Problem 63 - Elementary Algebra

Question

A retail outlet is offering \(15 \%\) off the original \(\$ 29.99\) price of branded sweaters. What is the price after the discount?

Step-by-Step Solution

Answer

The price after the discount is $25.49.

Step 1: Determine the Discount Amount

First, calculate the discount amount by finding 15% of the original price of the sweater. Use the formula for percentage: \( \text{Discount Amount} = \text{Original Price} \times \frac{\text{Discount Percentage}}{100} \). Plug in the values to get \( \text{Discount Amount} = 29.99 \times \frac{15}{100} = 4.4985 \). Round this to two decimal places, which gives \( 4.50 \).

Step 2: Calculate the Discounted Price

Next, subtract the discount amount from the original price to get the price after the discount. Use the equation: \( \text{Discounted Price} = \text{Original Price} - \text{Discount Amount} \). Substitute the values: \( \text{Discounted Price} = 29.99 - 4.50 = 25.49 \).

Key Concepts

Understanding Discounts

When shopping, you often encounter discounts, which are reductions from the original price. They are usually expressed as a percentage. This percentage reflects how much of the original price you don't have to pay. For example, a 15% discount means you pay 85% of the original price. Understanding discounts can help you save money on purchases.

To calculate a discount, you'll need to determine two things:

• The original price of the item
• The percentage discount offered

Once you have these, multiply the original price by the discount percentage (expressed as a decimal). This gives you the discount amount, which you subtract from the original price to find the final price.

This process involves a bit of math, but with practice, it becomes second nature. Knowing how to calculate discounts keeps you informed and helps make smart purchasing decisions.

Basic Arithmetic for Discounts

Basic arithmetic is a fundamental math skill that forms the foundation for calculating discounts. It involves operations such as addition, subtraction, multiplication, and division.

When calculating discounts, you typically deal with:

• Multiplication: To find the discount amount, multiply the original price by the discount percentage turned into a decimal.
• Subtraction: To find the final price, subtract the discount amount from the original price.

Here's a quick reminder of how percentages can convert into decimals. For example, a 15% discount can be expressed as 0.15 in decimal form. You use this by multiplying it with the original price to find how much the discount saves you.

These basic arithmetic operations are not just useful in finding discounts, they are vital in managing finances and handling everyday math scenarios.

Price Calculation with Discounts

Price calculation is a vital skill for budgeting and shopping. When discounts are a factor, calculating the price involves a two-step process.

First, identify the original price of the item and the discount percentage. In our example, the sweater's original price is $29.99 and the discount is 15%.

Use the formula to find the discount amount:

• Discount Amount = Original Price \( \times \) (Discount Percentage / 100)
• e.g., \( 29.99 \times \frac{15}{100} = 4.50 \)

Then, subtract the discount from the original price to find the discounted price:

• Discounted Price = Original Price - Discount Amount
• e.g., \( 29.99 - 4.50 = 25.49 \)

This method ensures that you get the best deal by understanding exactly how much you'll pay after the sale. Practicing with different scenarios will refine your skills and confidence in shopping smartly.