Problem 50 - Algebra 2

Question

For Exercises \(48-50,\) use the following information. Liluye wants to buy a pair of inline skates that are on sale for 30\(\%\) off the original price of \(\$ 149 .\) The sales tax is 5.75\(\% .\) How much will Liluye pay for the inline skates?

Step-by-Step Solution

Answer

Liluye will pay \( \$110.29 \) for the inline skates.

Step 1: Calculate the Discounted Price

First, calculate the discount amount. The original price is \( \\(149 \), and the discount rate is 30\( \% \). Use the formula for discount: \( \text{Discount} = \text{Original Price} \times \frac{\text{Discount Rate}}{100} \). Substitute the values: \( 149 \times \frac{30}{100} = 44.70 \). So, the discount amount is \( \\)44.70 \).

Step 2: Determine the Sale Price

Subtract the discount from the original price to find the sale price: \( \text{Sale Price} = \text{Original Price} - \text{Discount} \). Substitute the values: \( 149 - 44.70 = 104.30 \). Therefore, the sale price is \( \$104.30 \).

Step 3: Calculate the Sales Tax

Now calculate the sales tax on the sale price. The sales tax rate is 5.75\( \% \). Use the formula: \( \text{Sales Tax} = \text{Sale Price} \times \frac{\text{Sales Tax Rate}}{100} \). Substitute the values: \( 104.30 \times \frac{5.75}{100} = 5.99425 \). The sales tax amount is approximately \( \$5.99 \).

Step 4: Determine the Total Cost

Add the sales tax to the sale price to find the total amount Liluye needs to pay: \( \text{Total Cost} = \text{Sale Price} + \text{Sales Tax} \). Substitute the values: \( 104.30 + 5.99 = 110.29 \). Thus, Liluye will pay \( \$110.29 \) for the skates.

Key Concepts

Understanding Discount Calculation

When buying items on sale, understanding how to calculate the discount is crucial. A discount is a reduction in the price, usually expressed as a percentage of the original price. In this exercise, Liluye is buying skates that are 30% off, which is a common discount amount. To find out how much money Liluye saves with this discount, use the discount formula:

• Identify the original price: This is the starting cost, which, in this case, is \( \\(149 \).
• Determine the discount rate: Here, it's 30\( \% \).

Substitute these into the formula: \[\text{Discount} = \text{Original Price} \times \frac{\text{Discount Rate}}{100}\] For this scenario: \[149 \times \frac{30}{100} = 44.70\] So, the discount amount is \( \\)44.70 \), meaning Liluye will pay \( \$44.70 \) less than the original price. This discount is important as it helps consumers save money.
Understanding how to calculate discounts allows you to make cost-effective purchasing decisions.

Exploring Sales Tax Calculation

Sales tax is an additional amount charged on the sale of goods or services, which is usually established by the government. The rate can vary depending on the location and the type of goods purchased. For Liluye, the sales tax is 5.75\( \% \). Calculating the sales tax is fairly straightforward:

• Identify the sale price, which, after deducting the discount, is \( \\(104.30 \).
• Use the sales tax rate to determine the tax amount.

Apply these to the sales tax formula: \[\text{Sales Tax} = \text{Sale Price} \times \frac{\text{Sales Tax Rate}}{100}\]In Liluye's case: \[104.30 \times \frac{5.75}{100} = 5.99425\]Rounding this amount, we get a sales tax of approximately \( \\)5.99 \). Understanding sales tax is crucial because it represents the extra costs that buyers must consider, beyond the sticker price.

Calculating the Total Cost

After understanding the discount and calculating the sales tax, the next step is determining the total cost. This means finding out how much Liluye will actually pay for her skates, including all applicable costs. The total cost is essentially the sale price plus the sales tax:

• You've already calculated the sale price as \( \\(104.30 \).
• You then found the sales tax to be approximately \( \\)5.99 \).

Combine these two components: \[\text{Total Cost} = \text{Sale Price} + \text{Sales Tax}\] For Liluye's skates, this would be: \[104.30 + 5.99 = 110.29\]Thus, the total amount Liluye will pay is \( \$110.29 \). This total cost highlights why it's important to account for all steps in a purchase process. Calculating the total ensures you know exactly how much you'll spend, including hidden costs like sales tax.