Problem 13 - Prealgebra

Question

Solve each of these problems using the method developed in this section. During a clearance sale, a three-piece suit that usually sells for \(\$ 300\) is marked \(-15 \%\) off." What is the discount? What is the sale price?

Step-by-Step Solution

Answer

The discount is \(\$45\) and the sale price is \(\$255\).

Step 1: Calculate the Discount Amount

To find the discount amount, we need to calculate 15% of the original price. The formula for this is: \( \text{Discount} = \left(\frac{15}{100}\right) \times 300 \).

Step 2: Compute the Discount

Now, perform the multiplication to find the discount: \( 0.15 \times 300 = 45 \). The discount amount is \( \$45 \).

Step 3: Determine the Sale Price

Subtract the discount amount from the original price to find the sale price: \( \text{Sale Price} = 300 - 45 \).

Step 4: Calculate the Sale Price

Now perform the subtraction: \( 300 - 45 = 255 \). The sale price of the suit is \( \$255 \).

Key Concepts

Discount Amount

Understanding how to calculate the discount amount is a vital skill when shopping during sales or clearance events. The discount amount is essentially the portion of the original price that you don't have to pay due to the discount. To calculate the discount amount, you'll need two key pieces of information: the original price and the discount rate.

• The original price is the initial price set by the retailer before any discounts are applied. In our example, this was \(300 for a three-piece suit.
• The discount rate is the percentage by which the original price is reduced. In the suit example, the discount rate is 15%.

To find out how much money you're saving, you multiply the original price by the discount rate expressed as a decimal. Here's the formula: \(\text{Discount Amount} = \left(\frac{\text{Discount Rate}}{100}\right) \times \text{Original Price}\)For our suit example, that would be \( \left(\frac{15}{100}\right) \times 300 \) which results in a discount amount of \)45. This means you save $45 from the original price.

Sale Price Calculation

Once we know the discount amount, the next step is to find the sale price. The sale price is what you actually pay after the discount has been applied. It is calculated by subtracting the discount amount from the original price. Here's the simple formula to determine the sale price:\(\text{Sale Price} = \text{Original Price} - \text{Discount Amount}\)In our specific example, the original price of the suit was \(300, and the discount amount we've calculated is \)45. Subtracting these gives: \(300 - 45 = 255\)So, the sale price for the three-piece suit is $255. This is the amount you would pay if you decided to purchase the item during the sale. Calculating the sale price is beneficial because it highlights the effective cost of the item after discounts.

Problem Solving Steps

To effectively solve problems involving discounts, it's important to follow a systematic approach. This ensures that you don't miss any critical steps and allows you to apply the same logic to different scenarios. Knowing the right steps can help make complex calculations seem a lot simpler.Here are the fundamental problem-solving steps:

• Identify the Original Values: Determine the original price and the discount rate. This is essential as these are the values you will use to determine the discount amount and the sale price.
• Calculate the Discount Amount: Use the formula \( \left(\frac{\text{Discount Rate}}{100}\right) \times \text{Original Price}\) to find out how much money is being reduced from the original price.
• Calculate the Sale Price: Subtract the discount amount from the original price to get the sale price. This gives you the actual cost after the discount is applied.

Following these methodical steps can simplify the process considerably and allow you to accurately determine both the discount amount and the resulting sale price in any sales scenario. Whether you’re shopping for clothes, electronics, or groceries, this structured approach will serve you well in straightforward and more complex discount calculations alike.