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Chapter 6: Problem 18

Translate to an equation and solve. 60 is what percent of \(20 ?\)

Short Answer

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Step by step solution

01

- Understand the problem

We need to find what percent 60 is of 20. To do this, we'll set up an equation where a certain percentage of 20 equals 60.
02

- Set up the equation

Let the percentage be represented by the variable \(x\). The equation to determine the percentage would be \[20 \times (\frac{x}{100}) = 60\].
03

- Solve for x

To solve the equation, first multiply both sides by \100\ to get rid of the fraction: \[20x = 6000\]. Next, divide both sides by \20\: \[x = \frac{6000}{20} = 300\].

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Key Concepts

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

Basic Algebra
Basic algebra involves understanding how to work with variables and equations. In this problem, we use a variable, commonly represented by a letter like \(x\), to stand in for the unknown percentage we are looking to find. This approach helps us transform a word problem into a more manageable mathematical equation.

Variables are used in algebra to generalize and solve a wide range of problems. Here, the variable acts as a placeholder for the percent value in the equation, which ultimately helps in determining the correct percentage. Basic algebra skills involve knowing how to manipulate these variables to isolate the unknown and solve the equation effectively.
Mathematical Equations
Mathematical equations are statements that show the equality of two expressions. In this problem, we set up an equation to find out what percent of 20 is equal to 60. This is done by creating the equation \[20 \times \left( \frac{x}{100} \right) = 60\]. By understanding that a percentage is essentially a fraction of 100, we can transform this word problem into a mathematical statement.

We start with the basic equation and solve for the unknown variable:
  • First, multiply both sides by 100 to eliminate the fraction: \[20x = 6000\]
  • Then, divide both sides by 20 to solve for \(x\): \[x = \frac{6000}{20} = 300\]

By following these logical steps, we solve the equation and find the solution.
Problem-Solving Steps
When approaching any mathematical problem, it鈥檚 important to follow a structured set of problem-solving steps. Here's how to effectively work through this percentage problem:

  1. Understand the Problem: Begin by clearly identifying what you are trying to find. In this case, we need to determine what percent 60 is of 20.

  2. Set Up the Equation: Translate the word problem into a mathematical equation. Use a variable (e.g., \(x\)) to represent the unknown value. The equation we use is \[20 \times \left( \frac{x}{100} \right) = 60\].

  3. Solve for the Variable: Perform algebraic operations to isolate the variable and solve the equation. First, multiply both sides by 100, and then divide by 20 to get \[x=300\].

  4. Review Your Solution: Finally, double-check your calculations to ensure accuracy and that the solution makes sense in the context of the problem.


By following these systematic steps, you can break down complex problems into simpler parts and arrive at the correct solution.

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Most popular questions from this chapter

A person earns $$\$ 28,600$$ one year and receives a \(5 \%\) raise in salary. What is the new salary?

Find percent notation for the decimal notation(s) in each sentence. A recent survey showed that children prefer playing with touch screen devices to playing with construction blocks and puzzles. Of the 300 parents surveyed, 0.62 said that their children "often" or "very often" play with touch screens; only 0.49 gave the same responses for construction blocks and only 0.38 for puzzles.

Convert to standard notation. $$ 42.7 \text { million } $$

Convert to standard notation. $$ 6.09 \text { billion } $$

Simplify: \((12-3)^{2}-9+5^{2}\)
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