Problem 56 - Prealgebra

Question

A suit that normally sells for \(\$ 221\) is on sale for \(\frac{1}{4}\) off. What is the sale price of the suit?

Step-by-Step Solution

Answer

The sale price of the suit is \(\$ 165.75\).

Step 1: Determine the Discount Amount

First, we need to find out how much the discount is by multiplying the original price of the suit by the discount fraction. The original price of the suit is \(\\( 221\), and the discount is \(\frac{1}{4}\) or 0.25.Calculate \[\text{Discount Amount} = 221 \times \frac{1}{4} = 221 \times 0.25 = 55.25\]So, the discount amount is \(\\) 55.25\).

Step 2: Calculate the Sale Price

Next, subtract the discount amount from the original price to determine the sale price.The original price is \(\\( 221\) and the discount amount is \(\\) 55.25\).Calculate \[\text{Sale Price} = 221 - 55.25 = 165.75\]Therefore, the sale price of the suit is \(\$ 165.75\).

Key Concepts

Percentages

In everyday life, percentages are often used to express how one quantity relates to another. A percentage is essentially a fraction out of 100. For example, if you have a discount of 25%, it means you are saving 25 parts out of every 100. When translating this to a mathematical operation, it's important to remember that

• 25% equals \( \frac{25}{100} \), which can be simplified to \( 0.25 \).
• This percentage represents the portion of the original price being deducted.

To find out how much you save, you multiply the original amount by this percentage in decimal form. This is a crucial step in calculating discounts and sales prices effectively.

Sale Price

The sale price is what you end up paying after any discount has been applied. Understanding how to determine the sale price is practical and straightforward. Once you have calculated the discount amount, finding the sale price involves one simple subtraction. Here’s how it works:

• First, identify the discount amount. This is done by multiplying the original price by the discount rate, as a decimal.
• Then, subtract this discount amount from the original price.

So, with an original price of \( \\(221 \) and a discount of \( \\)55.25 \), the sale price is \( \\(221 - \\)55.25 = \$165.75 \). This represents the cost you pay after the discount has been applied.

Basic Arithmetic

Basic arithmetic forms the foundation of more complex math problems. It encompasses basic operations such as addition, subtraction, multiplication, and division. In calculating discounts and sale prices, these operations are vital.

• Multiplication helps determine the discount amount; you multiply the total price by the discount rate.
• Subtraction is used to find the price you actually pay, by deducting the discount from the original price.

These fundamental skills are not only applicable to this kind of problem but also in everyday scenarios, such as budgeting, shopping, and financial planning, making them indispensable life tools.