Decoding The Discount Finding The Original Price Of Henrik's Hockey Stick

Introduction: Unveiling the Mystery of the Hockey Stick Price

In the realm of mathematical problem-solving, we often encounter scenarios that require us to apply our understanding of percentages and discounts. This article delves into a practical problem involving a discount and aims to determine the original price of a hockey stick. Discounts are a common aspect of retail, and understanding how to calculate them is a valuable skill. In this particular scenario, Henrik had a coupon for a 25% discount on a hockey stick and ultimately paid $172.50. Our mission is to unravel the mystery and discover the original price of this coveted piece of sports equipment. To solve this, we'll use our knowledge of percentages, discounts, and algebraic equations. The problem presents a real-world scenario, making it relatable and engaging. By understanding how discounts work and applying the appropriate formulas, we can determine the original price of the hockey stick before the discount was applied. This exercise not only enhances our mathematical skills but also equips us with practical knowledge that can be applied in everyday situations, such as shopping and budgeting. So, let's embark on this mathematical journey and uncover the original price of Henrik's hockey stick. As we work through the solution, we'll break down each step, ensuring clarity and understanding. The goal is not just to find the answer but also to grasp the underlying concepts and techniques. Through this process, we'll strengthen our problem-solving abilities and gain a deeper appreciation for the role of mathematics in our lives. Remember, mathematics is not just about numbers and equations; it's about logical thinking and problem-solving, skills that are essential in various aspects of life. This problem serves as a testament to the practical applications of mathematics and its ability to help us make informed decisions.

Setting up the Equation: Translating Words into Math

To effectively tackle this problem, the first crucial step is to translate the given information into a mathematical equation. This involves representing the unknown original price with a variable, say 'x'. The key here is to understand how the discount affects the price. A 25% discount means that Henrik paid 100% - 25% = 75% of the original price. Therefore, $172.50 represents 75% of the original price, which we've denoted as 'x'. Now, we can express this relationship as an equation. 75% can be written as a decimal by dividing by 100, which gives us 0.75. So, the equation becomes 0.75x = $172.50. This equation is the foundation of our solution. It represents the core relationship between the original price, the discount, and the final price paid. By setting up the equation correctly, we've transformed the word problem into a mathematical problem that we can solve using algebraic techniques. The process of translating words into equations is a fundamental skill in mathematics. It allows us to take real-world scenarios and represent them in a way that we can manipulate and solve. This skill is not only essential for mathematical problem-solving but also for critical thinking and decision-making in various contexts. In this case, the equation 0.75x = $172.50 encapsulates the essence of the problem. It tells us that 75% of the original price is equal to $172.50. Our next step will be to solve this equation for 'x', which will reveal the original price of the hockey stick. Remember, the equation is a powerful tool that allows us to represent relationships and solve for unknowns. By mastering the art of setting up equations, we can tackle a wide range of problems and gain a deeper understanding of the world around us. This problem serves as a practical example of how equations can be used to solve real-world scenarios involving discounts and prices.

Solving for x: Unveiling the Original Price

With the equation 0.75x = $172.50 established, the next step is to isolate 'x' and solve for the original price. To do this, we need to divide both sides of the equation by 0.75. This is a fundamental algebraic operation that maintains the equality of the equation while isolating the variable we're interested in. Dividing both sides by 0.75, we get: x = $172.50 / 0.75. Now, we perform the division. $172.50 divided by 0.75 equals $230. Therefore, x = $230. This means that the original price of the hockey stick was $230. This is the solution to our problem. We've successfully used algebraic techniques to determine the original price after accounting for the discount. The process of solving for 'x' demonstrates the power of algebraic manipulation. By applying the appropriate operations to both sides of the equation, we can isolate the variable and find its value. This skill is crucial for solving a wide range of mathematical problems, from simple equations to complex systems of equations. In this case, the division operation was the key to unlocking the original price. It allowed us to undo the effect of the discount and reveal the initial cost of the hockey stick. The solution, $230, is not just a number; it's the answer to our problem. It represents the original price that Henrik would have paid before the 25% discount was applied. By understanding the steps involved in solving for 'x', we've not only found the answer but also reinforced our understanding of algebraic principles. This problem serves as a valuable exercise in applying mathematical concepts to real-world scenarios. It demonstrates how algebra can be used to solve practical problems involving discounts and prices.

Verification: Ensuring the Accuracy of Our Solution

To ensure the accuracy of our solution, it's crucial to verify that the original price of $230, when subjected to a 25% discount, results in the final price of $172.50. This verification step is essential in any mathematical problem-solving process. It helps us catch any potential errors and confirms that our solution is indeed correct. To verify, we first calculate the discount amount. A 25% discount on $230 is calculated as 0.25 * $230, which equals $57.50. This is the amount of money that Henrik saved due to the discount. Next, we subtract the discount amount from the original price to find the final price. $230 - $57.50 = $172.50. This matches the price that Henrik actually paid, as stated in the problem. Therefore, our solution of $230 is indeed correct. The verification process is a critical step in mathematical problem-solving. It's not enough to just find a solution; we must also verify that the solution makes sense in the context of the problem. This involves checking our calculations and ensuring that the answer aligns with the given information. In this case, the verification process confirmed that our solution of $230 is accurate. By calculating the discount amount and subtracting it from the original price, we were able to verify that the final price matched the price paid by Henrik. This step not only ensures the accuracy of our solution but also reinforces our understanding of the concepts involved. It demonstrates the importance of paying attention to detail and double-checking our work. The verification process is a valuable skill that can be applied in various contexts, not just in mathematics. It helps us develop a critical and analytical mindset, which is essential for problem-solving and decision-making.

Conclusion: Reflecting on the Solution and its Implications

In conclusion, by carefully applying our understanding of percentages, discounts, and algebraic equations, we have successfully determined that the original price of the hockey stick was $230. This problem serves as a practical example of how mathematical concepts can be used to solve real-world scenarios. The process involved translating a word problem into a mathematical equation, solving for the unknown variable, and verifying the accuracy of the solution. Understanding discounts and how they affect prices is a valuable skill in everyday life. It allows us to make informed decisions when shopping and budgeting. By mastering the techniques used in this problem, we can confidently tackle similar scenarios and make sound financial choices. Furthermore, this problem highlights the importance of problem-solving skills in general. The ability to break down a complex problem into smaller, manageable steps, to apply appropriate formulas and techniques, and to verify the accuracy of the solution is crucial in various aspects of life, both personal and professional. Mathematics is not just about numbers and equations; it's about logical thinking and problem-solving. By engaging with problems like this one, we strengthen our critical thinking skills and develop a deeper appreciation for the role of mathematics in our lives. The solution to this problem is not just a number; it's a testament to our ability to apply mathematical concepts to real-world situations. It demonstrates the power of mathematics to help us understand and navigate the world around us. By reflecting on the solution and its implications, we reinforce our learning and gain a deeper understanding of the concepts involved. This problem serves as a valuable learning experience that can be applied in various contexts.