Calculate Cost Price: Bromato Sold At 20800 (15% Profit)

by Viktoria Ivanova 57 views

Hey guys! Let's dive into a fun and practical math problem today. We're going to figure out the original cost price of a product, Bromato, that was sold for 20800 with a 15 percent profit. This kind of calculation is super useful in real life, whether you're running a business or just trying to understand how pricing works. So, grab your thinking caps, and let's get started!

Understanding the Basics: Cost Price, Selling Price, and Profit

Before we jump into the calculation, let's make sure we're all on the same page with some key terms. Knowing these basics is crucial for understanding the problem and solving it effectively. It’s like having the right tools before you start a DIY project – makes everything much smoother!

  • Cost Price (CP): This is the original price at which a product is purchased or manufactured. Think of it as the baseline cost – what it took to get the product ready to sell. For example, if you're a bakery, the cost price of a cake would include the cost of ingredients, labor, and other overheads.
  • Selling Price (SP): This is the price at which the product is sold to the customer. It's the amount of money you actually receive when someone buys the item. So, if you sell that cake for $30, that's your selling price.
  • Profit: Profit is the financial gain you make when the selling price is higher than the cost price. It’s the difference between what you spent and what you earned. In simple terms, it's the money you make after covering your initial costs. For instance, if your cake cost $20 to make and you sell it for $30, your profit is $10.

Why is this important? Well, understanding these terms helps you manage your finances, whether in a business or personal setting. Knowing your cost price allows you to set appropriate selling prices to ensure you make a profit. It also helps in analyzing the financial health of your business or even in making smart purchasing decisions in your daily life. Imagine trying to run a store without knowing how much things cost you – it would be chaos!

In our Bromato example, we know the selling price (20800) and the profit percentage (15%), and we need to find the cost price. We'll use these basic concepts to set up our equation and solve the problem. So, let's keep these definitions in mind as we move forward – they're the building blocks of our solution!

Setting Up the Equation: The Key to Unlocking the Cost Price

Now that we have a good handle on the basics, let's translate the problem into a mathematical equation. This is a crucial step because it gives us a clear roadmap to finding the cost price. Think of it like writing down the recipe before you start cooking – it ensures you don’t miss any important steps!

We know that the selling price (SP) is equal to the cost price (CP) plus the profit. And the profit is a percentage of the cost price. So, we can express this relationship as:

  • Selling Price (SP) = Cost Price (CP) + Profit

But how do we express the profit mathematically? Since the profit is 15% of the cost price, we can write it as:

  • Profit = 15% of CP = 0.15 * CP

Now, we can substitute this expression for profit back into our original equation:

  • SP = CP + 0.15 * CP

We know the selling price (SP) is 20800, so we can plug that into the equation:

  • 20800 = CP + 0.15 * CP

This equation is the key to solving our problem. It tells us how the cost price and the profit combine to give us the selling price. The next step is to simplify this equation and isolate the cost price (CP). It's like solving a puzzle – we just need to rearrange the pieces to reveal the answer!

By setting up the equation correctly, we’ve laid a solid foundation for our calculation. Without this step, we’d be trying to solve the problem in the dark. So, remember, a well-structured equation is half the battle won! Let’s move on to solving it and finding the cost price of Bromato.

Solving the Equation: Step-by-Step Calculation

Alright, let’s roll up our sleeves and solve the equation we set up earlier! This is where we put our math skills to the test and find the actual cost price of Bromato. Think of it like the actual cooking part – we’ve got the recipe (the equation), now we need to follow it step-by-step to get the delicious result (the cost price).

Our equation is:

  • 20800 = CP + 0.15 * CP

First, we need to simplify the right side of the equation. We have CP + 0.15 * CP, which can be rewritten as 1 * CP + 0.15 * CP. Combining these terms gives us:

  • 20800 = 1.15 * CP

Now, we want to isolate CP (the cost price) on one side of the equation. To do this, we need to divide both sides of the equation by 1.15. This will cancel out the 1.15 on the right side, leaving us with CP alone:

  • 20800 / 1.15 = CP

Performing this division, we get:

  • CP = 18086.96 (approximately)

So, the cost price of Bromato is approximately 18086.96. This means that the original cost to acquire or produce Bromato was around 18086.96 before it was sold for 20800 with a 15% profit.

Breaking down the calculation into these steps makes it much easier to follow and understand. Each step builds on the previous one, leading us to the final answer. And remember, it’s always a good idea to double-check your calculations to make sure you haven’t made any mistakes – just like tasting your dish while you cook to make sure the flavors are right!

Now that we’ve solved the equation, we have the cost price. But let’s not stop there. It’s always a good practice to verify our answer to ensure it makes sense in the context of the problem.

Verifying the Answer: Ensuring Our Calculation Makes Sense

We've crunched the numbers and found that the cost price of Bromato is approximately 18086.96. That's awesome! But before we pat ourselves on the back, let's take a moment to verify our answer. It's like proofreading your work before submitting it – you want to make sure everything adds up and makes sense!

To verify our answer, we can plug the cost price back into our original equation and see if it gives us the selling price we started with. Remember our equation:

  • Selling Price (SP) = Cost Price (CP) + Profit
  • Profit = 15% of CP

Let's calculate the profit using our cost price:

  • Profit = 0.15 * 18086.96
  • Profit ≈ 2713.04

Now, let's add the profit to the cost price to see if we get the selling price:

  • Selling Price = 18086.96 + 2713.04
  • Selling Price ≈ 20800

Hey, look at that! Our calculated selling price matches the selling price given in the problem (20800). This confirms that our cost price calculation is correct. High five!

Verifying the answer is a crucial step in problem-solving. It ensures that our solution is not only mathematically correct but also logically sound in the context of the problem. It's like double-checking your GPS directions to make sure you're on the right track – you don't want to end up in the wrong place!

By taking the time to verify our answer, we've added an extra layer of confidence to our solution. We know we've not only solved the problem but also solved it correctly. So, remember, always verify your answers – it's a smart habit to develop!

Real-World Applications: Why This Matters

Okay, we've successfully calculated the cost price of Bromato, but you might be wondering,