Problem 45 - Prealgebra

Question

A department store was advertising that leather jackets that cost \(\$ 149.95\) are now on sale for \(\$ 112.46 .\) Find the percent of discount. F \(35 \%\) G \(30 \%\) H \(25 \%\) J \(20 \%\)

Step-by-Step Solution

Answer

The percent of discount is 25\%.

Step 1: Determine the Amount of Discount

First, find the difference between the original price and the sale price of the leather jacket. The original price is \( \\(149.95 \) and the sale price is \( \\)112.46 \). The amount of discount is calculated as follows: \[ \text{Discount} = \text{Original Price} - \text{Sale Price} = 149.95 - 112.46 = 37.49 \] So, the discount amount is \( \$37.49 \).

Step 2: Calculate the Percent Discount

To find the percent discount, divide the amount of discount by the original price, and then multiply by 100 to convert it to a percentage: \[ \text{Percent Discount} = \left( \frac{37.49}{149.95} \right) \times 100 \approx 25\% \] This calculation tells us what percent of the original price the discount represents.

Key Concepts

calculation of percent

Understanding how to calculate a percent is essential in determining many daily life scenarios, such as finding discounts, interest rates, and data comparisons. Here's a simple way to grasp this concept: - **Percent** essentially means "per hundred." When you express a number as a percent, you are expressing it as a fraction of 100. For example, 25% is the same as saying 25 out of 100. - To convert a fraction or a ratio into a percentage, you multiply by 100. This gives you the value out of 100, or your percent value. In the context of finding discounts, you take the difference between the original and sale price to find the "part." Then, you compare this part to the "whole," which is the original price, to get the percent. This is achieved by: 1. Dividing the difference (discount) by the original price. 2. Multiplying the result by 100 to convert it into a percentage. This sequence helps translate a simple discount into meaningful percent terms, an accessible way to express savings.

original price vs sale price

When shopping, it's crucial to understand the difference between the original price and the sale price. These figures help shoppers understand potential savings. - **Original Price**: This is the initial cost of an item before any discounts. It represents the baseline value from which discounts are calculated. - **Sale Price**: After applying a discount, this is the new cost of the item. It shows the price a customer will pay at the end of a sale. To determine if a sale is good, compare these two prices. If the sale price is significantly lower, it's usually a better deal. This concept helps consumers make informed decisions about their purchases without second-guessing.

discount amount

The discount amount is the value you save when purchasing an item at a reduced price. It's a direct indicator of how much money you're saving.- To find the discount amount, subtract the sale price from the original price: \ \ \- **Discount Amount Formula**: \ \\[ \text{Discount Amount} = \text{Original Price} - \text{Sale Price} \]Knowing this amount is not only satisfying but also a useful way to calculate your percent saving (as covered above). By using this number, both consumers and sellers can better understand the value of a sale item in monetary terms. This understanding enhances financial literacy and smarter shopping habits.