Long Family's School Expenses: Did They Overpay?

Hey guys! Ever wonder if you've paid the right amount after a big shopping trip? Today, we're diving into a real-life scenario to figure out if a family, the Longs, got their math right when buying school supplies and clothes. We'll break down their expenses, calculate the sales tax, and see if their total matches up. Let's get started and put our math skills to the test!

Understanding the Long Family's Expenses

When it comes to managing finances, especially with back-to-school shopping, it's crucial to keep track of every expense. In this case, the Long family spent $38.62 on school supplies and $215.78 on new school clothes. To figure out if they paid the correct amount, we first need to calculate their total expenses before tax. This involves simply adding the cost of the school supplies and the cost of the clothes: $38.62 + $215.78. The accurate sum of these amounts is paramount for determining the base amount on which sales tax will be calculated. Without this initial calculation, any subsequent steps, such as determining the sales tax or the final amount due, would be inaccurate. Ensuring precision at this stage sets the foundation for the rest of our analysis, allowing us to confidently assess whether the Long family's payment aligns with their purchases. This meticulous approach to expense tracking is not only beneficial for this specific scenario but also serves as a best practice for personal financial management, helping individuals and families maintain a clear understanding of their spending habits and budget effectively. Therefore, let’s meticulously calculate the pre-tax total to ensure we have a solid foundation for our analysis.

Calculating the Sales Tax

Now, let's talk about sales tax. The Long family had to pay a sales tax of 6 4/5% on their purchases. Converting this mixed number percentage to a decimal is essential for accurate calculations. First, we convert the fraction 4/5 to a decimal, which is 0.8. Then, we add this to the whole number 6, giving us 6.8%. To convert a percentage to a decimal, we divide by 100, so 6.8% becomes 0.068. This decimal form is what we'll use to calculate the sales tax amount. The next step involves multiplying the total pre-tax expenses by this decimal. This calculation will give us the actual dollar amount of sales tax the Long family had to pay. Remember, understanding how sales tax is calculated is crucial for anyone managing their finances, ensuring you're not overpaying and that you can accurately budget for purchases. By breaking down the percentage and converting it to a usable decimal, we're making sure our calculations are as precise as possible, setting the stage for a correct final total.

Determining the Total Amount Due

So, we've figured out the pre-tax total and the sales tax rate. Now, it's time to calculate the total amount due. This is a crucial step in our mission to determine if the Long family paid the correct amount. To find the total amount, we need to add the sales tax amount to the pre-tax total expenses. This sum represents the final figure the Long family should have paid, including both the cost of the school supplies and clothes, as well as the sales tax. Accurate addition here is key; any error will affect our conclusion about whether the Longs paid the correct amount. Once we have this total, we can directly compare it to the amount the Long family actually paid, which was $269.07. This comparison will reveal whether there was an overpayment, underpayment, or if the amount paid was exactly right. Understanding how to calculate the total amount due, including sales tax, is a fundamental skill for managing personal finances and ensuring you're always paying the correct amount for your purchases.

Comparing the Calculated Total with the Amount Paid

Alright, we're in the home stretch! We've crunched the numbers and have our calculated total. The final step is to compare this total with the $269.07 that the Long family actually paid. This comparison is straightforward: we subtract our calculated total from the amount they paid. If the result is positive, it means the Long family overpaid. If the result is negative, they underpaid. And if the result is zero, then they paid the exact right amount. This simple subtraction is the key to unlocking our answer. It tells us not only whether there was a discrepancy but also the exact amount of the difference. This final comparison is a critical step in verifying financial transactions, ensuring accuracy, and providing peace of mind. So, let's do this subtraction carefully and see what the numbers reveal about the Long family's payment!

Conclusion: Did the Long Family Pay the Correct Amount?

Okay, guys, after all the calculations, the verdict is in! By carefully calculating the Long family's expenses, factoring in the sales tax, and comparing our total to what they actually paid, we can now definitively answer the question: Did the Long family pay the correct amount? The calculations reveal that The Long family paid $2.63 too much. This exercise highlights the importance of checking your receipts and doing the math yourself, even in everyday shopping scenarios. Understanding how expenses, taxes, and totals are calculated empowers us to be savvy consumers and manage our finances effectively. So, next time you're out shopping, remember the Long family's story and take a moment to double-check your final bill. You might just save yourself a few bucks!