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Magazine Chapter 2: Problem 48
Solve. 54 is \(24 \%\) of what number?
Short Answer
Expert verified
225
Step by step solution
01
Understand the problem
We need to find out the total number that 54 is 24% of. In other words, if 24% of some number is 54, what is that number?
02
Set up the equation
Let the unknown number be represented as \( x \). According to the problem, we have: 54 = 24% of x.
03
Convert percentage to a decimal
Convert the percentage to a decimal by dividing 24 by 100. So, 24% = 0.24.
04
Write the equation
Replace 24% with 0.24 in the equation. Therefore, our equation becomes: 54 = 0.24 \( x \).
05
Solve for x
To find \( x \), divide both sides of the equation by 0.24: \[ x = \frac{54}{0.24} \].
06
Calculate the value
Perform the division to find the value of \( x \): \[ x = \frac{54}{0.24} = 225 \].
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
solving equations
Solving equations is a fundamental skill in algebra that allows us to find unknown values in mathematical relationships. Typically, an equation will include variables (like \( x \)) and constants (fixed numbers).
To solve an equation, follow these steps:
\[ x = \frac{54}{0.24} \].
Once the variable is isolated, you can solve for its value.
To solve an equation, follow these steps:
- Identify the variable you need to solve for.
- Isolate the variable on one side of the equation.
- Perform the same operation on both sides of the equation to maintain equality.
\[ x = \frac{54}{0.24} \].
Once the variable is isolated, you can solve for its value.
percentage calculations
Percentage calculations are used to determine how much of a part is taken from a whole. The term percent means per hundred, and is represented by the symbol \( \% \).
To solve percentage problems, use this general approach:
Let the total (unknown) number be \( x \). The equation is 54 is 24% of \( x \), or
54 = 0.24x.
By solving this equation, you can find the value of \( x \), which represents the total number.
To solve percentage problems, use this general approach:
- Convert the percentage to a decimal.
- Set up an equation representing the relationship between the part, the whole, and the percentage.
Let the total (unknown) number be \( x \). The equation is 54 is 24% of \( x \), or
54 = 0.24x.
By solving this equation, you can find the value of \( x \), which represents the total number.
decimal conversion
Decimal conversion is the process of converting a percentage into a decimal number. This step is crucial in solving many mathematical problems involving percentages.
To convert a percentage to a decimal:
24 / 100 = 0.24.
This decimal form can then be used in equations. In our example, converting 24% to 0.24 allowed us to set up the equation \( 54 = 0.24x \).
To convert a percentage to a decimal:
- Simply divide the percentage by 100.
24 / 100 = 0.24.
This decimal form can then be used in equations. In our example, converting 24% to 0.24 allowed us to set up the equation \( 54 = 0.24x \).
basic algebra
Basic algebra involves understanding and manipulating expressions and equations to find unknown values. Here are the key elements:
1. Identified the problem and variable:
54 is 24% of what number?\( x \)
2. Set up an equation based on the problem description:
54 = 0.24\( x \)
3. Solved for \( x \) by isolating the variable:\[ x = \frac{54}{0.24} \]=225.
Understanding these basic principles helps solve more complex algebra problems efficiently.
- Variables: symbols that represent unknown values (e.g., \( x \)).
- Constants: fixed numbers in equations.
- Operations: addition, subtraction, multiplication, and division.
1. Identified the problem and variable:
54 is 24% of what number?\( x \)
2. Set up an equation based on the problem description:
54 = 0.24\( x \)
3. Solved for \( x \) by isolating the variable:\[ x = \frac{54}{0.24} \]=225.
Understanding these basic principles helps solve more complex algebra problems efficiently.
