Calculating the Cost of Juice Cans with Proportional Reasoning

Proportional reasoning is a fundamental mathematical concept that can be applied to a variety of real-world problems, including calculating the cost of goods. In this article, we will explore a practical example involving the cost of juice cans and demonstrate how to use proportional reasoning to solve similar problems efficiently.

Introduction

The given problem involves determining the cost of a specific quantity of juice cans based on the cost of a different quantity. This type of problem requires an understanding of proportional relationships, where the cost of goods is directly proportional to the number of goods.

The Problem

Problem Statement: 32 cartons each containing 15 juice cans cost $8640. What is the cost of 24 cartons each containing 14 juice cans of the same type?

Step-by-Step Solution

Let's break down the problem into manageable steps to understand the solution better.

Step 1: Determine the Cost per Can

First, calculate the total number of cans in the original batch:

32 cartons x 15 cans per carton 480 cans

Next, find the cost per can by dividing the total cost by the total number of cans:

Cost per can $8640 / 480 cans $18 per can

Now that we have the cost per can, we can determine the cost of the new batch.

Step 2: Calculate the Cost of the New Batch

Determine the total number of cans in the new batch:

24 cartons x 14 cans per carton 336 cans

Multiply the number of cans by the cost per can to find the total cost:

Total cost 336 cans x $18 per can $6048

Therefore, the cost of 24 cartons each containing 14 juice cans is $6048.

Additional Insights

This problem highlights the importance of proportional reasoning in solving real-world problems. Understanding proportion allows us to make accurate calculations and make informed decisions based on given data.

Conclusion

In summary, by breaking down the problem into smaller steps and using the concept of proportion, we can easily determine the cost of a different quantity of juice cans. This method can be applied to various similar scenarios, making it a valuable tool in everyday calculations and business operations.