Scaling Apple Costs: Discovering the True Value

Have you ever encountered a problem involving the conversion of the total cost to a different quantity, like the one where 20 apples cost Rs 450? This article explains how to calculate the cost for a different number of apples, specifically 30 apples, using a straightforward method. We'll explore the step-by-step calculations and ensure that the solution is verified through logical proof.

Understanding the Problem

Suppose the cost for 20 apples is Rs 450. A common question asked might be: 'If 20 apples cost Rs 450, what would be the cost for 30 apples?' This seemingly simple problem requires a few basic steps to find the accurate answer.

Calculating the Cost of 30 Apples

To solve this problem, we can follow these steps:

Step 1: Find the Cost of One Apple

The first step is to determine the cost of one apple. We can do this by dividing the total cost for 20 apples by the number of apples:

If 20 apples cost Rs 450, then the cost of 1 apple is Rs 450 / 20 Rs 22.5

Step 2: Calculate the Cost for 30 Apples

Now that we know the cost of one apple, we can find the cost for 30 apples by multiplying the cost per apple by 30:

The cost of 30 apples is Rs 22.5 * 30 Rs 675

Verification Through Logical Proof

To ensure our solution is correct, we can verify it using the original problem statement:

Given: 20 apples cost Rs 450 We want to find the cost for 30 apples

Using the derived formula:

y Rs 30 / 20 * 450 y 3 * 450 / 2 y 675

The proof shows that the cost for 30 apples is indeed Rs 675, confirming our solution.

Conclusion

Understanding how to scale costs is crucial for various real-life scenarios, from grocery shopping to budgeting. Whether you're calculating the total cost for a different number of apples or similar items, following the steps outlined here will help you find the right answer. The verification through logical proof provides a solid foundation for accuracy.

If you have any questions or need further assistance with similar problems, feel free to reach out. Happy calculating!