Problem 29 - Introductory Algebra for College Students

Question

Use the percent formula, \(A=P B: A\) is \(P\) percent of \(B,\) to solve. What is \(18 \%\) of \(40 ?\)

Step-by-Step Solution

Answer

18% of 40 equals 7.2.

Step 1: Understand the Problem

In this problem, need to find 18% of 40. The formula is expressed as: \(A = P*B\) where: \n\nA = the amount that P percent of B represents\nP = the percentage\nB = the base amount.

Step 2: Plug in the given values to the formula

Substitute the given values into the formula: \(A = 18\% * 40\). In the percentage calculation, it's necessary to express the percentage as a decimal. Thus, the formula now looks like this: \(A = 0.18 * 40\).

Step 3: Solve the equation

Perform multiplication to get the value of A: \(A = 0.18 * 40 = 7.2\).

Key Concepts

Basic Algebra

Basic algebra is an essential foundation in the world of mathematics. It serves as the building blocks for higher-level math concepts. At its core, basic algebra deals with symbols and the rules for manipulating these symbols. In its simplest form, algebra is the study of mathematical symbols and the rules for combining them.
When working with basic algebra, you often encounter equations. An equation like \( A = P \times B \) is used to find unknown values or verify solutions to a problem. Each of these symbols represents something specific:

• \( A \) is the amount.
• \( P \) stands for the percentage or rate.
• \( B \) is the base or original quantity.

Breaking down problems into these symbols and manipulating them to find a solution is a significant part of basic algebra. This technique applies to many types of problems, including percent calculations.

Percentage Calculation

Percentage calculation is a common and useful mathematical operation. It allows you to express numbers as a part of 100. This becomes particularly useful when comparing values of different sizes.
In the exercise using the percent formula \( A = P \times B \), the calculation helps us find what 18% of 40 is. Here's how you break it down:

• First, convert the percentage to a decimal: 18% becomes 0.18, since percentages are parts of 100, and hence \( 18\% = 18/100 = 0.18 \).
• Next, multiply 0.18 by 40: \( A = 0.18 \times 40 \).
• This results in \( A = 7.2 \).

With these steps, understanding, and applying percentage calculations becomes manageable. It's a tool used extensively in fields like finance, statistics, and general day-to-day activities.

Introductory Algebra

Introductory algebra sets the stage for all advanced mathematical concepts. It introduces you to the language of algebra and crucial techniques like simplifying expressions, solving equations, and understanding variables.
Here's how introductory algebra applies in the given problem:

• Recognizing what each variable in the formula \( A = P \times B \) represents - a vital first step.
• Converting percentages into decimals is an early algebraic skill that makes calculations easier, providing more clarity and simplicity during problem-solving.
• Solving the equation via multiplication helps build familiarity with combining numbers and variables, a fundamental algebraic operation.

Through these basic tasks, introductory algebra invites you to see the underlying structure of math problems, making it easier to solve them. This foundational knowledge is what students build upon to tackle more advanced topics.