Did The Long Family Pay The Right Amount For School Supplies And Clothes

by Henrik Larsen 73 views

Hey guys! Let's dive into a real-world math problem that involves calculating expenses, sales tax, and verifying if the final amount paid is correct. We'll break down the scenario step-by-step, making it super easy to understand. So, put on your thinking caps, and let's get started!

The Long Family's Back-to-School Shopping Spree

The Long family went on a back-to-school shopping trip and spent $38.62 on essential school supplies and $215.78 on some fresh, new school clothes. As we all know, shopping usually involves sales tax, and in this case, they had to pay a sales tax of 645%6 \frac{4}{5}\%. The family's total expenditure came out to be $269.07. Our mission, should we choose to accept it, is to determine if the Long family actually paid the correct amount. Let's break down how we can solve this problem.

Calculating the Total Cost Before Tax

First things first, we need to figure out the total cost of the items before sales tax is applied. This is a straightforward addition problem. We'll add the cost of the school supplies and the cost of the school clothes together:

$38.62 (school supplies) + $215.78 (school clothes) = $254.40

So, the Long family spent a total of $254.40 on school supplies and clothes before tax. This is a crucial number because we'll use it to calculate the sales tax amount. It’s like the foundation of our calculation, guys. Without this base amount, figuring out the tax would be like trying to build a house without a foundation – pretty tricky!

Converting the Sales Tax Percentage

Now, let's tackle the sales tax. We know it's 645%6 \frac{4}{5}\%, but to work with it easily, we need to convert this mixed number percentage into a decimal. Here's how we do it:

  1. Convert the mixed number to an improper fraction: 645=(6×5)+45=3456 \frac{4}{5} = \frac{(6 \times 5) + 4}{5} = \frac{34}{5}
  2. Convert the improper fraction to a decimal: 345=6.8\frac{34}{5} = 6.8
  3. Convert the percentage to a decimal: 6. 8% = 6. 8 / 100 = 0.068

So, the sales tax rate in decimal form is 0.068. This is the magic number we'll use to calculate the actual dollar amount of the tax. Remember, percentages are just fractions out of 100, so converting them to decimals makes them much easier to work with in calculations. It’s like translating a foreign language – once you understand the code (decimal), everything becomes clearer!

Calculating the Sales Tax Amount

Alright, we've got the total cost before tax ($254.40) and the sales tax rate (0.068). Now, we need to calculate how much sales tax the Long family paid. To do this, we simply multiply the total cost before tax by the sales tax rate:

$254.40 * 0.068 = $17.30

Therefore, the sales tax amount is $17.30. This is the extra amount the Long family had to pay on top of the cost of the items themselves. It’s like the price of admission to the world of consumerism, guys! Sales tax is a common part of shopping, and understanding how to calculate it is a super useful life skill.

Calculating the Total Amount Due

Now that we know the cost of the items before tax and the sales tax amount, we can calculate the total amount the Long family should have paid. We simply add the two amounts together:

$254.40 (cost before tax) + $17.30 (sales tax) = $271.70

So, according to our calculations, the Long family should have paid a total of $271.70. This is the final price tag, including both the cost of the goods and the government's share (sales tax). We’re almost at the finish line, guys! Now we just need to compare this amount with what the Long family actually paid.

Did the Long Family Pay the Correct Amount?

Here's the moment of truth! We calculated that the Long family should have paid $271.70, but they actually paid $269.07. Let's compare these two amounts:

  • Calculated Total: $271.70
  • Amount Paid: $269.07

It looks like there's a difference of $2.63 ($271.70 - $269.07 = $2.63). This means the Long family paid $2.63 less than what they should have, according to our calculations. This could be due to a number of reasons, such as a miscalculation at the store, a discount that wasn't initially accounted for, or perhaps a slight error in our calculations (though we've been pretty careful!).

Possible Explanations for the Discrepancy

So, what could explain this $2.63 difference? Here are a few possibilities:

  1. Store Error: It's possible that the store's system made a slight error when calculating the sales tax. Sometimes, technology glitches happen!
  2. Unaccounted Discount: Maybe the Long family had a coupon or received a discount that wasn't initially factored into our calculations. Stores often have promotions or special offers that can reduce the final price.
  3. Rounding Differences: Depending on how the store calculates sales tax on individual items and then rounds the total, there might be slight differences due to rounding.
  4. Our Calculation Error: While we've tried to be precise, there's always a small chance we might have made a minor error in our calculations. Math is fun, but it requires attention to detail!

Conclusion: A Penny Saved is a Penny Earned... Or Is It?

In conclusion, based on our calculations, the Long family paid $2.63 less than what we calculated they should have paid. While this might seem like a small amount, it's a great example of how important it is to double-check your receipts and understand how sales tax works. Whether it's a store error, a hidden discount, or a rounding issue, knowing how to calculate these things yourself can save you money and ensure you're paying the correct amount.

So, did the Long family pay the correct amount? Technically, no. But hey, maybe they got a lucky break! This exercise highlights the importance of understanding basic math concepts in everyday situations. Keep those calculators handy, guys, and always double-check your totals!

Keywords: school supplies, school clothes, sales tax, total cost, calculate