Parking Time: How Many Hours With $5500?

Hey guys! Ever found yourself wondering how long you can park your car with a certain amount of money? Let's break down a real-world math problem about parking fees. We'll explore how to figure out the maximum parking time given a starting fee and an hourly rate, just like our friend Luis trying to make the most of his $5500. This is super practical math that can help you plan your day and your budget. So, let’s dive in and make sure Luis (and you!) get the best parking deal possible!

Understanding the Parking Fee Structure

When tackling parking fee problems, the first crucial step is to understand the fee structure completely. In our case, the parking lot charges a flat rate of $1200 for the initial hour. This means that whether you park for just 15 minutes or the full hour, you'll pay the same $1200. After the first hour, the rate changes to $800 for each additional hour. This tiered system is common in many parking facilities, so grasping it is essential for accurate calculations.

Why is understanding the structure so important? Imagine if you just multiplied the total hours by the additional hourly rate – you’d completely miss the initial hour's fixed cost, leading to a significant underestimation of the total parking fee. By carefully identifying the fixed cost ($1200 for the first hour) and the variable cost ($800 for each subsequent hour), we set the stage for a precise calculation. Think of it like this: the initial hour is the entry ticket, and the additional hours are the cost of the ride. Getting this distinction right is the key to solving the problem accurately and making smart decisions about your parking time and budget.

To make it even clearer, let’s consider a few scenarios. If Luis parks for exactly one hour, he pays $1200. If he parks for two hours, he pays $1200 for the first hour plus $800 for the second hour, totaling $2000. See how the initial hour’s cost doesn’t change, but the additional hours add up? By recognizing this pattern, we can start building a formula to figure out the maximum number of hours Luis can park with his $5500. So, let's move on to the next step and start crunching those numbers!

Calculating Remaining Money After the First Hour

Okay, so we know the first hour costs $1200. Luis starts with $5500. The next logical step is figuring out how much money he has left after paying for that initial hour. This is a simple subtraction problem, but it's a critical step in solving the overall question. We need to know the remaining amount to determine how many additional hours Luis can afford. So, let's get right to it!

To find the remaining money, we subtract the cost of the first hour ($1200) from Luis's total budget ($5500). This calculation will tell us exactly how much money is available for the additional hours at the $800 per hour rate. Think of it as clearing the first hurdle – once we know what’s left, we can focus on the remaining challenge: how many $800 chunks fit into the leftover amount. The math looks like this:

$5500 (Total budget) - $1200 (Cost of the first hour) = $4300 (Remaining money)

So, after paying for the first hour, Luis has $4300 remaining. This is the amount we'll use to figure out how many additional hours he can park. This step highlights the importance of breaking down the problem into smaller, manageable parts. We didn't try to solve everything at once; instead, we focused on one specific piece of information: the money left after the first hour. By doing this, we've made the problem much clearer and set ourselves up for the next calculation. Now that we know Luis has $4300 for additional parking time, we can move on to determining how many of those $800 hourly charges he can cover. Let's keep going!

Determining the Number of Additional Hours

Alright, guys, we've reached the crux of the problem: figuring out how many additional hours Luis can park with his remaining $4300. We know each additional hour costs $800, so we need to determine how many times $800 fits into $4300. This is a division problem, and it will give us the number of additional hours Luis can afford. This step is vital because it directly answers the main question – how long can Luis park?

To find the number of additional hours, we'll divide the remaining money ($4300) by the cost per additional hour ($800). The result will tell us how many full hours Luis can park, and any remainder will indicate whether he can afford part of another hour. The math looks like this:

$4300 (Remaining money) / $800 (Cost per additional hour) = 5.375 hours

Now, here’s a super important point: we can’t have a fraction of a parking hour in this context. Luis can park for a full hour or not at all – the parking lot isn’t going to charge him for just 0.375 of an hour. So, we need to round down to the nearest whole number. In this case, 5.375 hours means Luis can afford 5 additional hours. This highlights the practical side of math – sometimes, you need to consider real-world constraints to get the right answer.

So, we've figured out that Luis can park for 5 additional hours. But remember, we also need to include that first hour we already accounted for. Let’s put it all together in the final step and find the total parking time!

Calculating Total Parking Time

Okay, we're in the home stretch! We've done all the hard work, and now it's time to put the pieces together. We know Luis can park for one initial hour and an additional 5 hours with his $5500. To find the total parking time, we simply need to add these two values together. This final step is crucial because it provides the complete answer to the question: for how many hours can Luis park?

The calculation is straightforward:

1 hour (Initial hour) + 5 hours (Additional hours) = 6 hours

So, Luis can park for a total of 6 hours with his $5500. This is the answer we were looking for! By breaking down the problem into smaller, manageable steps – understanding the fee structure, calculating the remaining money, and determining the number of additional hours – we were able to solve it accurately and efficiently.

This problem illustrates how math can be used in everyday situations, like planning your parking time and budget. By understanding the principles and applying them step-by-step, you can tackle similar challenges with confidence. Remember, it’s all about breaking it down and taking it one step at a time. You got this! Now you know exactly how to help Luis (and yourself) figure out parking situations. Keep practicing, and you’ll become a master of real-world math problems!