Lucas And The Cell Phone Price A Math Problem
Introduction
Hey guys! Let's dive into a fun math problem that involves our friend Lucas and his quest to buy a new cell phone. Lucas was super interested in getting a phone that initially cost 1000 BRL. However, he thought the price was a bit steep, so he decided to wait, hoping for a better deal. Little did he know, the price would first increase and then decrease! This scenario gives us a great opportunity to explore percentages and how they affect prices. We're going to break down the problem step by step, making sure we understand each calculation and what it means for Lucas's wallet. So, grab your calculators (or just your brains!) and let's get started on this mathematical adventure. We’ll see how the price changes and whether Lucas made the right decision to wait. Remember, math can be super practical, and this is a perfect example of how we use it in everyday situations, like shopping for the latest gadgets!
The Initial Price and the Price Increase
Okay, so our story begins with Lucas eyeing a cell phone that costs 1000 BRL. That's the initial price, our starting point. Lucas, being a smart shopper, decides to hold off on the purchase, thinking the price might drop later. But surprise! The price actually goes up by 30%. Now, how do we figure out what the new price is? This is where percentages come into play. A 30% increase means we need to add 30% of the original price to the original price. To calculate 30% of 1000 BRL, we multiply 1000 by 0.30 (which is the decimal equivalent of 30%). This gives us 300 BRL. So, the price increase is 300 BRL. To find the new price, we add this increase to the original price: 1000 BRL + 300 BRL = 1300 BRL. Wow, that's quite a jump! Now the phone costs 1300 BRL. Lucas might be feeling a bit bummed at this point, but let's see what happens next. Understanding this initial price increase is crucial because it sets the stage for the next part of our problem – the promotion and the subsequent discount. This is a classic example of how prices can fluctuate in the market, and it's important to be able to calculate these changes to make informed decisions.
The Promotion and the Discount
Alright, guys, here’s where things get interesting! After the price jumped up to 1300 BRL, the store decided to run a promotion. This is good news for Lucas! The promotion offers a 30% discount on the increased price. Now, it's super important to remember that this discount is calculated on the new price of 1300 BRL, not the original price of 1000 BRL. This is a common trick that stores use, and it’s something we need to be aware of as consumers. So, to calculate the discount amount, we need to find 30% of 1300 BRL. Just like before, we multiply 1300 by 0.30. This gives us 390 BRL. That's the amount of the discount. Now, to find the final price after the discount, we subtract the discount amount from the increased price: 1300 BRL - 390 BRL = 910 BRL. So, the final price of the phone after the 30% discount is 910 BRL. This is lower than the increased price, but is it lower than the original price? We'll discuss that in the next section. Understanding how discounts work is a key skill in personal finance. Stores often use percentages to make deals seem more attractive, but it's up to us to do the math and see if it's actually a good deal!
Comparing Prices: Was it Worth the Wait?
Now comes the big question: Was it worth it for Lucas to wait? Let's compare the prices to find out. The original price of the phone was 1000 BRL. After the 30% increase, the price went up to 1300 BRL. Then, with the 30% discount on the increased price, the final price became 910 BRL. So, if Lucas had bought the phone initially, he would have paid 1000 BRL. But by waiting, he ended up paying 910 BRL. That's a difference of 90 BRL! It seems like waiting paid off for Lucas, literally. He saved 90 BRL by holding out for the promotion. This is a great example of how timing can be everything when it comes to making purchases. Sometimes, patience can really save you money. However, it's also important to remember that prices can go up as well, as we saw in this case. So, there's always a bit of a gamble involved. In Lucas's case, the gamble paid off. He made a smart decision to wait and ended up getting the phone for a lower price than the original cost. This kind of scenario highlights the importance of understanding percentages and how they affect prices, so we can make informed decisions about our purchases. Always do the math, guys!
Conclusion
So, what have we learned from Lucas's adventure in cell phone shopping? We've seen how prices can change over time, both increasing and decreasing, and how percentages play a crucial role in these changes. Lucas started with a phone priced at 1000 BRL, saw it jump to 1300 BRL after a 30% increase, and finally snagged it for 910 BRL after a 30% discount on the increased price. This journey highlights the importance of understanding how percentages work and how they can impact the final cost of an item. By calculating the price increase and the subsequent discount, we were able to determine that Lucas actually saved money by waiting for the promotion. This is a valuable lesson for all of us as consumers. It shows us that sometimes patience can pay off, but it also reminds us to always do the math and compare prices before making a purchase. Remember, stores use percentages to make deals sound appealing, but it's our job to figure out if they really are. So, next time you're out shopping, channel your inner mathematician and make sure you're getting the best deal possible! And who knows, maybe you'll save some money like Lucas did. Math is everywhere, guys, even in shopping!
