Calculating Motorcycle Cost Price With 36% Profit And 12% Discount

Introduction

Hey guys! Ever wondered how businesses calculate the cost price of their products, especially when they're aiming for a certain profit margin while also offering discounts? It's a fascinating blend of math and business strategy! In this article, we're going to dive deep into a practical scenario: figuring out the cost price of a motorcycle that was sold with a 36% profit after a 12% discount was applied. This is a common situation in retail, and understanding the process can give you a solid grasp of pricing dynamics. So, let's put on our thinking caps and get started!

Understanding the Problem

Before we jump into the calculations, let's break down the problem. We know that a motorcycle was sold at a price that included a 36% profit. However, this price was reached after a 12% discount was given on the original selling price. Our mission is to find out the original cost price of the motorcycle – the amount the seller initially paid for it. This involves working backward from the final selling price, taking into account both the discount and the profit margin. It's like being a detective, piecing together clues to solve a mystery! To solve this, we need to understand the relationship between cost price, selling price, profit, and discounts. The cost price is what the seller paid for the motorcycle. The selling price is the price at which the motorcycle was offered to customers before any discounts. The discounted price is the final price after the discount is applied, and this is the price at which the motorcycle was actually sold. The profit is the difference between the discounted price and the cost price. Got it? Great! Now, let's move on to the mathematical part.

Setting up the Equations

To solve this problem effectively, we need to translate the information we have into mathematical equations. This might sound intimidating, but don't worry, we'll take it step by step. Let's start by defining our variables. Let's call the cost price "C," the original selling price "S," and the discounted price "D." We know that the motorcycle was sold with a 36% profit, so the discounted price (D) is the cost price (C) plus 36% of the cost price. This can be written as: D = C + 0.36C. This equation represents the profit margin. Next, we know that the 12% discount was applied to the original selling price (S) to arrive at the discounted price (D). This means that the discounted price is 88% (100% - 12%) of the original selling price. We can write this as: D = 0.88S. This equation represents the discount. Now we have two equations with three variables. To solve for C, we need to eliminate one of the other variables. Since both equations have D in them, we can set them equal to each other. This gives us: C + 0.36C = 0.88S. We can simplify the left side of the equation to get: 1.36C = 0.88S. Now we have one equation with two variables, C and S. To solve for C, we need to express S in terms of C or vice versa. Let's rearrange the equation to express S in terms of C: S = (1.36C) / 0.88. This equation tells us how the original selling price relates to the cost price. We're getting closer to finding the cost price! In this section, we've successfully translated the word problem into mathematical equations, which is a crucial step in solving it. By defining variables and setting up equations, we've created a roadmap for finding the solution. Now, let's move on to the next step: solving these equations to find the cost price.

Solving for the Cost Price

Alright, we've set up our equations, and now it's time to put our algebra skills to the test and solve for the cost price (C). Remember, we have the equation S = (1.36C) / 0.88. This equation expresses the original selling price (S) in terms of the cost price (C). However, we need to find the value of C. To do this, we need one more piece of information: the actual discounted price (D) at which the motorcycle was sold. Let's assume, for the sake of this example, that the motorcycle was sold for $10,000 after the discount. So, D = $10,000. Now we can use the equation D = 0.88S to find the original selling price (S). Plugging in the value of D, we get: $10,000 = 0.88S. To solve for S, we divide both sides of the equation by 0.88: S = $10,000 / 0.88. Calculating this, we get: S = $11,363.64 (approximately). So, the original selling price of the motorcycle was approximately $11,363.64. Now that we have the original selling price, we can use the equation 1.36C = 0.88S to find the cost price (C). Plugging in the value of S, we get: 1.36C = 0.88 * $11,363.64. Simplifying the right side of the equation, we get: 1.36C = $9,999.99 (approximately $10,000). To solve for C, we divide both sides of the equation by 1.36: C = $10,000 / 1.36. Calculating this, we get: C = $7,352.94 (approximately). Therefore, the cost price of the motorcycle was approximately $7,352.94. This means the seller initially paid around $7,352.94 for the motorcycle before applying the profit margin and discount.

