Problem 28 - Prealgebra

Question

RETAIL Find the discount to the nearest cent for a flat-screen television that costs \(\$ 999\) and is on sale at \(15 \%\) off.

Step-by-Step Solution

Answer

The discount is \(\$ 149.85\).

Step 1: Understand the Problem

The problem asks us to find out the discount amount for a television priced at \(\$ 999\), with a discount rate of \(15\%\).

Step 2: Calculate the Discount Amount

To find the discount amount, use the formula: \[ \text{Discount Amount} = \text{Original Price} \times \text{Discount Rate} \] Here, the original price is \(\$ 999\) and the discount rate is \(0.15\). Substituting the values, we get: \[ \text{Discount Amount} = 999 \times 0.15 = 149.85 \]

Step 3: Round to the Nearest Cent

Since the discount amount calculated is \(\$ 149.85\), it is already in dollars and cents format, and does not require any further rounding.

Key Concepts

Understanding Percentages

In mathematics, percentages are a way to express numbers as a fraction of 100. They are used to provide a standard format to compare values, making it easier to grasp quantities intuitively. When you see a percentage, like 15%, it simply means 15 out of 100.

• Percentages help in comparing proportions easily.
• They are widely used in various fields, such as finance, statistics, and shopping discounts.
• Commonly, percentages can translate into decimal form by dividing by 100. For instance, 15% becomes 0.15.

In our exercise, the television is on a 15% sale. This means that 15% of the original price will be subtracted as a discount. Calculating this discount involves multiplying the original price by the percentage in its decimal form.

Mathematics Behind the Discount

To explore the mathematics of calculating a discount, let's consider the formula used in the process:\[\text{Discount Amount} = \text{Original Price} \times \text{Discount Rate}\]Here, the original price is the price before any discounts have been applied. The discount rate is the percentage you convert to a decimal. This calculation determines how much money will be subtracted from the original price.

• The original price in the exercise is \( \$999 \).
• The discount rate is 15%, which is converted to 0.15 in decimal form.

This equation is useful because it applies straightforward arithmetic to solve a real-world issue. By understanding this mathematical principle, you can apply it to various scenarios beyond shopping, such as calculating interest rates, tax amounts, or profit margins.

Real-World Applications of Percentages

Percentages are not just theoretical; they play a significant role in our daily lives and understandings. Recognizing how percentages function allows for smarter financial decisions and greater awareness of everyday transactions. Consider some areas where percentages are prevalent:

• Shopping Discounts: Knowing how to calculate discounts helps you become an informed shopper and manage your budget better.
• Taxes: Both income tax rates and sales taxes are displayed as percentages, affecting how much you pay or owe.
• Financial Investments: Expected returns and interest rates are usually presented in percentages, facilitating an easier comprehension of potential gains.

In our exercise, finding a discount means benefiting financially by reducing the price paid for goods. Recognizing how to calculate and apply these percentages ensures a clearer grasp of finances, aiding in effective money management for the present and future.