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Chapter 2: Problem 94

Solve each problem. \(18 \%\) of what number is \(108 ?\)

Short Answer

Expert verified
The number is 600.

Step by step solution

01

Set up the equation

Use the given information to set up an equation. Let the unknown number be represented as . The problem states that 18% of is 108. This can be represented as
02

Convert percentage to decimal

Convert 18% to a decimal. This is done by dividing by 100. Thus, 18% becomes 0.18.
03

Write the mathematical expression

Using the decimal form, the equation becomes:
04

Solve for n

To isolate , divide both sides of the equation by 0.18:
05

Calculate the result

Divide 108 by 0.18 to find the value of .

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Key Concepts

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

percentage to decimal conversion
Understanding how to convert percentages to decimals is essential in solving percentage problems. A percentage represents a number out of 100. To convert a percentage to a decimal, you simply divide by 100. For example, 18% as a decimal is calculated as follows:
  • Take the percentage value, 18.
  • Divide 18 by 100.
  • The result is 0.18.
In general, converting a percentage like 25% to a decimal would be: 25 梅 100 = 0.25. By understanding this concept, you will be able to solve problems more efficiently, as it simplifies further calculations.
solving linear equations
Linear equations are equations of the first degree, meaning they involve no exponents higher than 1. In our problem, the linear equation is set up as follows:

Let the unknown number be represented by the variable, say, n. The problem states that 18% of n is 108. In mathematical terms, this is written as:
0.18n = 108 To solve this, we need to isolate the variable n. Here's how we do it:
  • Start with the equation 0.18n = 108.

  • Divide both sides of the equation by 0.18 to get n by itself:
  • n = 108 梅 0.18

This process of isolating the variable is called solving the equation, an important step in algebra to find the unknown value.
basic algebraic operations
Basic algebraic operations are fundamental in solving equations and include addition, subtraction, multiplication, and division. In the context of solving our problem, we often use multiplication and division.
Our problem has the equation: 0.18n = 108.
  • First, recognize that 0.18 is multiplied by n.
  • To isolate n, we need to perform the inverse operation, which is division.
  • We divide both sides by 0.18:
  • n = 108 梅 0.18

Doing this division gives us n, the unknown value we were looking for.
In our solution, n = 108 梅 0.18 = 600.
Understanding these basic operations helps in manipulating and solving different algebraic expressions effectively.

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