Problem 28 - Intermediate Algebra

Question

\(\quad\) A bedroom set regularly sells for \(\$ 983 .\) If it is on sale for \(\$ 737.25,\) what is the percent of markdown?

Step-by-Step Solution

Answer

The percent of markdown is 25%.

Step 1: Calculate the Discount Amount

To find the markdown percentage, we first need to determine the amount of the discount. We do this by subtracting the sale price from the regular price.Calculate:\[ 983 - 737.25 = 245.75 \]Thus, the discount amount is $245.75.

Step 2: Compute the Markdown Percentage

Next, we need to calculate what percentage the discount amount (\(245.75) is of the original price (\)983). We do this by dividing the discount amount by the original price and then multiplying by 100 to convert it into a percentage.Calculate:\[ \left(\frac{245.75}{983}\right) \times 100 = 25\% \]Thus, the percent of markdown is 25%.

Key Concepts

Markdown Calculation

Markdown calculation is a fundamental concept in percentage calculations, often used in retail marketing to highlight discounts. Understanding the markdown process helps shoppers evaluate the value of a discount and determine their savings. To perform a markdown calculation, you need two main prices:

• The original price of the item
• The sale price of the item

Start by identifying the original price, which is usually higher, and the sale price, which is often highlighted during promotions. The markdown is the difference between these two prices.
The formula to calculate the markdown is:\[\text{Markdown} = \text{Original Price} - \text{Sale Price}\]Using the markdown calculation, retailers can translate this information into a percentage to represent how much prices have been reduced. This is often more appealing and understandable to consumers, who prefer knowing the discount in percentage terms rather than in monetary value alone.

Discount Amount

The discount amount is simply the difference between the regular price and the sale price of an item. It indicates how much money you will save if you purchase the item at the discounted rate.

• To calculate, subtract the sale price from the original price.

For example, if a bedroom set is originally priced at \(983 and currently offered at a discount price of \)737.25, the discount amount is:\[\text{Discount Amount} = 983 - 737.25 = 245.75\]This $245.75 is the amount saved from purchasing the item at the sale price instead of the original price. Understanding the discount amount is crucial when comparing deals and ensuring you receive genuine savings. Shoppers can easily evaluate different offers by calculating the discount amount for each, helping them make informed purchasing decisions.

Algebra Problem Solving

Algebra problem solving allows us to express calculations and solve problems systematically using formulas. In the context of markdown and discounts, algebra helps us manipulate and solve the equations required to find the markdown percentage. To find the percentage markdown, we use the concept of expressing one quantity as a percentage of another.Once the discount amount is determined, divide it by the original price. This provides the fraction that describes what portion of the original price is being discounted. To convert this into a percentage:

• Divide the discount amount by the original price.
• Multiply the result by 100 to get a percentage.

Here's how it works for the problem:\[\text{Markdown Percentage} = \left(\frac{245.75}{983}\right) \times 100 \approx 25\%\]Thus, the bed set's price was reduced by approximately 25%. Algebra simplifies the way we approach and solve percentage problems, making it easier to apply these calculations to various scenarios, from shopping to financial analysis. It emphasizes the importance of breaking problems into steps, using formulas as guides, and accurately interpreting the outcomes.