Problem 61 - Elementary Algebra

Question

In the following exercises, solve each number word problem. Price before Sales Tax Tom paid \(\$ 1,166.40\) for a new refrigerator, including \(\$ 86.40\) tax. What was the price of the refrigerator?

Step-by-Step Solution

Answer

The price of the refrigerator before tax is \(1080.00\) dollars.

Step 1 - Identify the total amount paid

Tom paid a total amount of \(1166.40\) dollars for the refrigerator, including the tax.

Step 2 - Identify the amount of tax paid

The tax amount included in the total payment is \(86.40\) dollars.

Step 3 - Determine the price of the refrigerator before tax

Subtract the tax amount from the total amount paid: \(1166.40 - 86.40 = 1080.00\) dollars. This is the price of the refrigerator before tax.

Key Concepts

solving word problems

Word problems may seem tricky at first, but they are easier to handle if you follow a systematic approach. The key steps involve:

• Identifying the quantities involved
• Determining what you need to find out
• Setting up the corresponding mathematical operations

In the given exercise, we start with the total amount Tom paid, which includes sales tax. Our goal is to find the original price of the refrigerator before the tax was applied.
By carefully following the steps, you can break down the problem into manageable parts and arrive at the solution without confusion.

sales tax calculations

Understanding sales tax calculations is crucial when solving problems related to purchases. Sales tax is typically a percentage of an item's original price, added to the total amount paid.

Here’s a step-by-step way to tackle such problems:

• Firstly, identify the total amount paid, which in this case is \( \$1166.40 \)
• Next, determine the amount of tax paid. Tom paid \( \$86.40 \) in tax
• Finally, subtract the tax from the total to find the original price

For Tom’s refrigerator, we calculate the price before tax by subtracting \( \$86.40 \) from \( \$1166.40 \), which gives us \( \$1080.00 \). This process ensures that we isolate the pre-tax price accurately.

subtraction in algebra

Subtraction is a fundamental concept in algebra that allows you to find the difference between two numbers. It’s particularly useful in problems involving sales tax calculations, as seen in our exercise.

The steps are usually as follows:

• Identify the total amount and the amount to be subtracted
• Set up the subtraction equation
• Perform the subtraction to find the result

In Tom’s case, we have the total amount \( \$1166.40 \) and the tax amount \( \$86.40 \). By subtracting these, \( 1166.40 - 86.40 \), we find the original price of the refrigerator, which is \( \$1080.00 \).

Mastering basic subtraction in algebra helps you solve more complex problems efficiently.