Original CD Price: Solving A Discount Problem

Hey guys! Let's dive into this math problem together and figure out the original price of those CDs. It sounds like we got a sweet deal with a discount, but now we need to rewind and find out what each CD cost before the savings kicked in. So, grab your calculators (or your mental math muscles) and let's get started!

Breaking Down the Problem

Okay, so here's the situation: you bought four identical compact discs (CDs), and you received a discount of $18.00. The total amount you paid after the discount was $274.00. The mission? To find the original price of each CD before the discount was applied. To make this super clear, we're going to break down each piece of information step by step. This way, we can build a solid understanding and nail the solution like true math pros. First, we know the final price after the discount, which is our starting point for working backwards. Next, we have the discount amount, which we'll need to add back in to find the original total cost. Lastly, we know the number of CDs, which will help us calculate the original price per CD. By identifying these key pieces, we set ourselves up for success in solving the problem accurately. Remember, math problems are like puzzles – each piece of information is a clue that helps us uncover the final answer.

Understanding the Key Information

Let's really break down the key information we've got in this problem. This is super important because understanding what each number represents is the first step to solving it correctly. We know the discount amount is $18.00. This is the amount of money that was taken off the total price. Think of it like a coupon or a special deal you snagged. Then, we have the total paid, which is $274.00. This is the amount you actually handed over at the checkout after the discount was applied. It's the final price you paid. And finally, we know that you bought four CDs. This tells us how many items we're dealing with, which is crucial for finding the individual price of each CD. Now, why is this breakdown so important? Well, imagine trying to bake a cake without knowing the ingredients! You need to know what each number means before you can start using them in your calculations. By identifying these key pieces – the discount, the total paid, and the number of CDs – we're setting the stage for a smooth solution. We're like detectives gathering clues before cracking the case. So, always take a moment to understand the information before you jump into the math. It'll save you time and brainpower in the long run!

Setting Up the Equation

Alright, let's get down to the nitty-gritty and set up the equation that's going to help us solve this CD price mystery. Think of an equation like a recipe – it tells us exactly what steps to take to get to our answer. In this case, we need to figure out the original total cost before the discount, and then divide that by the number of CDs to find the price of each one. So, let's break it down. First, we need to reverse the discount. We know the total paid ($274.00) is the price after the $18.00 discount. To find the original price, we need to add the discount back in. This gives us the total cost before the discount. Then, once we have that original total cost, we'll divide it by the number of CDs (which is four) to find the original price per CD. We can represent this with an equation like this: (Total Paid + Discount) / Number of CDs = Original Price per CD. See? It's like a roadmap to the solution! By setting up the equation clearly, we're making sure we follow the right steps and don't get lost in the numbers. Now, let's plug in the values and solve this thing!

Solving for the Original Price

Now comes the fun part – actually solving the equation! We've already set up our roadmap, so let's follow it step-by-step to uncover the original price of each CD. Remember our equation? It looks like this: (Total Paid + Discount) / Number of CDs = Original Price per CD. So, let's plug in the values we know. The total paid is $274.00, the discount is $18.00, and the number of CDs is 4. Our equation now looks like this: ($274.00 + $18.00) / 4 = Original Price per CD. The first thing we need to do is tackle the addition inside the parentheses. What's $274.00 plus $18.00? That's $292.00! So, our equation now looks like this: $292.00 / 4 = Original Price per CD. Now, we're down to a simple division problem. We need to divide $292.00 by 4. If you whip out your calculator (or do some long division), you'll find that $292.00 divided by 4 is $73.00. Ta-da! We've found the original price of each CD. So, the original price of each CD was $73.00. See? By following our equation step-by-step, we arrived at the answer without any confusion. Let's break this down further to ensure everyone is following along.

Step-by-Step Calculation

Let's walk through the calculation step-by-step to make absolutely sure we've got it down. Sometimes, seeing the process laid out clearly can make all the difference. Remember, our goal is to find the original price of each CD, and we're doing that by working backwards from the discounted price. Step 1: Find the Original Total Cost. We know the total paid after the discount was $274.00, and the discount was $18.00. To find the original total cost, we add the discount back in: $274.00 + $18.00 = $292.00. So, the original total cost of the four CDs was $292.00. Step 2: Divide the Original Total Cost by the Number of CDs. Now that we know the original total cost, we can divide it by the number of CDs (which is 4) to find the price of each one: $292.00 / 4 = $73.00. This means each CD originally cost $73.00. And that's it! We've successfully calculated the original price of each CD. By breaking the problem down into these two simple steps, we made it much easier to solve. Always remember, when you're tackling a math problem, break it down into smaller, more manageable steps. It'll help you stay organized and avoid making mistakes.

Verifying the Solution

It's always a good idea to verify your solution to make sure you didn't make any sneaky errors along the way. Think of it as double-checking your work to ensure you got the right answer. So, how can we verify our solution in this case? Well, we found that the original price of each CD was $73.00. If that's correct, then four CDs should cost 4 * $73.00 = $292.00. Now, we know there was an $18.00 discount, so let's subtract that from the original total cost: $292.00 - $18.00 = $274.00. And guess what? That's exactly the total amount we paid! This confirms that our solution is correct. We can be confident that each CD originally cost $73.00. Verifying your solution is a super important habit to get into. It's like having a safety net – it catches you if you've made a mistake. Plus, it gives you peace of mind knowing that you've got the right answer. So, always take a few extra moments to double-check your work. It's worth it!

Final Answer and Explanation

Okay, let's bring it all together and give a clear final answer and explanation. We started with a problem where you bought four CDs, got an $18.00 discount, and paid a total of $274.00. Our mission was to figure out the original price of each CD before the discount. We tackled this by first understanding the key information: the discount amount, the total paid, and the number of CDs. Then, we set up an equation to guide our calculations: (Total Paid + Discount) / Number of CDs = Original Price per CD. We plugged in the values, did the math, and found that the original price of each CD was $73.00. To be extra sure, we verified our solution by multiplying the original price by the number of CDs and then subtracting the discount. This confirmed that our answer was correct. So, the final answer is: the original price of each CD was $73.00. We solved this problem by working backwards, adding the discount back in, and then dividing by the number of items. This is a common strategy for solving math problems, and it's a great tool to have in your problem-solving toolkit. Remember, math is like a puzzle, and every piece of information helps you find the solution. Keep practicing, and you'll become a math master in no time!

Conclusion

So, there you have it! We successfully navigated this math problem and discovered the original price of those CDs. By breaking down the problem, setting up an equation, and verifying our solution, we showed how to tackle similar challenges with confidence. Remember, math isn't about memorizing formulas – it's about understanding the logic and applying it step by step. We hope this explanation has helped you grasp the concepts and feel more comfortable with problem-solving. Keep practicing, keep exploring, and most importantly, keep having fun with math! You've got this!