Problem 108 - Algebra 1

Question

A coat regularly sells for 84 dollars You buy the coat on sale and save \(\$ 10 .\) What percent is the discount? (Review 3.8 )

Step-by-Step Solution

Answer

The discount is approximately 11.9%

Step 1: Identify the given values

The coat originally costs $84 and there is a discount of $10 on it.

Step 2: Set up the discount percentage formula

The formula for the discount percentage is: \(\frac{Discount \ Amount}{Original \ Price} \times 100\% \). In this case,the Discount amount is $10 and the Original Price is $84.

Step 3: Calculate the discount percentage

Plug in the given values into the formula as follows: \(\frac{10}{84} \times 100\% \).

Step 4: Solve for discount percentage

Performing the operations, you find that the result is approximately 11.9%.

Key Concepts

Understanding Percentage in Discounts

Calculating percentage discounts is a crucial skill in daily life, especially when shopping. A percentage represents a fraction of 100, which means it is a way to express a number as a portion of a whole. When you see that a coat regularly sells for \(84 and there's a \)10 discount, understanding what percentage of the original price the discount represents helps you make informed decisions.

To find out what percent \(10 is of \)84, you'll use the formula: \( \frac{\text{Discount Amount}}{\text{Original Price}} \times 100\% \). This formula calculates the percentage discount by dividing the discount by the original price and then multiplying by 100 to get a percentage.

In this way, you can understand how much of a price reduction you are getting in terms of percentage, which is often more intuitive than just the dollar amount.

Utilizing Algebraic Formulas

Algebraic formulas provide a systematic method to solve problems involving numbers, such as finding discount percentages. The formula \( \frac{\text{Discount Amount}}{\text{Original Price}} \times 100\% \) is a specific application used to calculate percentage discounts.

This formula uses division and multiplication operations, and it is structured to convert a fractional value into a percentage. It takes the discount (in this case \(10), divides it by the original price (\)84), and then converts that fraction into a percentage by multiplying by 100.

Moreover, algebraic formulas like this allow for flexibility. If you know two quantities (for example, the original price and the discount), you can easily find the third (percentage) by rearranging the formula, which is a fundamental part of algebraic thinking.

Step-by-Step Problem Solving

Breaking down a problem into manageable steps is the essence of problem-solving. Let's consider the problem of calculating what percent the \(10 discount is of the original \)84 price.

• First, identify and list known values: original price (\(84) and discount (\)10).
• Next, choose the correct formula: \( \frac{\text{Discount Amount}}{\text{Original Price}} \times 100\% \).
• Then, substitute your known values into the formula to set up the calculation: \( \frac{10}{84} \times 100\% \).
• Finally, perform the arithmetic. Divide 10 by 84 to get approximately 0.1190. Multiply by 100 to convert to a percentage, giving you 11.9%.

Following these steps systematically ensures clarity and accuracy, which is essential when tackling mathematical problems. Each step leads logically to the next, making complex problems easier to manage.