Calculating Total Cost With Sales Tax Alice's Cloth Purchase
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In this article, we will delve into a practical math problem involving calculating the total cost of a purchase with sales tax. We will break down the steps involved in finding the solution, providing a clear and concise explanation for anyone looking to improve their understanding of basic arithmetic and percentage calculations. Let's take a closer look at the problem presented and explore how to arrive at the correct answer. Math problems can be easily understood if we tackle them step by step. Our goal is to help you understand the process of calculation so you can apply the formula for your future needs. Understanding the fundamentals of sales tax calculation is vital for everyone. Whether you're a student studying basic math or simply someone looking to manage your personal finances effectively, grasping these concepts can empower you to make informed decisions and avoid financial pitfalls. In the following sections, we'll dissect the problem, break down each calculation, and highlight the key principles involved, ensuring that you gain a solid understanding of how to calculate costs with sales tax.
The Problem: Alice's Fabric Purchase
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The core of our discussion revolves around the following scenario: Alice Correa needed fabric to sew a dress. She found a fabric that was on sale for $1.93 per yard. Alice bought exactly three yards. The local sales tax rate was 5%. The main question that we will answer is: How much did Alice ultimately pay for the fabric, including the sales tax? This is a common type of problem involving basic multiplication and percentage calculations, skills essential for everyday financial literacy. By carefully working through this example, you'll gain confidence in tackling similar scenarios, whether you're shopping at a store, budgeting for expenses, or analyzing financial data. Let's break down the problem and identify the steps we need to solve it.
Step 1: Calculating the Initial Cost
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The first crucial step in solving this problem is determining the cost of the fabric before the sales tax is applied. We know Alice purchased three yards of cloth, and each yard was priced at $1.93. To find the total cost, we need to multiply the number of yards by the price per yard. This can be expressed as a simple multiplication problem: 3 yards * $1.93/yard. When performing this calculation, it's important to align the decimal points correctly to ensure accuracy. The multiplication process involves multiplying each digit of $1.93 by 3 and then summing the results. We can manually calculate the result, or we can also use a calculator. Calculating the initial cost is a crucial step as it forms the basis for subsequent calculations, including the sales tax and the final amount due. A precise calculation at this stage ensures the accuracy of the final answer. Make sure to double-check your calculations and be attentive to details like decimal placement to minimize errors.
Manual Calculation
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To calculate the total cost manually, we multiply 3 by each digit of $1.93:
- 3 * 3 (cents) = 9 cents
- 3 * 9 (dimes) = 27 dimes, which is $2.70
- 3 * 1 (dollar) = $3
Now, we add these values together:
$3 + $2.70 + $0.09 = $5.79
Result
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Therefore, the initial cost of the cloth before sales tax is $5.79. This result represents the amount Alice would have paid if there were no sales tax involved. It's a fundamental value that we'll use in the next step to calculate the sales tax amount.
Step 2: Calculating the Sales Tax
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Having determined the initial cost of the fabric, our next crucial step is to calculate the sales tax. We know the sales tax rate is 5%, which means we need to find 5% of the initial cost, $5.79. Percentage calculations are a fundamental aspect of everyday financial transactions, so mastering this skill is essential. The sales tax is calculated by multiplying the initial cost by the sales tax rate (expressed as a decimal). In this case, we need to multiply $5.79 by 0.05 (which is the decimal equivalent of 5%). The result of this multiplication will give us the amount of sales tax Alice has to pay. This amount will then be added to the initial cost to determine the final amount due.
Manual Calculation
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To calculate 5% of $5.79, we multiply $5.79 by 0.05:
$5.79 * 0.05 = $0.2895
Since we're dealing with currency, we need to round this to two decimal places. The third decimal place is 9, which is greater than or equal to 5, so we round up the second decimal place:
$0.2895 ≈ $0.29
Result
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Thus, the sales tax amount is approximately $0.29. This value represents the additional cost that Alice will incur due to the sales tax. Now that we know both the initial cost and the sales tax, we can move on to the final step of calculating the total cost.
Step 3: Calculating the Total Cost
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Now that we've calculated both the initial cost of the fabric ($5.79) and the sales tax ($0.29), we can determine the total amount Alice paid. The total cost is simply the sum of the initial cost and the sales tax. This calculation is straightforward: we add the two amounts together. The result will give us the final price Alice paid for the fabric, including all applicable taxes. This is the answer we're seeking – the total expenditure Alice made on her fabric purchase. Understanding how to calculate total cost is crucial for budgeting, managing finances, and making informed purchasing decisions. It allows us to know the actual cost of an item after accounting for taxes and other fees, thereby ensuring transparency in transactions.
Calculation
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To find the total cost, we add the initial cost and the sales tax:
$5.79 (initial cost) + $0.29 (sales tax) = $6.08
Result
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Therefore, the total amount Alice paid for the cloth, including sales tax, is $6.08. This is the final answer to our problem.
The Correct Answer
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Based on our calculations, the correct answer to the question "How much did Alice pay for the cloth if the sales tax was 5%?" is:
C. $6.08
We arrived at this answer by systematically breaking down the problem into smaller, manageable steps: first, calculating the initial cost, then determining the sales tax, and finally, adding the two amounts together to find the total cost. This step-by-step approach is a valuable strategy for solving math problems, as it helps to minimize errors and promotes a clear understanding of the process.
Conclusion
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In conclusion, this exercise demonstrates the practical application of basic arithmetic skills in real-life scenarios. By understanding how to calculate costs with sales tax, we can make informed financial decisions and effectively manage our budgets. The problem involving Alice's fabric purchase highlights the importance of breaking down complex problems into simpler steps, ensuring accuracy in calculations, and applying fundamental mathematical principles. The final result, $6.08, represents the total cost Alice incurred, illustrating the cumulative effect of initial prices and sales tax. Whether it's shopping, budgeting, or financial analysis, the ability to perform these calculations accurately is a valuable skill for everyone. We encourage you to practice these types of problems to further enhance your understanding and confidence in handling financial calculations.
