Tean's Candy Bar Fundraiser Explained An Algebraic Adventure

Introduction

Let's dive into a fun math problem about Tean's candy bar fundraiser! This is a classic example of how algebra can help us solve real-world situations. We'll break down the problem step-by-step, making sure you understand every part of it. We will explain Tean's financial adventure by describing how she managed her candy sales to reach her fundraising goal. We will explore the equation she wrote, $2.5c - 25 = 75$, and what each part of it means in the context of her candy sales. So, whether you're a math whiz or just starting to learn, this explanation will help you see how equations can be used to solve everyday problems.

Understanding the Problem

The problem tells us that Tean was selling candy bars to raise money. She started by spending $25 on a box of candy bars. Think of this as her initial investment. Then, she sold each candy bar for $2.50. This is the price she charged her customers. The main goal of any fundraiser is to make a profit, and Tean's profit was $75. Profit is the money you make after you've paid for your expenses. So, the $75 represents the amount Tean had left over after she bought the candy bars. Tean then wrote the equation $2.5c - 25 = 75$ to describe her situation, where 'c' represents the number of candy bars she sold. After solving the equation, she found that c = 40, meaning she sold 40 candy bars. Now, the question asks us to determine the meaning of this solution in the context of the problem. This involves understanding what the numbers in the equation represent and how they relate to Tean's candy bar sales.

Breaking Down the Equation

Let's take a closer look at Tean's equation: $2.5c - 25 = 75$. This equation is the heart of our problem, and understanding each part is crucial. The term '2.5c' represents the total revenue Tean made from selling candy bars. Remember, 'c' stands for the number of candy bars sold, and $2.50 is the price of each bar. So, if Tean sold 10 candy bars, 2.5c would be 2.5 * 10 = $25. This is the money she collected before considering her initial expense. The '- 25' in the equation represents the $25 Tean spent on the box of candy bars. This is a cost she had to cover before she could start making a profit. Think of it as the cost of doing business. Finally, the '= 75' tells us that Tean's profit, after subtracting her initial cost, was $75. Profit is the ultimate goal, and this number shows how much money Tean earned above and beyond her expenses. By putting these pieces together, the equation shows how Tean's revenue, cost, and profit are related. It's a mathematical snapshot of her candy bar fundraiser.

Solving for 'c'

Now, let's see how Tean solved the equation $2.5c - 25 = 75$ to find the value of 'c', which represents the number of candy bars she sold. The first step in solving this equation is to isolate the term with 'c' on one side. To do this, we need to get rid of the '- 25'. The opposite of subtracting 25 is adding 25, so we add 25 to both sides of the equation. This keeps the equation balanced. So, we get: $2.5c - 25 + 25 = 75 + 25$. This simplifies to $2.5c = 100$. Now, we have 2.5 times 'c' equals 100. To find 'c', we need to undo the multiplication. The opposite of multiplying by 2.5 is dividing by 2.5. So, we divide both sides of the equation by 2.5: $2.5c / 2.5 = 100 / 2.5$. This gives us $c = 40$. So, Tean found that she sold 40 candy bars. This is a crucial piece of information, as it tells us how many candy bars she needed to sell to make a $75 profit.

Interpreting the Solution

The final step is to interpret what the solution, $c = 40$, means in the context of the problem. Remember, 'c' represents the number of candy bars Tean sold. So, $c = 40$ means that Tean sold 40 candy bars. This is not just a number; it's a real-world quantity. Tean needed to sell 40 candy bars to achieve her profit goal. We can check this by plugging 40 back into the original equation: $2.5 * 40 - 25 = 75$. This simplifies to $100 - 25 = 75$, which is true. This confirms that our solution is correct. Tean sold 40 candy bars, which earned her $100 in revenue. After subtracting her initial cost of $25, her profit was indeed $75. This interpretation shows how math connects to the real world. The equation and its solution tell a story about Tean's successful fundraiser.

Conclusion

In conclusion, Tean's candy bar fundraiser is a great example of how math, especially algebra, can be used to solve practical problems. By understanding the problem, breaking down the equation, solving for the variable, and interpreting the solution, we can see how math helps us make sense of the world around us. Tean successfully used an equation to figure out how many candy bars she needed to sell to reach her fundraising goal. This problem not only reinforces our understanding of algebraic equations but also highlights the importance of math in everyday life. So, the next time you're faced with a problem, remember how Tean used math to sell candy bars and achieve her goal.