Problem 28 - Introductory and Intermediate Algebra for College Students 4th

Question

Use the percent formula, \(A=P B: A\) is \(P\) percent of \(B,\) to solve Exercises \(27-42\) What is \(8 \%\) of \(300 ?\)

Step-by-Step Solution

Answer

8 percent of 300 is 24.

Step 1: Convert the Percentage

Firstly, the percentage needs to be converted to its decimal equivalent. This can be done by dividing the percentage by 100. Thus, 8% becomes \(0.08\).

Step 2: Apply the Percent Formula

Next, substitute the known values into the percentage formula. Let \(A\) be the unknown quantity. \(P\) is 0.08 (the decimal equivalent of 8%), and \(B\) is 300. Substituting these values into the formula gives: \(A = 0.08 \cdot 300\).

Step 3: Calculate the Value

Finally, perform the multiplication to find the value of \(A\): \(A = 0.08 \cdot 300 = 24\).

Key Concepts

Percentage to Decimal Conversion

Understanding the transition from percentage to decimal is crucial when dealing with calculations in mathematics. A percentage represents a fraction of 100, which means to convert a percentage to a decimal, you simply divide by 100.

For example, if you have an 8% rate, you'll convert it by dividing 8 by 100, which equates to 0.08. This step is important because it makes further calculations easier, as dealing with decimals is a more common operation in algebra.

Let's break down the conversion process:

• Write the percentage as a whole number or a fraction (e.g., 8% or 8/100).
• Divide the number by 100 by moving the decimal point two places to the left.
• Drop the percent sign and use the resulting decimal for your calculations.

Applying Percentage Formula

The percentage formula is a fundamental expression in mathematics that allows you to find 'parts of the whole'. The general formula is expressed as: \( A = P \times B \), where \( A \) is the resultant amount, \( P \) is the percentage converted into decimal form, and \( B \) is the base or whole quantity.

To apply this formula effectively, start by ensuring that \( P \) is in decimal form. Then, multiply it by \( B \). This multiplication gives you \( A \), which is the portion of \( B \) that correlates to \( P \) percent. For instance, to find 8% of 300, you multiply the decimal form of 8%, which is 0.08, by 300. Consequently, you end up with 24, meaning 8% of 300 is 24.

Basic Algebraic Manipulation

Basic algebraic manipulation refers to rearranging, adding, subtracting, dividing, and multiplying algebraic expressions to simplify them or solve for variables. Understanding these techniques is necessary in applying the percentage formula.

For example, simplified algebraic manipulation is used in the previous example when multiplying 0.08 by 300 to find 8% of 300. Here, multiplication is the operation required to manipulate the expression to solve for \( A \), the final answer.

It’s essential to familiarize oneself with these operations and the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction), to ensure accuracy in problem-solving.