Problem 7 - Prealgebra

Question

A jacket that normally sells for \(\$ 180\) is on sale at a \(35 \%\) discount. What is the sale price of the jacket?

Step-by-Step Solution

Answer

The sale price of the jacket is \(\$117\).

Step 1: Understand the Given Discount

The original price of the jacket is given as \(\\(180\), and the discount percentage is \(35\%\). This means we need to calculate what \(35\%\) of \(\\)180\) is to find out the discount amount.

Step 2: Calculate the Discount Amount

The formula to calculate the discount is: \[ \text{Discount} = \text{Original Price} \times \frac{\text{Discount Percentage}}{100} \]Substitute the known values into the formula: \[ \text{Discount} = 180 \times \frac{35}{100} = 63 \]So, the discount amount is \(\$63\).

Step 3: Determine the Sale Price

Subtract the discount amount from the original price using the formula:\[ \text{Sale Price} = \text{Original Price} - \text{Discount} \]Substitute the values:\[ \text{Sale Price} = 180 - 63 = 117 \]Thus, the sale price of the jacket is \(\$117\).

Key Concepts

Understanding Discount Calculation

When you see an item on sale with a discount percentage, it's essential to understand how to find the actual discount amount. A discount is simply a reduction in the item's original price, often expressed as a percentage. To compute the discount amount, which is what you save, you will need two pieces of information: the original price and the discount percentage.

This calculation can be easily done using a simple formula:

• Discount Amount = Original Price × (Discount Percentage / 100)

In our example, a jacket is priced at \(180\), with a 35% discount. The calculation involves multiplying the original price by the discount percentage expressed as a fraction. Thus, multiplying \(180\) by \(\frac{35}{100}\) results in a discount amount of \(63\).

Understanding this will ensure you know exactly how much less you are paying during sales, effectively allowing for smarter shopping decisions!

Sale Price Determination

Once you've figured out the discount amount, determining the sale price becomes a breeze. The sale price is how much you end up paying after the discount is applied. To find the sale price, simply subtract the discount amount from the original price of the item.

This is done using the following straightforward formula:

• Sale Price = Original Price - Discount Amount

For the jacket in our example, the calculation goes as follows: \(\text{Sale Price} = 180 - 63 = 117\).

In this way, the final amount you pay for the jacket is \(\$117\). Knowing how to determine the sale price helps in budgeting and ensures you recognize the value of your saving compared to the retail price.

Mastering Mathematical Operations with Percentages

Percentages are an integral part of mathematics used in various scenarios, such as discounts, interest rates, and more. Understanding how to use mathematical operations with percentages is crucial for solving real-life problems efficiently.

When working with percentages:

• Always convert the percentage to a decimal or a fraction before using it in calculations. For example, 35% becomes \(\frac{35}{100}\) or 0.35.
• Use multiplication to find a percentage of a number, as seen in discount calculations (e.g., Original Price × Percentage as a Decimal).
• Subtraction is used when computing the sale price, subtracting the percentage-derived discount from the original amount.

Once you grasp these basic operations, you can tackle more complex problems involving percentages with confidence. Practicing these operations will enable you to efficiently handle various situations that require percentage calculations.