLEM: Rohit scored 15 runs more than Virat in a cricket match. If their total score was 145 runs, how many runs did Virat score?

STEP 1: Identify what we need to find. We need to find Virat's score. Let's represent Virat's score with a variable, say 'V'.
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STEP 2: Express Rohit's score in terms of Virat's score. Rohit scored 15 runs more than Virat, so Rohit's score = V + 15.
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STEP 3: Use the total score information to form the equation. Their total score was 145 runs. So, Virat's score + Rohit's score = 145.
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STEP 4: Substitute the expressions from Step 1 and 2 into the equation. V + (V + 15) = 145.
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STEP 5: Simplify and solve the equation. 2V + 15 = 145.
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STEP 6: Subtract 15 from both sides: 2V = 145 - 15 => 2V = 130.
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STEP 7: Divide by 2: V = 130 / 2 => V = 65.
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ANSWER: Virat scored 65 runs.

Why It Matters

This skill is super important for thinking logically and solving problems, just like a detective! It's used in building AI models, designing games in Computer Science, and even calculating rocket trajectories in Physics. Future engineers and data scientists use this every day to solve complex real-world challenges.

Common Mistakes

MISTAKE: Not reading the problem carefully and mixing up what the variable represents. For example, assigning 'x' to the total instead of one part. | CORRECTION: Clearly define what each variable stands for (e.g., 'Let x be the cost of one pencil') before writing the equation.

MISTAKE: Confusing operations like 'more than' with subtraction or 'less than' with addition. For example, writing 'x + 5' for '5 less than x'. | CORRECTION: Remember 'more than' means addition, 'less than' means subtraction, 'times' or 'product' means multiplication, and 'divided by' or 'quotient' means division.

MISTAKE: Forgetting to include all parts of the problem in the equation, or including extra information that isn't needed. | CORRECTION: Break the problem into smaller pieces. List all the given facts and what you need to find. Make sure every piece of relevant information is used once.

Practice Questions

Try It Yourself

QUESTION: A number increased by 7 is 25. What is the equation? | ANSWER: x + 7 = 25

QUESTION: The cost of a mobile phone is Rs. 5000 more than three times the cost of a tablet. If the tablet costs Rs. 8000, write an equation for the cost of the mobile phone. | ANSWER: M = 3 * 8000 + 5000 (where M is the mobile phone cost)

QUESTION: In a school canteen, a plate of idli costs Rs. 20. A dosa costs Rs. 15 more than a plate of idli. If a student bought 2 plates of idli and 1 dosa for a total of Rs. 'T', write an equation for 'T'. | ANSWER: T = (2 * 20) + (20 + 15)

MCQ

Quick Quiz

Rina has 5 fewer candies than Sameer. If Sameer has 'c' candies, which expression represents the number of candies Rina has?

c + 5

5 - c

c - 5

The Correct Answer Is:

If Rina has 5 fewer candies than Sameer, it means we need to subtract 5 from Sameer's number of candies. So, 'c - 5' is the correct expression. 'c + 5' would mean 5 more, '5 - c' is incorrect order, and '5c' means 5 times 'c'.

Real World Connection

In the Real World

When a delivery app like Swiggy or Zomato calculates the total bill, including item costs, delivery fees, and discounts, it's forming and solving equations. Even the algorithms that recommend products to you on Amazon use similar logic to balance factors like price, popularity, and your past purchases.

Key Vocabulary

Key Terms

VARIABLE: A symbol (usually a letter like x, y) that represents an unknown number | EQUATION: A mathematical statement showing that two expressions are equal (e.g., x + 5 = 10) | EXPRESSION: A combination of numbers, variables, and operation signs (e.g., 2x + 3) | WORD PROBLEM: A mathematical problem presented in text form, describing a real-life scenario

What's Next

What to Learn Next

Great job learning to translate words into equations! Next, you should learn 'Solving Simple Linear Equations'. This will teach you how to find the actual value of the unknown variable, using the equations you've just learned to form. You're building a strong foundation for advanced math!