Choose The Best Equation To Represent The Following:Five Times The Difference Of A Number And 3 Is 17.A. 5 N − 3 = 17 5n - 3 = 17 5 N − 3 = 17 B. 5 ( N − 3 ) = 17 5(n - 3) = 17 5 ( N − 3 ) = 17 C. 5 N 3 = 17 \frac{5n}{3} = 17 3 5 N ​ = 17 D. 5 ( N 3 ) = 17 5\left(\frac{n}{3}\right) = 17 5 ( 3 N ​ ) = 17

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Understanding the Problem

When faced with a word problem, it's essential to translate the given information into a mathematical equation. This process involves identifying the key elements of the problem, such as the unknown quantity, the operations involved, and the relationships between the variables. In this case, we're given the problem: "Five times the difference of a number and 3 is 17." Our goal is to choose the best equation to represent this problem.

Breaking Down the Problem

Let's break down the problem into smaller parts to understand it better.

  • "Five times" indicates that we need to multiply the difference of the number and 3 by 5.
  • "the difference of a number and 3" suggests that we need to subtract 3 from the number.
  • "is 17" indicates that the result of the multiplication is equal to 17.

Analyzing the Options

Now, let's analyze the given options to determine which one best represents the problem.

Option A: 5n−3=175n - 3 = 17

This equation represents the difference of the number and 3 being multiplied by 5, but it doesn't accurately capture the "five times" aspect of the problem. Instead, it suggests that the difference is being added to 5, which is not the case.

Option B: 5(n−3)=175(n - 3) = 17

This equation correctly represents the problem. The expression "(n - 3)" represents the difference of the number and 3, and multiplying it by 5 gives us the desired result. This equation accurately captures the "five times" aspect of the problem.

Option C: 5n3=17\frac{5n}{3} = 17

This equation is incorrect because it suggests that the number is being divided by 3, rather than the difference of the number and 3 being multiplied by 5.

Option D: 5(n3)=175\left(\frac{n}{3}\right) = 17

This equation is also incorrect because it suggests that the number is being divided by 3, rather than the difference of the number and 3 being multiplied by 5.

Conclusion

Based on our analysis, the best equation to represent the problem is Option B: 5(n−3)=175(n - 3) = 17. This equation accurately captures the "five times" aspect of the problem and represents the difference of the number and 3 being multiplied by 5.

Tips for Translating Word Problems into Equations

When faced with a word problem, follow these steps to translate it into an equation:

  1. Identify the key elements of the problem, such as the unknown quantity, the operations involved, and the relationships between the variables.
  2. Break down the problem into smaller parts to understand it better.
  3. Analyze the given options to determine which one best represents the problem.
  4. Use mathematical notation to represent the problem accurately.
  5. Check your work by plugging in values or using algebraic manipulations to ensure that the equation is correct.

By following these steps, you'll be able to choose the right equation to represent the given problem and solve it accurately.

Common Mistakes to Avoid

When translating word problems into equations, avoid the following common mistakes:

  • Misinterpreting the problem: Make sure to read the problem carefully and understand what is being asked.
  • Using the wrong notation: Use mathematical notation to represent the problem accurately.
  • Failing to check your work: Plug in values or use algebraic manipulations to ensure that the equation is correct.
  • Ignoring the context: Consider the context of the problem and how it relates to the equation.

By avoiding these common mistakes, you'll be able to choose the right equation to represent the given problem and solve it accurately.

Real-World Applications

Translating word problems into equations has numerous real-world applications. In mathematics, it's essential to be able to translate word problems into equations to solve problems in algebra, geometry, and other areas of mathematics. In science, technology, engineering, and mathematics (STEM) fields, word problems are often used to model real-world scenarios and solve problems.

Conclusion

In conclusion, choosing the right equation to represent a word problem requires careful analysis and attention to detail. By following the steps outlined in this article, you'll be able to translate word problems into equations accurately and solve them with confidence. Remember to avoid common mistakes and consider the context of the problem to ensure that you're choosing the right equation.

