Problem 54 - Elementary Algebra

Question

Answer the question by setting up and solving an appropriate equation. 72 is what percent of 120 ?

Step-by-Step Solution

Answer

72 is 60% of 120.

Step 1: Identify the Unknown

We need to find what percent of 120 is 72. Let's denote the unknown percent by \( x \).

Step 2: Set Up the Equation

We know that 72 is \( x \) percent of 120, which translates to the equation: \( 72 = \frac{x}{100} \times 120 \).

Step 3: Isolate the Variable

To isolate \( x \), multiply both sides of the equation by 100 and then divide by 120: \( x = \frac{72 imes 100}{120} \).

Step 4: Calculate the Value

Now, perform the multiplication and division: \( x = \frac{7200}{120} \), resulting in \( x = 60 \).

Step 5: Check Your Work

Verify the solution by calculating \( 60\% \) of 120 and ensure it equals 72: \( 0.60 \times 120 = 72 \).

Key Concepts

Algebra Equations

Algebra equations are mathematical statements that show the equality between two expressions. They are essential in solving problems where one or more values are unknown. In this exercise, we are using an algebra equation to find out what percent 72 is of 120. We'll denote the unknown percentage as \( x \). The equation format here is set up to express one quantity as a percentage of another using the basic formula:

• \( Quantity = \left( \frac{Percentage}{100} \right) \, \times \, Total \)

Algebra equations are powerful because they allow us to manipulate variables. By reorganizing the equation and solving for \( x \), we can effectively determine unknown quantities. To solve such problems, you'll need to understand the basic principles of isolating variables and performing operations like multiplication or division on both sides of the equation.

Percent Calculations

Percent calculations are crucial when you want to express a number as a fraction of 100. In the context of the problem, we want to find what percentage 72 is of 120. To do this, follow these steps:

• Set up the equation: \( 72 = \frac{x}{100} \times 120 \)
• Reorganize the equation to find \( x \): Multiply both sides of the equation by 100, then divide by 120.

This will give you the value of \( x \), which is the percentage representation of the number. Percent calculations help in understanding proportions and comparing different quantities on a consistent scale of 100. Real-life scenarios like discounts, tax rates, and statistics use percentage calculations to communicate information effectively.

Solving Linear Equations

Solving linear equations involves finding the value of unknown variables that make the equation true. These are the basic steps followed in our percentage problem:

• Isolate the variable: Ensure that the unknown variable \( x \) is separated on one side of the equation.
• Eliminate fractions or coefficients by multiplying or dividing as necessary.
• In our case, multiplying both sides by 100 and dividing by 120 efficiently isolated \( x \).

Linear equations are simple but fundamental. They form the basis of more complex algebraic operations and are used extensively in various fields such as engineering, finance, and everyday decision-making. Once you get the structure of how to solve linear equations, you can apply these skills to solve percentage problems, as demonstrated in the exercise.