The Profit Quest: How Many Pencils Must Be Sold to Make a $100 Profit?

Imagine you found the perfect deal on pencils: a store owner bought 1,500 pencils at $0.10 each. An ambitious plan forms in your mind: to sell these pencils at $0.25 each, thus turning a profit of exactly $100. But is this plan feasible? Let's delve into the numbers and uncover the magic behind the profit calculation.

Understanding the Basics

The key to solving this puzzle lies in understanding the concept of profit, which is the difference between the revenue from selling the pencils and the cost of purchasing them. In this scenario, the profit per pencil is the difference between the selling price and the cost price. Here's the equation:

Profit per pencil Selling price - Cost price

In this case:

Profit per pencil $0.25 - $0.10 $0.15

Calculating the Number of Pencils Needed

To find out how many pencils must be sold to make a profit of exactly $100, we can use a straightforward equation:

Profit Revenue - Cost

Given the target profit:

$100 0.25x - (1,500 * 0.10)

$100 0.25x - 150

Adding 150 to both sides:

$250 0.25x

Solving for x:

x $250 / 0.25

x 1,000 pencils

Discussion and Reflection

Is selling 1,000 pencils to make a $100 profit a good business move? Let's break down the numbers:

1. At $0.25 each, selling 1,000 pencils yields a revenue of:

1,000 * $0.25 $250

2. The initial cost for 1,500 pencils is:

1,500 * $0.10 $150

3. The profit made from selling 1,000 pencils:

Profit $250 - $150 $100

While the plan seems sound, it's crucial to consider the practicality. Selling 1,000 pencils is a significant undertaking, even for a small business. Are the target consumers willing to purchase at this price? Is the market demand strong enough to support this number of sales?

Alternative Possibilities

Let's explore some alternative approaches:

1. If the goal is to make a profit of $100 and sell fewer pencils:

Profit per pencil $0.15

Total required profit $100

x $100 / $0.15

x 666.6667

Since you can't sell a fraction of a pencil, you would need to sell 667 pencils.

2. If the goal is to make an additional $1,500 in profit:

Total profit $1,500 $100 $1,600

Revenue needed $1,600 $150 $1,750

Selling price per pencil $0.25

x $1,750 / $0.25

x 7,000 pencils

This scenario is even more challenging, suggesting that the original plan might need to be adjusted or that the business model might need reevaluation.

Conclusion

While the math is clear, the feasibility of the plan depends on various factors such as market demand, pricing strategies, and other business costs. What seems like a simple profit calculation transforms into a complex business challenge when you consider the practical aspects.

Whether you choose to sell 667 pencils to achieve your profit goal or reevaluate your business strategy, the lesson here is valuable: always consider the real-world implications of your financial goals.