Hey guys! Let's break down a common math problem related to calculating the total cost of an airplane ticket. We'll look at how to figure out the final price, including taxes and fees. This is super useful in real life, especially when you're planning your next vacation or trip!
Understanding the Problem
So, here's the scenario: Charlie bought a plane ticket for $288.00. The tax on the ticket was 7.5%, and he also had to pay an extra $26 in fees. The big question is, how do we figure out the total amount Charlie needs to pay? We need to carefully consider each component of the cost – the base ticket price, the tax, and the additional fees – and then combine them correctly.
Before we dive into the calculations, let's think about the different elements involved. The base ticket price is the initial cost, which is $288.00 in this case. Next, we have the tax, which is a percentage of the base price. In this problem, the tax rate is 7.5%. It's important to remember that percentages are just fractions or decimals in disguise, so we'll need to convert 7.5% into a decimal to do the math. Finally, we have additional fees, which are a flat amount of $26. These fees could be for anything from baggage handling to airport charges.
To find the total cost, we'll need to perform a few steps. First, we'll calculate the amount of tax by multiplying the base ticket price by the tax rate (as a decimal). Then, we'll add this tax amount to the base ticket price. Finally, we'll add the additional fees to get the total cost. It's like building the final price piece by piece, making sure we include all the necessary components.
Now, let's look at some expressions that might represent the total cost and see which one correctly captures the steps we just outlined. We'll pay close attention to the order of operations and make sure we're adding the right things together. Remember, the goal is to find the expression that accurately reflects the total amount Charlie will pay.
Breaking Down the Options
Let's analyze the options provided and see which one correctly calculates Charlie's total cost. The key is to understand the order of operations (PEMDAS/BODMAS) and how to calculate percentages. We'll look at each option step-by-step to see if it makes sense in the context of the problem.
Option A: $288 + (288 ÷ 0.075) - 26
This option starts with the base price of $288, which is a good start. However, the next part looks a little strange: (288 ÷ 0.075). This is dividing the base price by the decimal form of the tax rate. This calculation doesn't make sense in our context because dividing by the tax rate won't give us the tax amount. Instead, we need to multiply by the tax rate to find the tax. The last part, - 26, is subtracting the fees, which is also incorrect. We need to add the fees to the total cost, not subtract them. So, Option A doesn't seem to represent the correct calculation.
To further illustrate why this is incorrect, let's think about what dividing by a small decimal like 0.075 does. Dividing by a decimal less than 1 actually makes the number bigger. In this case, 288 divided by 0.075 results in a much larger number than the original price, which isn't what we want when calculating tax. We need a smaller number that represents the tax amount, not a larger one. The subtraction of fees at the end also deviates from the correct process of adding all costs together.
Option B: $288 - (288 × 0.075)
This option begins with the base price of $288, which is a positive sign. The next part, (288 × 0.075), correctly calculates the tax amount by multiplying the base price by the tax rate in decimal form. However, the minus sign in front of this calculation indicates that we're subtracting the tax from the base price. This is not what we want to do; we need to add the tax to the base price to find the total cost. This option also completely omits the additional fees, which are a crucial part of the total cost. Therefore, Option B is not the correct way to calculate the total amount Charlie will pay.
The expression in Option B only accounts for the price after deducting the tax amount, which is not a practical scenario in real-life purchases. When you buy something, you always have to pay the tax in addition to the original price. So, subtracting the tax doesn't align with the goal of finding the total cost. Furthermore, the absence of the additional fees in this expression means that it's missing a significant component of the total expense. To get an accurate total, we must ensure that all relevant costs, including the base price, tax, and fees, are included in our calculation.
Finding the Correct Expression
Now that we've ruled out the incorrect options, let's think about how we should correctly calculate Charlie's total cost. We need to include three main components: the base ticket price, the tax amount, and the additional fees. We already know the base price is $288.00, and the additional fees are $26. The missing piece is the tax amount, which we can calculate by multiplying the base price by the tax rate (as a decimal).
