Problem 74 - Algebra for College Students

Question

The Jurassic Park Collection in Blu-Ray was on sale for $29.96 . The list price (full price) of this three-disc set was 44.98. To the nearest tenth, what was the percent discount?

Step-by-Step Solution

Answer

The percent discount is 33.4%.

Step 1 - Calculate the discount amount

Start by finding the amount of money saved by subtracting the sale price from the list price. List Price: \(44.98 Sale Price: \)29.96 Discount Amount: \(44.98 - \)29.96 = $15.02

Step 2 - Find the discount rate

The discount rate is found by dividing the discount amount by the list price, and then multiplying by 100 to convert to a percentage. Discount Rate: \ \ \( \frac{15.02}{44.98} \times 100 = 33.4 \% \ \)

Step 3 - Round to the nearest tenth

Since 33.4 is already rounded to the nearest tenth, we can state that the percent discount to the nearest tenth is 33.4%.

Key Concepts

Understanding Percentage

A percentage is a way of expressing a number as a part of a whole. It is often denoted with the percent symbol (%). Essentially, percentages are used to compare different quantities on a common ground of 100. For example, if someone says they have completed 50% of their homework, that means they have finished half of it. In mathematical terms, percentage is calculated by \[ \text{Percentage} = \frac{\text{Part}}{\text{Whole}} \times 100 \] In our exercise, the part is the discount amount and the whole is the list price. By dividing the discount by the list price and then multiplying by 100, we get the discount percentage. This tells us how much of the original price the customer saves.

Determining the Discount Rate

The discount rate is the percentage reduction from the original list price. It's a crucial concept for understanding how much money you save when buying items on sale. To find the discount rate:

• Subtract the sale price from the list price to get the discount amount.
• Divide the discount amount by the list price.
• Multiply the result by 100 to get the percentage discount.

In our Blu-Ray example:
\[ \text{Discount Amount} = 44.98 - 29.96 = 15.02 \ \text{Discount Rate} = \frac{15.02}{44.98} \times 100 \ = 33.4\text{%} \]This means customers are saving 33.4% off the full price when they buy the Blu-Ray on sale.

Understanding List Price

The list price, also known as the full or retail price, is the original price set by the seller or manufacturer before any discounts or promotions are applied. It is the starting point for any pricing adjustments that may occur due to sales, special offers, or discounts. Understanding the list price is essential for calculating savings and discounts. For example, in our exercise, the list price of the Blu-Ray set is $44.98. This means that without any sale or discount, a customer would pay this amount. Knowing the list price, we can easily find out how much money is being saved when a sale price is offered. By comparing the list price to the sale price, customers can determine the value of the deal they are getting.

• The list price is the original cost before any discounts.
• Savings are determined by subtracting the sale price from the list price.
• The percent discount shows how much cheaper the sale price is compared to the list price.

Understanding these terms helps shoppers make informed decisions when purchasing items on sale.