Calculate Original Price Golf Clubs R Us Sale

In this article, we'll tackle a real-world problem involving discounts and original prices. We'll walk through the process of calculating the original selling price of a set of golf clubs that were marked on sale with a 35% discount. This is a practical application of percentage calculations, a fundamental concept in mathematics and everyday financial transactions. Understanding how discounts work and how to determine original prices is essential for both consumers and businesses. Whether you're shopping for a new set of golf clubs or managing inventory for a retail store, the ability to calculate discounts and original prices accurately is a valuable skill.

Golf Clubs R Us had a set of 10 golf clubs on sale for $850. This price reflected a 35% discount off the original selling price. Our goal is to determine the original selling price of the golf club set. This problem requires us to work backward from the discounted price to find the initial price before the discount was applied. We'll use algebraic principles and percentage calculations to solve this problem, demonstrating a common application of mathematics in retail settings.

To solve this problem, we'll use a step-by-step approach that breaks down the calculation into manageable parts. First, we'll understand the relationship between the original price, the discount, and the sale price. The sale price represents the original price minus the discount amount. Since the discount is 35% of the original price, the sale price represents 100% - 35% = 65% of the original price. This understanding is crucial for setting up the equation correctly. Next, we'll set up an algebraic equation to represent this relationship. We'll let 'x' represent the original selling price. The equation will state that 65% of x is equal to the sale price of $850. This equation will allow us to isolate 'x' and solve for the original price. Once we have the equation, we'll solve for 'x' by dividing both sides of the equation by 0.65 (which is the decimal equivalent of 65%). This will give us the original selling price. Finally, we'll round the answer to the nearest cent, as is standard practice in financial calculations, and present the final result. This systematic approach ensures accuracy and clarity in problem-solving.

Step 1: Understand the Relationship

The first crucial step in solving this problem is to understand the relationship between the original price, the discount, and the sale price. The sale price is what you pay after the discount has been applied. The discount is a percentage reduction from the original price. In this case, the golf clubs are on sale for $850, which is a 35% discount off the original selling price. This means that the $850 represents the price after a 35% reduction from the original price. It's important to recognize that the $850 is not 35% of the original price; rather, it's the original price minus 35% of the original price. Therefore, the sale price represents 100% of the original price minus the 35% discount, which equals 65% of the original price. This understanding is the foundation for setting up the correct equation to solve the problem. If we misunderstand this relationship, we might incorrectly calculate the original price. For instance, mistakenly calculating 35% of $850 and adding it to $850 would not give us the correct original price because the $850 already reflects the discount. Therefore, a clear grasp of how discounts work is essential for accurate calculations.

Step 2: Set up the Equation

Now that we understand the relationship between the original price, the discount, and the sale price, we can set up an algebraic equation to represent the problem. This is a critical step in translating the word problem into a mathematical form that we can solve. Let's use the variable 'x' to represent the unknown original selling price. This is a common practice in algebra, where variables are used to represent quantities we want to find. We know that the sale price ($850) is equal to 65% of the original price (x). We determined this in the previous step by subtracting the 35% discount from the 100% original price. To express 65% as a decimal, we divide it by 100, which gives us 0.65. Therefore, we can write the equation as: 0. 65x = $850. This equation states that 0.65 times the original price (x) is equal to the sale price of $850. This equation is the key to solving the problem because it directly relates the known sale price to the unknown original price. Setting up the equation correctly is crucial; a mistake here will lead to an incorrect answer. Once we have the correct equation, we can use algebraic techniques to isolate 'x' and find the original selling price.

Step 3: Solve for the Original Price

With the equation 0.65x = $850 set up, the next step is to solve for 'x', which represents the original selling price of the golf clubs. To isolate 'x' on one side of the equation, we need to undo the multiplication by 0.65. We can do this by dividing both sides of the equation by 0.65. This is a fundamental principle of algebra: whatever operation we perform on one side of the equation, we must also perform on the other side to maintain the equality. So, we divide both sides of the equation by 0.65: (0.65x) / 0.65 = $850 / 0.65. This simplifies to x = $850 / 0.65. Now, we perform the division: $850 divided by 0.65. This calculation will give us the value of 'x', which is the original selling price before the discount was applied. Using a calculator or performing long division, we find that $850 / 0.65 ≈ $1307.6923. This result tells us the approximate original selling price of the golf clubs. However, we're not quite done yet. The final step is to round the answer to the nearest cent, as is standard practice when dealing with monetary values. This rounding ensures that our answer is practical and accurate in a real-world context.

Step 4: Round to the Nearest Cent

After dividing $850 by 0.65, we obtained an approximate value of $1307.6923 for the original selling price. However, in practical financial situations, prices are typically expressed to the nearest cent (two decimal places). Therefore, the final step in our problem-solving process is to round this number to the nearest cent. To round to the nearest cent, we look at the third decimal place. If it is 5 or greater, we round up the second decimal place. If it is less than 5, we leave the second decimal place as it is. In our case, the number is $1307.6923. The third decimal place is 2, which is less than 5. Therefore, we do not round up the second decimal place. The rounded value is $1307.69. This is the original selling price of the golf clubs, rounded to the nearest cent. Rounding to the nearest cent ensures that our answer is both accurate and practical for real-world applications, such as pricing in a retail setting. This final step is crucial for presenting a professional and usable solution to the problem.

After following our problem-solving process, we have determined that the original selling price of the golf clubs was approximately $1307.69. This answer is the result of carefully setting up an equation based on the relationship between the sale price, the discount, and the original price, and then solving that equation using algebraic principles. We also rounded our answer to the nearest cent to ensure accuracy and practicality. This final answer provides a clear and concise solution to the problem posed, demonstrating the application of mathematical concepts to a real-world scenario.

In conclusion, we have successfully calculated the original selling price of the golf clubs using a systematic problem-solving approach. We began by understanding the relationship between the sale price, the discount, and the original price. We then set up an algebraic equation to represent this relationship, solved for the unknown original price, and rounded our answer to the nearest cent. This process highlights the importance of understanding percentages and discounts in practical situations. By breaking down the problem into smaller, manageable steps, we were able to arrive at the correct solution. This type of problem-solving is not only useful in academic settings but also has real-world applications in personal finance, retail, and other areas. The ability to calculate discounts and original prices is a valuable skill for anyone who wants to make informed financial decisions. Furthermore, this example illustrates how mathematical concepts can be applied to everyday scenarios, making math relevant and engaging.