What is Number Problems using Algebra?

S3-SA1-0419

Grade Level:

Class 7

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

Definition

What is it?

Number problems using algebra are word problems where you use letters (like 'x' or 'y') to represent unknown numbers and then form equations to find their values. It helps us solve puzzles about numbers that are linked in different ways, like sums, differences, or products.

Simple Example

Quick Example

Imagine your friend says, 'I'm thinking of a number. If you add 5 to it, you get 12.' To find the number, you can say, 'Let the number be x.' Then, you write the equation: x + 5 = 12. Solving this gives x = 7.

Worked Example

Step-by-Step

PROBLEM: An auto-rickshaw driver earned some money on Monday. On Tuesday, he earned Rs. 150 more than Monday. If his total earning for both days was Rs. 750, how much did he earn on Monday?

Step 1: Understand the unknown. We need to find Monday's earning. Let Monday's earning be 'x' rupees.
---Step 2: Express Tuesday's earning in terms of 'x'. Tuesday's earning was Rs. 150 more than Monday, so Tuesday's earning = x + 150.
---Step 3: Form an equation using the total earning. Total earning = Monday's earning + Tuesday's earning. So, x + (x + 150) = 750.
---Step 4: Simplify the equation. Combine the 'x' terms: 2x + 150 = 750.
---Step 5: Isolate the term with 'x'. Subtract 150 from both sides: 2x = 750 - 150, which means 2x = 600.
---Step 6: Solve for 'x'. Divide both sides by 2: x = 600 / 2.
---Step 7: Calculate the value. x = 300.

Answer: The auto-rickshaw driver earned Rs. 300 on Monday.

Why It Matters

Solving number problems with algebra is like being a detective for numbers! It's super useful in fields like Data Science to analyze trends, in Physics to calculate forces, and in Economics to model market changes. Engineers use it to design everything from bridges to mobile apps.

Common Mistakes

MISTAKE: Not reading the problem carefully and mixing up 'more than' with 'less than' or 'times'. For example, writing x + 5 for '5 times a number'. | CORRECTION: Highlight keywords like 'sum', 'difference', 'product', 'quotient', 'increased by', 'decreased by' and translate them correctly into mathematical operations.

MISTAKE: Making calculation errors when simplifying the equation, especially with negative numbers or fractions. | CORRECTION: Always double-check your arithmetic after each step. Use a rough sheet for calculations if needed.

MISTAKE: Forgetting to define the variable. For example, just writing 'x' without saying 'Let x be the number of apples'. | CORRECTION: Always start by clearly stating 'Let x represent...' or 'Let the unknown number be y...'. This makes your solution clear and easy to follow.

Practice Questions

Try It Yourself

QUESTION: A number when increased by 10 gives 25. What is the number? | ANSWER: 15

QUESTION: The cost of 3 chai cups and 2 samosas is Rs. 90. If one samosa costs Rs. 15, what is the cost of one chai cup? | ANSWER: Rs. 20

QUESTION: The sum of two consecutive odd numbers is 64. Find the two numbers. (Hint: If the first odd number is x, the next consecutive odd number is x + 2). | ANSWER: 31 and 33

MCQ

Quick Quiz

If a number is multiplied by 4 and then 7 is subtracted from the product, the result is 13. What is the number?

The Correct Answer Is:

Let the number be x. The equation is 4x - 7 = 13. Adding 7 to both sides gives 4x = 20. Dividing by 4 gives x = 5. So, option B is correct.

Real World Connection

In the Real World

When a delivery app like Swiggy or Zomato calculates your total bill based on item prices, discounts, and delivery fees, it's using algebra. Or when ISRO scientists calculate the fuel needed for a rocket based on its weight and destination, they are solving complex number problems using algebraic equations.

Key Vocabulary

Key Terms

VARIABLE: A letter (like x or y) used to represent an unknown number. | EQUATION: A mathematical statement showing that two expressions are equal. | EXPRESSION: A combination of numbers, variables, and operation signs. | SOLVE: To find the value of the unknown variable that makes the equation true. | CONSTANT: A value that does not change.

What's Next

What to Learn Next

Great job understanding number problems! Next, you should explore 'Linear Equations in One Variable'. This will build on what you've learned here, helping you solve even more complex real-life problems with confidence.