Problem 62 - Elementary Algebra

Question

In the following exercises, solve each number word problem. Price before Sales Tax Kenji paid \(\$ 2,279\) for a new living room set, including \(\$ 129\) tax. What was the price of the living room set?

Step-by-Step Solution

Answer

The price of the living room set was \(\$2,150\).

Step 1: Identify the total amount paid

Kenji paid a total of \(\$2,279\) for the new living room set, including the tax.

Step 2: Identify the amount of sales tax

The amount of sales tax included in the total payment is \(\$129\).

Step 3: Subtract the sales tax from the total amount

To find the price of the living room set before the sales tax, subtract the amount of the sales tax from the total amount paid: \(\$2,279 - \$129 = \$2,150\).

Key Concepts

sales tax calculation

Sales tax is an additional amount of money added to the price of goods or services. Understanding how to calculate it is crucial for solving many real-world math problems. In the given exercise, Kenji's total payment includes the sales tax, which is \(\$ 129\) out of \(\$ 2,279\). When you know the sales tax amount and the total price, you can work backwards to determine the price before tax. This process helps in understanding how percentages and additional costs are factored into pricing.

Also, this concept is essential for budgeting. If you know the tax rate, you can set aside the right amount of money to ensure you can afford the final total. When shopping, always note the tax, so there are no surprises at checkout.

subtraction

Subtraction is the process of taking one number away from another. It’s a fundamental math operation that's crucial in everything, from basic arithmetic to advanced math.

In this exercise, we used subtraction to find the price of the living room set before tax. The total amount paid is effectively the original price plus the sales tax. By subtracting the tax amount, \(\$129\), from the total amount, \(\$2,279\), we found the original price of the living room set, which is \(\$2,150\).

Practicing subtraction with real-world problems helps solidify this core skill. It’s especially useful in everyday tasks like shopping, budgeting, and even cooking recipes.

problem-solving steps

Solving word problems often involves a methodical approach. Here, let's revisit the problem-solving steps used in the exercise:

• **Identify the total amount paid:** Recognize the total money spent. Here, it's \(\$2,279\).
• **Identify the sales tax amount:** Notice the additional cost, which in this exercise is \(\$129\).
• **Subtract the sales tax from the total:** Use subtraction to find the base price. Subtract \(\$129\) from \(\$2,279\), resulting in \(\$2,150\).

This step-by-step method helps break down the problem into manageable parts. It's crucial for students to practice this approach, especially for word problems that combine various math operations. By mastering these steps, students can tackle more complex problems with confidence.