Verifying the Solution

We've crunched the numbers and arrived at a cost price, but it's always a good idea to double-check our work. Let's verify our solution to make sure everything adds up correctly. We calculated the cost price (C) to be approximately $7,352.94. We also know that the profit margin was 36%, so the profit amount is 36% of the cost price: Profit = 0.36 * $7,352.94. Calculating this, we get: Profit = $2,647.06 (approximately). This means the seller made a profit of around $2,647.06 on the motorcycle. Now, let's add the profit to the cost price to find the price before the discount: Price before discount = $7,352.94 + $2,647.06. Calculating this, we get: Price before discount = $10,000. This should match the discounted price we used earlier, which it does! Next, we need to check if the 12% discount on the original selling price leads to the discounted price of $10,000. We calculated the original selling price (S) to be approximately $11,363.64. A 12% discount on this price is: Discount amount = 0.12 * $11,363.64. Calculating this, we get: Discount amount = $1,363.64 (approximately). Subtracting the discount amount from the original selling price, we get: Discounted price = $11,363.64 - $1,363.64. Calculating this, we get: Discounted price = $10,000. This matches the discounted price we used, so our calculations are consistent. By verifying our solution, we've gained confidence that our answer is correct. This step is crucial in any problem-solving process, as it helps catch any potential errors and ensures accuracy.

Real-World Applications

Understanding how to calculate cost price, profit margins, and discounts isn't just an academic exercise; it has tons of real-world applications! Whether you're running a business, managing a budget, or just trying to get the best deal while shopping, these skills are incredibly valuable. For business owners, accurately calculating the cost price is essential for setting prices that are both competitive and profitable. It allows them to factor in expenses, desired profit margins, and potential discounts to create a pricing strategy that maximizes revenue. Without a clear understanding of the cost price, businesses risk selling products at a loss or pricing themselves out of the market. Moreover, this knowledge helps in making informed decisions about inventory management, promotions, and sales strategies. Profit margins are a key indicator of a business's financial health. By knowing how to calculate profit margins, businesses can track their performance, identify areas for improvement, and make strategic decisions about pricing and cost control. Understanding discounts is equally important. Businesses use discounts to attract customers, clear inventory, or respond to market changes. However, discounts can also impact profitability, so it's crucial to understand how they affect the bottom line. For consumers, understanding these concepts can help you make smarter purchasing decisions. When you know how discounts work, you can evaluate whether a sale is truly a good deal. You can also use this knowledge to negotiate prices or compare offers from different retailers. In personal finance, these skills can be applied to budgeting, investing, and financial planning. Understanding profit margins can help you evaluate investment opportunities, while knowing how to calculate discounts can help you save money on everyday purchases. In short, the ability to calculate cost price, profit margins, and discounts is a valuable life skill that can benefit you in various aspects of your personal and professional life. So, the next time you're faced with a pricing puzzle, you'll be well-equipped to solve it!

Conclusion

So, there you have it, guys! We've successfully navigated the world of cost price calculations, profit margins, and discounts. We started by understanding the problem, setting up equations, solving for the cost price, and verifying our solution. Along the way, we saw how these calculations are relevant in real-world scenarios, from running a business to making smart purchasing decisions. Remember, the key to solving these types of problems is to break them down into smaller, manageable steps. Define your variables, set up equations based on the information you have, and then use your algebra skills to solve for the unknown. And always, always verify your solution to make sure everything checks out! This process not only helps you arrive at the correct answer but also deepens your understanding of the underlying concepts. Whether you're a student learning about pricing or a business owner making strategic decisions, these skills are essential for success. We hope this article has shed some light on the intricacies of cost price calculations and empowered you to tackle similar challenges with confidence. Keep practicing, keep exploring, and most importantly, keep learning! Who knows, maybe you'll be the next pricing whiz in your circle. Thanks for joining us on this mathematical journey!