Laptop Discount: Unraveling The Original Price

by Dimemap Team 47 views

Hey guys, let's dive into a fun math problem! Imagine you're eyeing a brand-new laptop at the store. It's got a fantastic 20% discount, bringing the price down to 12,000 Ukrainian hryvnias (UAH). But hold on, the price tag tells a story! This discount is layered on top of another discount, a 15% reduction from a previous price. And guess what? That price itself was already slashed by 10% from the original cost. Our mission? To uncover the original price of this techy treasure. Sounds like a challenge, right? Don't worry, we'll break it down step by step, making it super easy to understand. We'll be using some basic algebra to work our way backward and uncover the laptop's journey from its original price to the final discounted price. Get ready to flex those math muscles and become a discount detective! This problem isn't just about numbers; it's about understanding how percentages work and how discounts can be combined. So, grab a pen and paper (or your favorite calculator), and let's unravel this price puzzle together. Are you ready to crack the code and find out the true cost of that laptop? Let the calculations begin!

This is a classic example of a multi-step percentage problem. These types of problems are common in real-world scenarios, from shopping to finance. Understanding how to solve them can help you make informed decisions. We need to remember that each discount is applied to the reduced price from the previous discount. This means we can't simply add the percentages together. We'll need to work backward, undoing each discount to reveal the original price. This involves a bit of algebra, but it's nothing too scary, I promise! We'll start with the final price and work our way back, step by step, to find the initial price before any discounts were applied. It's like peeling back the layers of an onion, or in this case, a price tag. Let's get started!

Unpacking the Final Discount: Finding the Price Before the 20% Reduction

Alright, let's start with the last piece of the puzzle: the final 20% discount. We know the laptop's price after this discount is 12,000 UAH. This price represents 80% of the price before the 20% reduction because 100% - 20% = 80%. In mathematical terms, let's say 'x' is the price before the 20% discount. We can set up the equation: 0.80 * x = 12,000 UAH. Now, to solve for 'x', we need to divide both sides of the equation by 0.80. This gives us: x = 12,000 UAH / 0.80 = 15,000 UAH. So, the price of the laptop before the 20% discount was 15,000 UAH. We've already made some progress, and it's starting to get clearer! This step is crucial because it helps us understand the price at the beginning of the journey. Next, we will use that value to find the next part, so keep reading!

This is where understanding the concept of percentages is critical. Remember that a percentage is just a fraction out of 100. So, 20% means 20/100, or 0.20 when written as a decimal. When we apply a discount, we're essentially taking a percentage off the original price. The remaining price is the percentage that we pay. In this case, we're paying 80% (or 0.80) of the price. Dividing the final price by 0.80 effectively 'undoes' the discount and takes us back to the original price before the discount was applied. Now we know, before that 20% off it was 15,000 UAH, we need to know what was the price before the 15% discount. Now, let's go on to the next phase!

Reversing the 15% Discount: Uncovering the Price Before the Second Reduction

Okay, now that we know the price before the final 20% discount (15,000 UAH), let's rewind a bit further. The price of 15,000 UAH was itself the result of a 15% discount. This means 15,000 UAH represents 85% of the price before the 15% reduction because 100% - 15% = 85%. Let's denote this price as 'y'. Our equation becomes: 0.85 * y = 15,000 UAH. To solve for 'y', we divide both sides by 0.85: y = 15,000 UAH / 0.85 ≈ 17,647.06 UAH. So, the price of the laptop before the 15% discount was approximately 17,647.06 UAH. Great, we're making excellent progress! We're steadily working our way back to the initial price. Each step brings us closer to the solution. Now, let us go to the first discount, the 10% one!

This step highlights the importance of understanding the order in which discounts are applied. Each discount is calculated based on the previous reduced price, not the original price. This means that a 15% discount on a reduced price isn't the same as a 15% discount on the original price. The final price is lower. Be careful about where the discount is applied! Also, the values that we calculated are approximate, since the actual value includes many decimals. Just remember that the approximation is not precise but is sufficient for the exercise's end. We're now two steps away from the original price, and the final step is on its way, so buckle up and keep reading!

Unveiling the Original Price: Undoing the Initial 10% Discount

We're in the home stretch, guys! We've successfully reversed the 20% and 15% discounts. Now, it's time to tackle the 10% discount from the very beginning. We know that the price before the 15% discount (approximately 17,647.06 UAH) was the result of a 10% discount. This means 17,647.06 UAH represents 90% of the original price because 100% - 10% = 90%. Let 'z' be the original price. Our equation is: 0.90 * z = 17,647.06 UAH. To find 'z', we divide both sides by 0.90: z = 17,647.06 UAH / 0.90 ≈ 19,607.84 UAH. Therefore, the original price of the laptop was approximately 19,607.84 UAH! We did it! We successfully traced the discounts back to reveal the laptop's original price. Well done, everyone!

This final step demonstrates how to work backward through multiple discounts. Each discount changes the base price for the next discount, making it essential to reverse each step carefully. Also, note that due to rounding, the final answer might vary slightly depending on how you round the intermediate values, but the difference is minimal. Remember to use at least two decimal places for accuracy. Now, you should be able to solve these types of problems in the future. Congratulations!

Conclusion: Decoding the Laptop's Price Journey

Congratulations, guys! We've successfully unraveled the puzzle of the laptop's original price. Through careful calculations and step-by-step analysis, we've gone from the discounted price back to the beginning. We've shown that the original price was approximately 19,607.84 UAH. This entire process demonstrates the importance of understanding how percentages and discounts work in the real world. Now you know the value of your shopping discount! These skills can be applied to other financial situations, such as calculating sales tax, understanding interest rates, and making informed purchasing decisions. So, the next time you see a discount, you'll be able to confidently figure out the original price and make a smart decision. Keep practicing these types of problems, and you'll become a discount detective in no time! Remember, math is everywhere, and with a little practice, it can be fun and empowering. Happy shopping, and keep those math muscles flexed!

Summary of Steps and Equations

Let's recap the steps and equations we used:

  1. Final Discount (20%):

    • Final Price: 12,000 UAH
    • Equation: 0.80 * x = 12,000 UAH
    • Price before 20% discount (x) = 15,000 UAH

  2. Second Discount (15%):

    • Price before 20% discount: 15,000 UAH
    • Equation: 0.85 * y = 15,000 UAH
    • Price before 15% discount (y) ≈ 17,647.06 UAH

  3. Initial Discount (10%):

    • Price before 15% discount: ≈ 17,647.06 UAH
    • Equation: 0.90 * z = 17,647.06 UAH
    • Original Price (z) ≈ 19,607.84 UAH

This summary makes it easy to review the steps we took and the equations we used. It's a great reference for solving similar problems in the future. Remember that understanding the concepts behind the calculations is just as important as the math itself. Keep up the excellent work, and enjoy your new skills!