The tax rate is 7.5%, which is equivalent to 0.075 as a decimal. So, the tax amount is $288.00 × 0.075. Once we have this tax amount, we simply need to add it to the base price and the additional fees to get the total cost. This means the correct expression should look something like: Base Price + (Base Price × Tax Rate) + Additional Fees.
To write this out with the specific numbers from our problem, the expression should be: . This expression accurately represents the steps we need to take to find the total cost. First, we calculate the tax amount (288 × 0.075). Then, we add this tax amount to the base price ($288). Finally, we add the additional fees ($26) to get the total amount Charlie will pay. This is the logical and correct way to approach the problem.
Now, let's put this all together and show the final calculation. First, we calculate the tax: $288 × 0.075 = $21.60. Next, we add the tax to the base price: $288 + $21.60 = $309.60. Finally, we add the additional fees: $309.60 + $26 = $335.60. So, the total amount Charlie will pay is $335.60. This step-by-step calculation confirms that our expression is correct and leads us to the accurate answer.
The Correct Calculation
Based on our analysis, the correct way to calculate Charlie's total cost is to add the tax amount and the additional fees to the base ticket price. The tax amount is calculated by multiplying the base price by the tax rate (as a decimal). So, the correct expression is:
$288 + (288 × 0.075) + 26
Let's break this down step by step to make sure we understand each part:
- Calculate the tax amount: $288 × 0.075 = $21.60
- Add the tax to the base price: $288 + $21.60 = $309.60
- Add the additional fees: $309.60 + $26 = $335.60
So, Charlie will pay a total of $335.60. This calculation ensures that we've included all the costs associated with the airplane ticket: the base price, the tax, and the additional fees. By following these steps, we can accurately determine the total expense.
Understanding how to calculate these costs is super practical. Whether you're buying a plane ticket, booking a hotel, or making any purchase with taxes and fees, you can use this method to figure out the final amount you'll need to pay. It's all about breaking down the problem into smaller steps and making sure you're adding the right things together. This way, you can avoid any surprises at the checkout and budget effectively.
Real-World Application
This type of calculation isn't just for math problems; it's something you'll use in real life all the time! Think about it – whenever you buy something, there's often tax involved. And for services like flights or event tickets, there are usually additional fees. Knowing how to calculate these costs can help you budget effectively and make informed decisions.
For example, let's say you're planning a trip. You see a flight advertised for $300, but you know there will be taxes and fees on top of that. If the tax is 8% and the fees are $50, you can quickly calculate the total cost. First, you find the tax amount: $300 × 0.08 = $24. Then, you add the tax to the base price: $300 + $24 = $324. Finally, you add the fees: $324 + $50 = $374. So, the total cost of the flight is $374. This is a significant difference from the advertised price of $300, and it's important to know this upfront so you can plan your budget accordingly.
Another common scenario is when you're shopping online. Many online retailers add sales tax and shipping fees to your order. Before you click the "checkout" button, it's a good idea to review the total cost and make sure you're comfortable with the amount. You can use the same method we discussed earlier to calculate the total cost: add the tax (if applicable) and the shipping fees to the price of the items you're buying.
Understanding these calculations also helps you compare prices from different vendors. Sometimes, a lower base price might seem like a better deal, but once you factor in taxes and fees, it might actually be more expensive than another option with a slightly higher base price but lower additional costs. Being able to quickly calculate the total cost allows you to make the most cost-effective choice.
So, whether you're booking a flight, shopping online, or just making everyday purchases, remember the importance of calculating the total cost, including taxes and fees. It's a valuable skill that will help you manage your finances and make smart spending decisions.
Conclusion
In conclusion, calculating the total cost of something like an airplane ticket involves adding the base price, the tax amount, and any additional fees. We learned that the correct expression to calculate Charlie's total cost was:
$288 + (288 × 0.075) + 26
This expression accurately represents the steps needed to find the total amount: calculate the tax, add it to the base price, and then add the fees. Remember, it's super important to consider all these components to get an accurate final price. This skill is useful in many real-life situations, from booking travel to shopping online. So, next time you're faced with a similar problem, you'll know exactly how to solve it! Keep practicing, and you'll become a pro at calculating total costs in no time. You've got this!