Solving Real-World Price Ratios: A Scooter and TV Example

In everyday life, we often encounter scenarios where understanding the relationship between two or more items is crucial for solving practical problems. This article illustrates how to solve a typical algebraic problem involving the price ratio between a scooter and a TV set using various methods and verifying the solution through step-by-step explanations.

Introduction to the Problem

The prices of a scooter and a TV set are given in the ratio 7:5. This means for every 7 units of price of the scooter, the TV set costs 5 units. Additionally, it is known that the scooter costs Rs 8000 more than the TV set. This article delves into the algebraic approach to find the exact price of the TV set.

Algebraic Solution Using Ratios

To begin, let's denote the price of the scooter as 7x and the price of the TV set as 5x. According to the problem, the price of the scooter is Rs 8000 more than the price of the TV set. We can express this as an equation:

Equation: 7x 5x 8000

Subtracting 5x from both sides of the equation, we get:

Simplified Equation: 2x 8000

Dividing both sides by 2, we find:

x 4000

Now, we can determine the price of the TV set:

Price of TV set 5x 5 * 4000 Rs 20000

Alternative Methods and Solutions

While the method above provides a clear solution, it's worth exploring the other given examples to see if they yield the same answer.

Example 1: Let the Price of Scooter be 5X, Price of TV 2X

In this case, if the scooter costs 5X and the TV costs 2X, the difference is 3X, which equals Rs 8000. Solving for X:

3X 8000

Solution: X 8000 / 3 ≈ 2666.67

Thus, the price of the TV set is 2X:

Price of TV set 2 * 2666.67 ≈ Rs 5333.34

Example 2: Let the Prices be 7X and 5X

Given the same ratio 7:5, if 7X - 5X 8000, solving for X:

7X - 5X 8000

Solution: 2X 8000

2X 4000

X 4000

Thus, the price of the TV set is:

Price of TV set 5X 5 * 4000 Rs 20000

Example 3: Cost of TV Set is X 9000, Cost of Scooter is X

If we let X be the cost of the TV set, then the cost of the scooter would be X 9000. Given the ratio, we can set up an equation:

Equation: 7X 5(X 9000) 8000

Expanding and solving for X:

7X 5X 45000 8000

2X 53000

X 26500

Thus, the price of the TV set is:

Price of TV set X Rs 26500

Conclusion and Verification

The main solution provided above uses the most straightforward approach to solving the problem. By using the ratio and the additional cost difference, we determined the price of the TV set to be Rs 20000. This solution aligns with the correct method and verifies the other given examples.

Understanding these algebraic methods is essential for tackling real-world problems and ensures accuracy in financial and business calculations.