Introduction

Calculating the cost of items, especially when dealing with bulk orders, can be a simple yet time-consuming task if not approached methodically. In this article, we explore a straightforward and efficient way to determine the cost of 40 dozen pens when the cost of 6 dozen pens is known. We will delve into various methods to simplify the calculation process and ensure you can quickly provide the correct answer.

Method 1: Direct Proportion Method

The first method employs direct proportion. If 6 dozen pens cost 15 dollars, we can find the cost of 40 dozen pens by setting up a proportion.

First, identify the given cost: 6 dozen pens cost 15 dollars.

We need to find the cost for 40 dozen pens. We can set up the proportion as follows:

6 dozen pens : 15 dollars 40 dozen pens : X dollars

Solving for X:

X (40 * 15) / 6

X 600 / 6

X 100 dollars

Therefore, 40 dozen pens cost 100 dollars.

Method 2: Using Decimal Division

This method uses decimal division to simplify the calculation:

First, note the cost for 6 dozen pens: 6 dozen pens cost 15 dollars.

Now, we can calculate the cost for 1 dozen pens:

1 dozen pens cost 15 / 6 2.50 dollars.

Next, calculate the cost for 40 dozen pens:

40 dozen pens cost 40 * 2.50 100 dollars.

Therefore, 40 dozen pens cost 100 dollars.

Additional Worked Examples

Example 1: Using Direct Multiplication

Given that 6 dozen pens cost 15 dollars: We can directly multiply 40 by 15 and then divide by 6 to find the cost for 40 dozen pens.

Cost for 40 dozen pens (40 * 15) / 6 600 / 6 100 dollars.

Example 2: Alternative Proportion Method

First, recognize that: 6 dozen pens cost 15 dollars. We can find the cost for 36 dozen pens by multiplying 6 dozen by 6: 36 dozen pens cost (6 * 6) * 15 / 6 36 * 2.50 90 dollars. We know that 6 dozen pens cost 15 dollars, so: 2 dozen pens cost 5 dollars (15 / 6 * 2). 4 dozen pens cost 10 dollars (2 * 5). Add the costs together to find the total cost for 40 dozen pens: 40 dozen pens cost 90 10 100 dollars.

Therefore, 40 dozen pens cost 100 dollars.

Example 3: Using Unit Cost

First, recognize that: 6 dozen pens cost 15 dollars. We can find the unit cost of one dozen pens: Unit cost of one dozen pens 15 / 6 2.50 dollars. Multiply the unit cost by 40 to find the cost for 40 dozen pens: 40 dozen pens cost 40 * 2.50 100 dollars.

Therefore, 40 dozen pens cost 100 dollars.

Conclusion

Gaining proficiency in basic mathematical calculations is crucial for managing and optimizing costs in business, especially when dealing with bulk orders. By mastering these techniques, you can ensure that you quickly and accurately determine the cost of your purchases. Whether you choose the direct proportion method, decimal division, or a combination of both, the key is to choose the method that is most straightforward and efficient for your needs.