The Mathematics Behind Price Increases: A Simple Breakdown

Understanding the intricacies of price adjustments can sometimes feel like attempting a tricky math puzzle, can't it? Especially when you're faced with real-world questions like, “After its price increased by 20% and then by another $24, what was the final price of the Bluetooth speaker?” If you cringed a little at that thought, don't worry! This breakdown will make everything crystal clear.

Let’s kick this off by setting the stage. We’ve got a Bluetooth speaker here, and we need to determine its final price after two distinct increases: a percentage increase followed by a flat dollar increase. We'll dig into the nitty-gritty of the calculations, but hold tight—this isn't just for the math whizzes in the crowd. This is relatable stuff for anyone who's ever wondered how much more they'd pay at the checkout.

Step 1: Define the Original Price

First things first, let’s establish a baseline. Suppose we call the original price of the Bluetooth speaker "x." It feels more official that way, right? After all, knowing where you start makes it easier to see the changes down the line.

Step 2: Calculate the Price Increase Percentage

Now, this is where it gets a bit tricky. When we increase the price by 20%, the new price becomes:

[ 1.20x ]

This might sound a touch complicated, but all we’re doing is taking the original price and multiplying it by 1.20 (which accounts for both the original price and the 20% increase). It's sort of like adding a slice of cake to a whole cake—you're not losing anything, just gaining extra sweetness.

Step 3: Add the Flat Dollar Increase

Next up, we need to factor in that additional $24. So, our equation now transforms into:

[ 1.20x + 24 ]

But hang on! We’ve got to figure out what x needs to be in order for the final price to hit $168, as given in our question choices. Let’s set up an equation, shall we?

[ 1.20x + 24 = 168 ]

Step 4: Isolate x

Now, let’s isolate our variable (which we called x). It’s like trying to find your car keys—you just need to hunt down that sneaky little variable!

Subtract 24 from both sides:

[ 1.20x = 168 - 24 ]

Simplifying that gives us:

[ 1.20x = 144 ]

To find x, divide both sides by 1.20:

[ x = \frac{144}{1.20} = 120 ]

Aha! So the original price of our Bluetooth speaker was $120. But let’s see where this takes us next.

Step 5: Verify and Conclude

Now that we know x, let’s apply our findings back to confirm everything fits, like a perfect puzzle piece.

1. Starting with the original price of $120, we apply the 20% increase: [ 1.20 \times 120 = 144 ]

2. Next, sprinkle in that extra $24: [ 144 + 24 = 168 ]

And voilà! The final price is indeed $168.

Wrapping Up

Understanding how to solve problems like these is not just crucial for a test but also pretty handy in daily life. Whether you’re shopping online or budgeting for a special purchase, realizing how price adjustments work can save you some serious cash (or at least help you plan ahead!). So, the next time you face a price increase of your own, you’ll handle it like a pro!

Curious about other math concepts? Or perhaps you'd like to tackle different types of questions? The world of cognitive aptitude tests is vast and rich with challenges that develop useful skills for various situations. Continue exploring, and keep honing those calculations!