91Ó°ÊÓ

In algebra, variables are symbols used to represent unknown values. They can be any letter, but common choices include \( x \), \( y \), or \( z \).
Variables allow us to create equations and expressions that model real-world situations. In this particular exercise, we use the variable \( x \) to represent the number we are trying to find.
Understanding how to work with variables is crucial because they form the foundation for creating equations and solving various problems in algebra. When we see a variable in an equation, like \( x + 0.60x = 192 \), it signifies a quantity that can change or that we are trying to determine.

Percentage problems often involve finding a part of a whole or determining what a percentage of a number represents. In this exercise, we deal with finding 60% of a number and adding it back to the original number.
To express a percentage as a decimal in calculations, convert the percentage by dividing by 100. For example, to find 60% of a number, express 60% as \(0.60\).
The exercise sets up the problem as follows: the number \(x\) plus 60% of the number, which is \(0.60x\), equals \(192\).
Recognizing that percentage problems require converting percentages to decimals is essential. This allows us to manipulate the values algebraically, paving the way for setting up and solving equations.

Solving equations involves finding the value of the variable that makes the equation true. Let's walk through the steps using our example equation:
1. **Set up the equation**: We start by translating the word problem into a mathematical equation: \(x + 0.60x = 192\). 2. **Simplify the equation**: Combine like terms on the left side. \(x + 0.60x\) becomes \(1.60x\). Now the equation is \(1.60x = 192\). 3. **Solve for the variable**: To isolate \(x\), divide both sides of the equation by \(1.60\). This results in \(x = \frac{192}{1.60}\).
The process requires understanding each step, from setting up the equation to simplifying and solving it. Each part relies on simple arithmetic techniques but requires careful manipulation to arrive at the correct solution. Mastering these steps helps in tackling a wide variety of algebraic problems.