Problem 68 - Elementary Algebra

Question

The original price of a phone is \(\$ 199\). If it is marked down \(32 \%\), find the sale price.

Step-by-Step Solution

Answer

The sale price is \( \$135.32 \).

Step 1: Understand the problem

We need to find the sale price of a phone after a markdown. The original price of the phone is \( \$199 \), and it is marked down by \( 32 \% \).

Step 2: Calculate the markdown amount

To find the markdown amount, multiply the original price by the percentage of the markdown. \[ \text{Markdown Amount} = \text{Original Price} \times \frac{\text{Markdown Percentage}}{100} \] \[ \text{Markdown Amount} = 199 \times \frac{32}{100} = 199 \times 0.32 = 63.68 \]

Step 3: Subtract the markdown amount from the original price

To find the sale price, subtract the markdown amount from the original price. \[ \text{Sale Price} = \text{Original Price} - \text{Markdown Amount} \] \[ \text{Sale Price} = 199 - 63.68 = 135.32 \]

Key Concepts

sale price calculation

Calculating the sale price is an essential skill for both everyday shopping and financial literacy. Let's break it down in a simple way. The sale price represents how much you will pay for an item after a markdown or discount has been applied.
To find the sale price, you need two key pieces of information:

• The original price
• The amount of the markdown in percentage

With this information, you can calculate the markdown amount, subtract it from the original price, and then get the sale price. This step-by-step method ensures you clearly understand how much you are saving and the final cost to you.

original price

The original price is the initial cost of an item before any discounts or markdowns are applied. In our example, the original price of the phone is \(\$199\). Knowing the original price is the starting point for any markdown calculation.

It’s crucial to have the original price as it provides the baseline for calculating how much you will save and, consequently, what the new price will be after the markdown. Think of the original price as the *full price* tag you see before any sale or promotional discounts are added.

• The original price for our exercise is \(\$199\)

percentage reduction

The percentage reduction indicates how much of a discount is being applied to the product in percentage terms. In the exercise here, the phone is marked down by \(32\%\).

To utilize the percentage reduction, you convert the percentage to a decimal for easy calculation. This is done by dividing the percentage by 100.

For example:

• \(32\% = \frac{32}{100} = 0.32\)

This decimal form is then used to calculate the markdown amount.

markdown amount

The markdown amount is the actual monetary value deducted from the original price based on the percentage reduction. This shows how much you are saving.

To calculate the markdown amount, you multiply the original price by the decimal form of the percentage reduction:

• Original Price \(\times\) Markdown Percentage = Markdown Amount

For our example:

• \(199 \times 0.32 = 63.68\)

This means \(\$63.68\) is taken off the original price. Then, subtract the markdown amount from the original price to get the sale price:

• Original Price \(\$199\) - Markdown Amount \(\$63.68\) = Sale Price \(\$135.32\)