Q: What is the first step in translating a word problem into an equation?

A: The first step in translating a word problem into an equation is to identify the key elements of the problem, such as the unknown quantity, the operations involved, and the relationships between the variables.

Q: How do I know which operation to use in the equation?

A: To determine which operation to use in the equation, read the problem carefully and identify the key words that indicate the operation. For example, "add," "subtract," "multiply," and "divide" are all key words that indicate the operation to use.

Q: What is the difference between the expressions (n - 3) and 5n - 3?

A: The expression (n - 3) represents the difference of the number and 3, while the expression 5n - 3 represents the result of multiplying the difference by 5. In other words, (n - 3) is the input, and 5n - 3 is the output.

Q: How do I know which option is the correct equation?

A: To determine which option is the correct equation, analyze each option carefully and check if it accurately represents the problem. Use mathematical notation to represent the problem accurately, and check your work by plugging in values or using algebraic manipulations to ensure that the equation is correct.

Q: What is the importance of checking your work when translating a word problem into an equation?

A: Checking your work is essential when translating a word problem into an equation because it ensures that the equation is correct and accurately represents the problem. By plugging in values or using algebraic manipulations, you can verify that the equation is correct and avoid making mistakes.

Q: How do I avoid common mistakes when translating a word problem into an equation?

A: To avoid common mistakes when translating a word problem into an equation, read the problem carefully and understand what is being asked. Use mathematical notation to represent the problem accurately, and check your work by plugging in values or using algebraic manipulations to ensure that the equation is correct.

Q: What are some real-world applications of translating word problems into equations?

A: Translating word problems into equations has numerous real-world applications in mathematics, science, technology, engineering, and mathematics (STEM) fields. Word problems are often used to model real-world scenarios and solve problems in areas such as algebra, geometry, and physics.

Q: How can I improve my skills in translating word problems into equations?

A: To improve your skills in translating word problems into equations, practice regularly and work on a variety of problems. Read the problem carefully and understand what is being asked, and use mathematical notation to represent the problem accurately. Check your work by plugging in values or using algebraic manipulations to ensure that the equation is correct.

Q: What are some common mistakes to avoid when translating word problems into equations?

A: Some common mistakes to avoid when translating word problems into equations include misinterpreting the problem, using the wrong notation, failing to check your work, and ignoring the context of the problem. By avoiding these common mistakes, you can ensure that the equation is correct and accurately represents the problem.

Q: How can I use technology to help me translate word problems into equations?

A: There are many online tools and resources available that can help you translate word problems into equations. Some popular options include online equation solvers, graphing calculators, and math software. These tools can help you check your work, visualize the problem, and solve equations accurately.

Q: What is the role of algebra in translating word problems into equations?

A: Algebra plays a crucial role in translating word problems into equations. Algebraic notation and techniques, such as variables, constants, and equations, are used to represent the problem accurately and solve it. By using algebraic notation and techniques, you can translate word problems into equations and solve them with confidence.

Q: How can I use word problems to improve my algebra skills?

A: Word problems are an excellent way to improve your algebra skills. By working on a variety of word problems, you can practice translating the problem into an equation, solving the equation, and checking your work. This will help you develop your algebra skills and become more confident in your ability to solve equations.

Q: What are some tips for translating word problems into equations?

A: Some tips for translating word problems into equations include:

  • Read the problem carefully and understand what is being asked.
  • Identify the key elements of the problem, such as the unknown quantity, the operations involved, and the relationships between the variables.
  • Use mathematical notation to represent the problem accurately.
  • Check your work by plugging in values or using algebraic manipulations to ensure that the equation is correct.
  • Practice regularly and work on a variety of problems to improve your skills.

By following these tips and practicing regularly, you can become more confident in your ability to translate word problems into equations and solve them with accuracy.