Problem 64 - Elementary Algebra

Question

The sales tax rate in a state is \(8 \%\). Find the sales tax on a purchase of \(\$ 550\).

Step-by-Step Solution

Answer

The sales tax on a \(\$ 550\) purchase is \(\$ 44\).

Step 1: Identify the given values

The problem states that the sales tax rate is \(8\%\) and the purchase amount is \(\$ 550\).

Step 2: Convert the sales tax rate to a decimal

To convert the percentage to a decimal, divide \(8\%\) by \(100\): \[ \text{Sales tax rate as a decimal} = \frac{8}{100} = 0.08 \]

Step 3: Calculate the sales tax amount

Multiply the purchase amount by the sales tax rate in decimal form: \[ \text{Sales tax} = 550 \times 0.08 \]

Step 4: Perform the multiplication

Calculate the result: \[ 550 \times 0.08 = 44 \]

Key Concepts

Percentage to Decimal Conversion

When dealing with percentages, it's often necessary to convert them into decimals.
This is especially useful in calculations like finding the sales tax. The conversion process is simple: you divide the percentage by 100.
For example, an 8% sales tax rate can be converted to a decimal as follows:
\ \ \ \ \ \ \[ \text{Decimal form of Sales Tax Rate} = \frac{8}{100} = 0.08 \]\ \ Now that we have the decimal form, it becomes easier to use this in our calculations. Remember, converting percentages is a crucial skill for various mathematical problems, especially those involving financial calculations.

Multiplication in Algebra

Multiplication is a fundamental operation in algebra. In our sales tax example, we need to multiply the purchase amount by the sales tax rate.
This is done because multiplying gives us the part (sales tax) of the whole (purchase amount). Here is how you can think about it:
\ \ \ \ \ \ \[ \text{Sales Tax} = \text{Purchase Amount} \times \text{Sales Tax Rate (Decimal)} \] \ \ Substituting the values from our problem, we get:
\ \ \[ \text{Sales Tax} = 550 \times 0.08 \] \ \ When multiplying, consider each digit placement and sum the partial products to get the final result. Crucial to mastering multiplication in algebra is to practice regularly and understand the steps involved.

Problem-Solving Steps

Solving mathematical problems is systematic. Here is a step-by-step approach to ensure clarity and accuracy:

• Identify Given Values: Start by pinpointing what information you already have.
• Convert as Necessary: Make necessary conversions (like percentage to decimal).
• Set Up the Equation: Formulate the problem into a mathematical equation.
• Calculate: Perform calculations carefully.
• Verify Your Answer: Double-check your calculations to ensure accuracy.

Let’s apply this to our sales tax problem:
1. Identify Given Values: Sales tax rate is 8%, purchase amount is \(550.
2. Convert as Necessary: Convert 8% to 0.08.
3. Set Up the Equation: \ \ \ \ \ \ \ \[ \text{Sales Tax} = 550 \times 0.08 \] \ \ 4. Calculate: \ \[ 550 \times 0.08 = 44 \] \ \ 5. Verify Your Answer: Confirm steps and calculation - sales tax on \)550 is $44.
Following these structured steps can greatly enhance problem-solving efficiency and accuracy.