Calculating Earnings from Chocolate Bar Sales: A Simple Problem with a Profitable Solution

Peter, a chocolate lover, decided to buy a large quantity of chocolate bars with the plan to sell them for profit. This example will guide you through the step-by-step process of determining his earnings using a straightforward problem-solving approach.

Understanding the Problem

Peter bought 32 chocolate bars for a special deal: 4 bars for $3. After enjoying some of them, he sold the rest at a different rate: 3 bars for $4.

Step-by-Step Solution

Step 1: Calculate the Cost of Chocolate Bars

The first step is to determine the total cost of the chocolate bars.

Peter bought 32 chocolate bars at a price of 4 bars for $3. To find out how many sets of 4 bars are in 32:

[text{Number of sets} frac{32}{4} 8 text{ sets}]

Now, calculate the total cost:

[text{Total cost} 8 text{ sets} times 3 text{ dollars/set} 24 text{ dollars}]

Step 2: Calculate the Number of Chocolate Bars Sold

Peter ate 2 chocolate bars, so the number of bars left to sell:

[text{Bars left} 32 - 2 30 text{ bars}]

Step 3: Calculate the Revenue from Selling Chocolate Bars

Peter sold the remaining 30 chocolate bars at a rate of 3 bars for $4. First, find out how many sets of 3 bars are in 30:

[text{Number of sets} frac{30}{3} 10 text{ sets}]

Now, calculate the total revenue:

[text{Total revenue} 10 text{ sets} times 4 text{ dollars/set} 40 text{ dollars}]

Step 4: Calculate Peter's Earnings

Finally, to find out how much money Peter earned, subtract the total cost from the total revenue:

[text{Earnings} text{Total revenue} - text{Total cost} 40 text{ dollars} - 24 text{ dollars} 16 text{ dollars}]

Conclusion

Peter earned a total of $16 from selling the chocolate bars.

What if Peter was not a glutton?

If Peter had not eaten any of the chocolate bars, he would have had 32 bars to sell. Using the same process, we can determine his earnings:

[text{Cost of 32 bars} 8 text{ sets} times 3 text{ dollars/set} 24 text{ dollars}] [text{Revenue from 32 bars} 10 text{ sets} times 4 text{ dollars/set} 40 text{ dollars}] [text{Earnings} 40 text{ dollars} - 24 text{ dollars} 18 text{ dollars}]

In this scenario, Peter would have earned $18.

Understanding Profit Calculation

This problem demonstrates the principles of profit calculation. By understanding cost (what you spend) and revenue (what you earn), you can determine your profit. In Peter's case, his initial cost was $24, and his revenue was $40, resulting in a profit of $16.

Cost and Revenue Formula

To calculate net profit:

[text{Profit} text{Revenue} - text{Cost}]

Key Takeaways

Understanding basic arithmetic is crucial for profit calculation. Sales rates and costs need to be calculated accurately to determine revenue. Not using resources unnecessarily can increase your net profit.

By applying the principles of profit calculation, you can make more informed decisions in business and everyday scenarios.