What is Modelling Word Problems? | Simple Explanation for Class 7

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What is Modelling Word Problems with Linear Equations?

Grade Level:

Class 7

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

Definition

What is it?

Modelling word problems with linear equations means taking a real-life situation described in words and translating it into a mathematical equation with a single unknown variable. This equation, usually in the form ax + b = c, helps us find the unknown value. It's like converting a story into a math puzzle.

Simple Example

Quick Example

Imagine you bought 3 samosas and a cup of chai. If each samosa costs Rs 10 and your total bill was Rs 45, how much did the chai cost? Here, the cost of chai is the unknown. We can write this as (3 * 10) + chai_cost = 45.

Worked Example

Step-by-Step

QUESTION: A mobile recharge shop offers a plan where you get 2GB of data for a fixed daily charge plus an extra Rs 5 for every additional GB used. If you paid Rs 45 for a day and used 5GB of data in total, what is the fixed daily charge? --- STEP 1: Identify the unknown. The unknown is the fixed daily charge. Let's call it 'x'. --- STEP 2: Identify the given information. Total data used = 5GB. Extra data used = Total data - 2GB (free data) = 5GB - 2GB = 3GB. Cost per extra GB = Rs 5. Total bill = Rs 45. --- STEP 3: Formulate the equation. Fixed charge + (Extra data used * Cost per extra GB) = Total bill. So, x + (3 * 5) = 45. --- STEP 4: Simplify the equation. x + 15 = 45. --- STEP 5: Solve for x. To find x, subtract 15 from both sides: x = 45 - 15. --- STEP 6: Calculate the answer. x = 30. --- ANSWER: The fixed daily charge is Rs 30.

Why It Matters

This skill is super important in fields like AI/ML, where you predict things based on data, and in Computer Science, where you write programs to solve problems. Engineers use it to design bridges and calculate forces, while economists use it to understand market trends. It's a foundational step to solving complex real-world challenges.

Common Mistakes

MISTAKE: Not correctly identifying the unknown variable. Students sometimes assign 'x' to a known value. | CORRECTION: Always read the question carefully and assign 'x' to the quantity you need to find. Look for phrases like 'how much', 'what is', 'find the value of'.

MISTAKE: Mixing up operations (addition, subtraction, multiplication, division) when translating words into math. For example, using addition instead of multiplication for 'times' or 'product'. | CORRECTION: Pay close attention to keywords: 'sum' means addition, 'difference' means subtraction, 'product' means multiplication, 'quotient' means division, 'is' or 'was' often means equals (=).

MISTAKE: Forgetting to include all parts of the problem in the equation. Students might miss a fixed cost or a discount. | CORRECTION: Break down the problem sentence by sentence. List all quantities and relationships before writing the full equation. Double-check if every piece of information is used.

Practice Questions

Try It Yourself

QUESTION: Sneha bought a storybook and a pen. The storybook cost Rs 80. If her total bill was Rs 105, what was the cost of the pen? | ANSWER: Rs 25

QUESTION: An auto-rickshaw charges a base fare of Rs 20 and Rs 8 for every kilometer travelled. If your total fare was Rs 68, how many kilometers did you travel? | ANSWER: 6 kilometers

QUESTION: Your mom distributed 5 kg of ladoos equally among her friends. If each friend received 500 grams of ladoos and there were 200 grams left for the family, how many friends did she distribute the ladoos to? (Hint: 1 kg = 1000 grams) | ANSWER: 9 friends

MCQ

Quick Quiz

Which equation correctly represents the following problem: 'If you double a number and add 15, you get 45.'

x + 15 = 45

2x + 15 = 45

2(x + 15) = 45

x/2 + 15 = 45

The Correct Answer Is:

Option B, 2x + 15 = 45, correctly translates 'double a number' (2x) and 'add 15' (+ 15) to 'you get 45' (= 45). The other options misinterpret the doubling or the addition.

Real World Connection

In the Real World

Delivery apps like Zomato or Swiggy use this logic! When you order food, the total bill is calculated using a fixed delivery charge plus a variable cost per item or distance. Behind the scenes, linear equations help figure out your final bill or even how many delivery partners are needed based on orders.

Key Vocabulary

Key Terms

VARIABLE: A symbol (usually 'x') representing an unknown quantity | LINEAR EQUATION: An equation where the highest power of the variable is 1 (e.g., ax + b = c) | COEFFICIENT: The number multiplied by the variable (e.g., 'a' in ax) | CONSTANT: A fixed numerical value in an equation (e.g., 'b' and 'c' in ax + b = c) | MODELLING: The process of translating a real-world problem into a mathematical form

What's Next

What to Learn Next

Great job learning to model word problems! Next, you can explore 'Solving Linear Equations with Variables on Both Sides'. This will help you tackle even more complex real-life scenarios where the unknown appears on both sides of the equation.