Alicia Buys 4 Scarves. She Pays $75.20 Plus An Additional $5.26 In Tax For The Scarves. Alicia Determines the total cost of her purchase, including taxes, and explores how to calculate the price per scarf. This scenario provides a practical example of understanding unit prices, calculating percentages, and applying basic algebra to real-world shopping situations. Whether you’re a student learning about percentages or a shopper trying to budget effectively, breaking down Alicia’s purchase helps illuminate key concepts in mathematics and financial literacy.
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Understanding Alicia’s Purchase: The Basics
When Alicia bought four scarves, she ended up paying a total of $75.20 plus an additional $5.26 in tax. To comprehend how much each scarf costs, we need to analyze the total amount paid, including taxes, and then determine the unit price per scarf.
Total amount paid = Price of scarves + Tax
- Price of scarves = $75.20
- Tax = $5.26
Total amount spent = $75.20 + $5.26 = $80.46
This total cost forms the basis for further calculations. To find the unit price of one scarf, divide the total amount (including tax) by the number of scarves purchased.
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Calculating the Cost Per Scarf
Step 1: Find the total amount paid
As established, the total amount Alicia paid for her four scarves, including taxes, is $80.46.
Step 2: Divide by the number of scarves
Since Alicia bought four scarves, the cost per scarf is:
\[
\text{Cost per scarf} = \frac{\text{Total amount paid}}{\text{Number of scarves}} = \frac{\$80.46}{4}
\]
Calculating this:
\[
\frac{\$80.46}{4} = \$20.115
\]
Therefore, each scarf costs approximately $20.12 when rounded to two decimal places.
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Understanding the Breakdown: Pre-Tax and Tax Prices
While Alicia’s total paid includes tax, it’s useful to understand the original price of the scarves before tax was added. This distinction helps in comparing prices and understanding the impact of taxes on purchases.
Calculating the Pre-Tax Price of the Scarves
Given:
- Total price of scarves (before tax) = $75.20
- Tax = $5.26
The pre-tax price per scarf is:
\[
\text{Pre-tax price per scarf} = \frac{\$75.20}{4} = \$18.80
\]
This means each scarf originally cost $18.80 before tax was added.
Calculating the Tax Rate
Knowing the total tax and the pre-tax total, we can find the tax rate as a percentage:
\[
\text{Tax rate} = \frac{\text{Tax}}{\text{Pre-tax total}} \times 100 = \frac{\$5.26}{\$75.20} \times 100
\]
Calculating:
\[
\frac{\$5.26}{\$75.20} \approx 0.07
\]
Multiplying by 100:
\[
0.07 \times 100 = 7\%
\]
Thus, the tax rate applied to Alicia’s purchase is approximately 7%.
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Applying the Calculations to Budgeting and Shopping
Understanding how to break down shopping costs is essential for effective budgeting. Alicia’s example illustrates how knowing the pre-tax cost and tax rate can help in planning future purchases.
Key takeaways for shoppers:
- Always distinguish between the pre-tax price and the total price including tax.
- Calculate unit prices to compare different products effectively.
- Understand the tax rate to estimate total costs in advance.
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Practical Applications of the Calculations
1. Comparing Prices of Similar Items
Suppose Alicia considers buying scarves from two different stores. Store A sells scarves at $18.80 each with a 7% tax, similar to her previous purchase, while Store B sells scarves at $20 each with a 5% tax.
- Store A:
Tax = 7% of $18.80 = 0.07 × $18.80 = $1.316
Total per scarf = $18.80 + $1.316 ≈ $20.116
- Store B:
Tax = 5% of $20 = 0.05 × $20 = $1.00
Total per scarf = $20 + $1.00 = $21.00
Comparing the total costs, Store A offers a slightly cheaper option per scarf, costing approximately $20.12, versus Store B at $21.00.
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2. Budgeting for Future Purchases
If Alicia wants to buy more scarves within a budget, understanding her per-scarf cost helps her set limits. For example, if she has $100 to spend on scarves, and each costs roughly $20.12, she can afford:
\[
\text{Number of scarves} = \frac{\$100}{\$20.12} \approx 4.97
\]
So, she can confidently buy four scarves and still have some money left over.
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Real-World Tips for Consumers
- Always check whether prices include taxes or if they are added at checkout.
- Use unit pricing to compare deals effectively.
- Be aware of tax rates in your area to accurately estimate total costs.
- When shopping online or in-store, ask about the tax percentage if it’s unclear.
Conclusion
Alicia’s purchase of four scarves for $75.20 plus $5.26 in tax offers a valuable example of how to analyze and understand shopping costs. By calculating the total amount paid, the per-unit cost, and the tax rate, consumers can make informed decisions, compare prices effectively, and budget wisely. Whether purchasing clothing, groceries, or other items, these basic mathematical skills empower shoppers to maximize their spending power and avoid surprises at checkout.
Understanding these concepts not only enhances financial literacy but also ensures that consumers like Alicia can make smarter, more economical choices every time they shop.
