Question

Solve. A desk is priced at $185.95. The sales tax rate is 5%. Find the sales tax and the total amount of the purchase.

Short answer

Answer: The sales tax is $9.30 and the total purchase amount is $195.25.

Step-by-step solution

Calculate the sales tax

To calculate the sales tax, we can use the formula: sales tax = price * tax rate. In this exercise, the desk price is $185.95 and the tax rate is 5%. First, we need to convert the tax rate from percentage to decimal form by dividing by 100. So, the tax rate will be 0.05. Therefore, the sales tax can be calculated as follows: Sales tax = $185.95 * 0.05

Calculate the total purchase amount

The total purchase amount is the sum of the desk price and the sales tax. After computing the sales tax in step 1, we can easily find the total purchase amount by adding the desk price and the sales tax. The formula for finding the total purchase amount is: Total purchase amount = Desk price + Sales tax Now, we can calculate the sales tax and the total purchase amount: Sales tax = \(185.95 * 0.05 = \)9.30 Total purchase amount = \(185.95 + \)9.30 = $195.25 Thus, the sales tax is \(9.30 and the total purchase amount is \)195.25.

Key concepts

Understanding the Sales Tax Formula

When you go shopping, the price tag isn't always the final amount you pay at the register. That's because most items are subject to sales tax, which is a percentage added onto the price of an item. The sales tax formula is straightforward: you simply multiply the price of the item by the sales tax rate.

Let's take our example, where a desk is priced at \(185.95, and the sales tax rate is 5%. In mathematical form, the calculation for the sales tax would be: \( Sales Tax = Item Price \times Tax Rate \).

To perform the calculation, it is crucial to convert the sales tax rate from a percentage to a decimal, which is a common step where some students stumble. Once you have calculated the sales tax, you add it to the original price to determine the total purchase amount. Understanding this process is key to managing your finances and being an informed consumer.

Percentage to Decimal Conversion

Many mathematical problems, including calculating sales tax, require you to convert percentages to decimals. This is because percentages are based on the number 100, signifying a part out of a hundred, whereas decimals represent a part out of one.

To convert a percentage to a decimal, you simply divide the percentage by 100. For example, a 5% sales tax rate becomes 0.05 when converted to decimal form (\(0.05 = \frac{5}{100} \)).

Why is this important?

Without converting the percentage to a decimal, calculations would be incorrect, leading to inaccurate results. Ensuring precise conversion is therefore crucial in financial computations and forms a fundamental skill for anybody working with percentages in real-life scenarios.

Total Purchase Amount Calculation

Once the sales tax is calculated by using the aforementioned formula and conversion process, the final step is to determine the total amount that will be paid. This includes both the original price of the item and the sales tax. The formula is \(Total Purchase Amount = Item Price + Sales Tax\).

Returning to our desk example with a price tag of \)185.95 and a calculated sales tax of \(9.30, we add these numbers to get the total purchase amount: \(Total Purchase Amount = \)185.95 + \(9.30 = \)195.25\).

Understanding this sum is important for budgeting purposes. Whether you are running a business, planning a shopping trip, or simply trying to manage your personal finances more effectively, the ability to calculate the total cost including sales tax is an invaluable tool.