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Chapter 6: Problem 112

Translate and solve. 11.5% of what number is $108.10?

Short Answer

Expert verified
940.00

Step by step solution

01

Convert Percentage to Decimal

First, convert the percentage 11.5% into a decimal. This is done by dividing 11.5 by 100, which results in 0.115. Therefore, 11.5% = 0.115.
02

Set Up the Equation

Next, set up an equation based on the given problem. Let the unknown number be denoted as x. According to the problem, 11.5% of x is 108.10. This can be written as \[0.115x = 108.10\]
03

Solve for x

Now, solve the equation for x by dividing both sides by 0.115. \[x = \frac{108.10}{0.115} = 940.00\]

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Convert Percentage to Decimal
Understanding how to convert percentages to decimals is crucial in various math problems. It's quite straightforward.
To convert a percentage to a decimal, divide the percentage by 100.
For example, if you have 11.5%, you'd perform the following calculation:
\[11.5\text{ percent} = \frac{11.5}{100} = 0.115\text{ [decimal]}\]
Here are steps you can follow to make sure you're always correct:
  • Remove the percentage sign.
  • Take the numerical value and divide by 100.
In the given exercise, 11.5% is converted to 0.115. This step is critical as it translates the problem into a form that can be easily worked with mathematically.
Set Up the Equation
Setting up the equation is about translating the language of the problem into mathematical expressions.
In this case, the exercise asks: 11.5% of what number is \(108.10?
We already converted 11.5% to decimal form as 0.115 from the first step.

Let's write down what we know:
  • 0.115 represents 11.5% in decimal form.
  • The unknown number we'll call 'x'.
  • \)108.10 is the result when 11.5% of x is calculated.
Putting this together, we get:
\[0.115x = 108.10\]
This equation represents the problem in a simple, solvable form. The variable 'x' signifies the number we need to find, and 0.115x simplifies the problem to a basic algebraic equation.
Solve for Variable
Solving for the variable 'x' is the final step. This follows the rules of algebra to isolate 'x' and find its value:
We start with the equation:
\[0.115x = 108.10\]
To isolate 'x', divide both sides by 0.115:
\[x = \frac{108.10}{0.115}\]
Perform the division to find 'x':
\[x = 940.00\]
So, the unknown number is 940.00.

Steps to remember when solving for a variable:
  • Identify the variable to isolate (in this case, 'x').
  • Apply inverse operations to both sides of the equation (here, division).
  • Simplify to find the value of the variable.
This ensures that the problem is not only translated correctly but also solved accurately, with the unknown variable clearly identified.

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Most popular questions from this chapter

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