Problem 14 - Prealgebra

Question

Solve each of these problems using the method developed in this section. On opening day, a new music store offers a \(12 \%\) discount on all electric guitars. If the regular price on a guitar is \(\$ 550,\) what is the sale price?

Step-by-Step Solution

Answer

The sale price is $484.

Step 1: Understand the problem

The problem asks for the sale price of a guitar that originally costs $550, with a 12% discount applied. Our goal is to calculate the new price after the discount.

Step 2: Calculate the discount amount

First, calculate the discount amount by finding 12% of \(550. Use the formula for the percentage: \[\text{Discount Amount} = \frac{12}{100} \times 550\] which simplifies to \[\text{Discount Amount} = 66\]. This means the discount amount is \)66.

Step 3: Subtract the discount from the original price

Now subtract the discount amount from the original price to find the sale price:\[\text{Sale Price} = 550 - 66\] which results in \[\text{Sale Price} = 484\].

Key Concepts

Understanding Discount Calculation

Discount calculation is a fundamental concept that helps determine how much you save when there's a markdown on a product. Picture this: you are interested in purchasing an electric guitar that costs \(550. The store graciously offers a 12% discount on this item during its opening day. So, how do we find out how much we save and what the final cost will be? Let's break it down together:

• First, know the original price of the item, which is \)550 in this scenario.
• Next, determine the discount percentage; here, it is 12%.
• To find out how much the discount is in dollars, use this step: Convert the percentage into a decimal by dividing by 100. This gives us 0.12.
• Now, multiply the original price by this decimal: \[\text{Discount Amount} = 0.12 \times 550 = 66\]
• This means you'll save $66 on your guitar purchase.

Discount calculation allows you to measure savings quickly, aiding in financial decisions while shopping.

Calculating the Sale Price

Once you've determined the discount amount, calculating the sale price is straightforward. This next step involves knowing how much you will actually pay after the discount has been applied. For the guitar example, the original price was \(550, and the discount you just calculated is \)66. Here's how you find the sale price:

• Start with the original price, which is \(550.
• Subtract the discount from this original price:\[\text{Sale Price} = 550 - 66 = 484\]
• The amount you will pay, or the sale price, is \)484.

By understanding sale price calculation, you can easily determine the final cost of an item following a discount. It's a practical skill that helps in budgeting and ensuring you are paying the expected amount.

Basic Arithmetic Operations in Discounts and Sales

Basic arithmetic operations are the backbone of solving percentage problems, specifically when dealing with discounts and sales.

These operations include multiplication, division, subtraction, and addition, all of which play a crucial role in determining discounts and sale prices:

• **Multiplication** is utilized when calculating the discount amount (e.g., multiplying the original price by the decimal form of the percentage).
• **Division**, although not explicitly visible in this example, is part of converting percentages into decimals (e.g., dividing by 100).
• **Subtraction** is essential when you subtract the discount from the original price to find the sale price.
• **Addition** would be used if taxes were added after the discount, though not necessary in this specific problem.

Understanding these basic arithmetic operations can help you navigate through similar problems with ease, enabling you to manage finances effectively.