Calculating the Cost of Apples: A Comprehensive Guide

Introduction

When dealing with pricing problems, understanding how to calculate the cost of a grouped quantity from a given rate can be crucial. This article will guide you through the process of determining how much 28 apples would cost given that 12 apples cost Rs 30. We will explore multiple methods to ensure a deep understanding of the concept.

Direct Variation Method

The first method to calculate the cost involves a direct variation approach. If 12 apples cost Rs 30, we can set up the following proportion:

12 apples : Rs 30 :: 28 apples : x

To find the cost of 28 apples, we use the formula:

12x 28 × 30

12x 840

x 840 / 12

x 70

Thus, the cost of 28 apples is Rs 70.

Unitary Method

The unitary method is another efficient way to solve such problems. By determining the cost of a single apple first, we can then scale up to the desired quantity. Here’s how it works:

12 apples cost Rs 30. So, the cost of 1 apple is:

30 / 12 Rs 2.5

Therefore, the cost of 28 apples is:

28 × 2.5 Rs 70

Hence, the cost of 28 apples is Rs 70.

Proportional Reasoning

Another way to approach this problem is through proportional reasoning. Since 28 apples are 2 1/3 times the quantity of 12 apples, the cost of 28 apples should be 2 1/3 times the cost of 12 apples:

Rs 30 × 2 1/3 Rs 70

Thus, the cost of 28 apples remains Rs 70.

Proportional Equations

For those who prefer a more algebraic approach, we can use the concept of proportions:

12 apples : Rs 30 :: 28 apples : x

12/30 28/x

Solving for x gives us:

12x 28 × 30

12x 840

x 840 / 12

x 70

Hence, the cost of 28 apples is Rs 70.

In-depth Explanation

To ensure a thorough understanding, let’s go step by step. Given 12 apples cost Rs 30, we first determine the individual cost of one apple:

Cost per apple Total cost / Number of apples

Cost per apple 30 / 12 Rs 2.5

Using this cost per apple, we can calculate the total cost for 28 apples:

Total cost for 28 apples Cost per apple × Number of apples

Total cost for 28 apples 2.5 × 28 Rs 70

Conclusion

By using these various methods, we can systematically determine the cost of 28 apples knowing that 12 apples cost Rs 30. This guide not only provides the answer, Rs 70, but also various methods to solve such problems efficiently. Understanding these methods is crucial for solving similar pricing and quantity-based problems in real life.

Keywords: cost calculation, mathematical reasoning, unitary method