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Chapter 6: Problem 25

Translate to a proportion. Do not solve. $$ 60 \% \text { of what is } 54 ? $$

Short Answer

Expert verified
Translate to: \[0.60 \times x = 54\]

Step by step solution

01

Identify the Percentage

First, identify the given percentage in the problem. The given percentage is 60%.
02

Convert Percentage to Decimal

Convert the given percentage to a decimal by dividing by 100. So, 60% becomes \( \frac{60}{100} = 0.60 \).
03

Set Up the Proportion

Set up the proportion based on the translation of the statement. Let x represent the unknown number.The proportion becomes: \[0.60 \times x = 54\]

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Key Concepts

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

Understanding Percentage Conversion
Percentages are a way to express a number as a fraction of 100. They are denoted using the percent symbol (%).
To convert a percentage into a decimal, you divide the percentage by 100. For example, to convert 60% to a decimal, perform the division:
\[ \frac{60}{100} = 0.60 \]
This conversion is crucial because many mathematical calculations, especially those involving algebra, require working with decimals rather than percentages.
Always remember:
  • 100% is the same as 1 in decimal
  • 50% is the same as 0.50 in decimal
  • 25% is the same as 0.25 in decimal
Practice converting percentages to decimals to become confident in handling such expressions in algebraic problems.
Basic Algebra Fundamentals
Algebra involves using symbols and letters to represent numbers in equations and formulas.
One of the most common symbols in algebra is the variable, often denoted by letters such as x or y. These variables stand in for unknown values that we aim to solve.
An algebraic expression can be something like \(0.60 \times x = 54\). Here, 'x' is the unknown number we're trying to find.
Remember these key algebra concepts:
  • An equation states that two expressions are equal, denoted by the '=' sign.
  • In the expression \(0.60 \times x = 54\), 'x' is the variable we need to solve for.
  • By performing operations (like multiplication or division), we can isolate the variable to find its value.
Developing a solid understanding of basic algebra will help in setting up and solving proportions effectively.
Proportion Setup Explained
Setting up a proportion is about forming an equation where two ratios are equal.
In the given exercise, you need to translate a statement into a proportion. The statement is: '60% of what is 54?'
Here's how you can do it:
  • First, translate the percentage into decimal: 60% becomes 0.60.
  • Next, we let 'x' represent the unknown number we are trying to find.
  • Our proportion setup becomes: \[0.60 \times x = 54\]
This equation tells us that 54 is the result of multiplying 0.60 by some unknown number 'x'. By solving this proportion, you could find the value of 'x'.
Practicing proportion setups with different statements will help you become proficient in translating word problems into mathematical equations properly.

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Most popular questions from this chapter

Michael has disposable monthly income of $$\$ 3400 .$$ Each month, he pays $$\$ 470$$ toward his credit-card debt. What percent of his disposable income is allotted to paying off credit-card debt?

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Solve. Joshua earns \(\$ 120\) for selling \(\$ 2400\) worth of television sets. What is the commission rate?
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