Problem 24 - Elementary Algebra

Question

The sum of a number and sixteen is forty-two. What is the number?

Step-by-Step Solution

Answer

Answer: The number is 26.

Step 1: Set up the equation

Based on the given information, we can set up the following equation: number + 16 = 42

Step 2: Solve for the number

To find the value of 'number', we need to isolate it on one side of the equation. We will subtract 16 from both sides of the equation: number + 16 - 16 = 42 - 16 number = 26

Step 3: State the answer

The number we are looking for is 26.

Key Concepts

Algebraic Equations

Algebraic equations are used to express relationships between different quantities using variables. In our exercise, the problem involves finding an unknown number, which we represent with the variable 'number'.

This equation is represented in a simple mathematical form as:

• Number + 16 = 42

This type of equation involves only one variable and is known as a linear equation. Understanding and setting up these equations is fundamental in algebra as it allows us to solve real-world problems by finding unknown values. The main goal of any algebraic equation is to isolate the variable on one side to find its value.

Solving Equations

Solving equations is a process that involves finding the value of an unknown variable that satisfies the equation. In our example, we want to find the value of 'number'. To do this, we perform operations that will isolate the variable on one side of the equation.

Here is the step-by-step process:

• Identify the operation being applied to the variable. In this case, it's the addition of 16.
• Do the reverse operation to both sides of the equation to cancel it out. So, we subtract 16 from both sides.
• The updated equation becomes: Number = 42 - 16
• Simplify the equation to find the value of the variable.

By performing these steps, you can solve the equation and find that the unknown number is 26.

Basic Arithmetic Operations

Basic arithmetic operations are the foundation of mathematics and are crucial for solving algebraic equations. The four basic operations are addition, subtraction, multiplication, and division.

In our exercise, subtraction is employed to isolate the variable. Here's how these operations work in algebraic contexts:

• Addition combines numbers to find a sum. For example, number + 16 = 42.
• Subtraction is used to find the difference between numbers. It helps in reversing an addition, so the equation number + 16 becomes number = 42 - 16.

Understanding how to manipulate these operations helps to simplify equations and solve for unknown values. Mastery of these basic operations is essential for solving more complex mathematical problems.