Question

Solve. A car is priced at \(\$ 26,450 .\) If the sales tax rate is \(6 \%\) calculate the sales tax and the total amount of the purchase.

Short answer

Answer: The sales tax amount is $1,587 and the total amount of the purchase is $28,037.

Step-by-step solution

Calculate Sales Tax Amount

To calculate the sales tax amount, we need to multiply the car price by the sales tax rate, which is given as 6%. Sales Tax Amount = Car Price × Sales Tax Rate We know the car price is $26,450 and the sales tax rate is 6%. Let's convert the percentage to its decimal form by dividing by 100. Sales Tax Rate (decimal) = 6% ÷ 100 = 0.06 Now, calculate the sales tax amount: Sales Tax Amount = $26,450 × 0.06 = \$1,587

Calculate Total Amount of the Purchase

Now that we have calculated the sales tax amount, we will add it to the initial car price to find the total amount of the purchase. Total Amount = Car Price + Sales Tax Amount Total Amount = $26,450 + \$1,587 = \$28,037 So, the sales tax amount is \$1,587, and the total amount of the purchase is \$28,037.

Key concepts

Prealgebra Problems

Prealgebra problems often involve fundamental arithmetic and basic algebraic concepts. Here, we deal with operations such as addition, subtraction, multiplication, and division without using complex equations. Problems like calculating sales tax and total purchase amounts are great examples of prealgebra in real-life situations.
Understanding these problems sets the foundation for algebra and more advanced mathematics. To solve prealgebra problems effectively, you should:

• Read the problem carefully to understand what is being asked.
• Identify the key numbers and operations required.
• Perform calculations step-by-step to avoid errors.
• Double-check your work for accuracy.

By mastering prealgebra, you build confidence to tackle diverse mathematical challenges.

Percentage Calculation

Percentage calculation is crucial in math, especially when dealing with taxes, interest rates, or discounts. It involves determining a part of a number in relation to 100. In our example, the sales tax rate is 6%, which means 6 out of every 100 units of currency spent is added as tax.
To perform percentage calculations, follow these steps:

• Divide the percentage by 100 to convert it to a decimal.
• Multiply this decimal by the number you want the percentage of.

For instance, converting 6% to a decimal gives us 0.06, which we then multiply by the car's price. This simple approach helps in accurately figuring out percentages for any need.

Decimal Conversion

Decimal conversion is the process of turning percentages into decimal form, simplifying many calculations. It's essential in various fields, from mathematics to everyday financial tasks. In calculations like tax, converting a percentage to a decimal allows for straightforward multiplier operations.
Here’s how to convert a percentage to a decimal:

• Take the percentage value.
• Divide by 100.

For example, converting 6% involves 6 divided by 100, resulting in 0.06. You can then use this decimal in further calculations, such as determining sales tax. Understanding decimal conversion ensures precise financial computations.

Financial Literacy

Financial literacy involves understanding and effectively using various financial skills, including personal financial management, budgeting, and investing. Grasping concepts like sales tax is a part of developing financial literacy.
In our exercise, knowing how to calculate sales tax and total amounts helps make informed purchasing decisions without falling prey to unexpected fees. Here’s why financial literacy matters:

• Enables smarter budgeting and spending decisions.
• Provides a better understanding of how taxes affect purchases.
• Helps in planning for larger expenses by forecasting total costs.

By being financially literate, you are better equipped to navigate economic challenges and make well-informed decisions.