If 73 Is Added To A Number, The Result Is 43 Less Than Three Times The Number. Find The Number.

by ADMIN 96 views

Problem Explanation

In this problem, we are given a mathematical equation that describes a relationship between a number and its result when 73 is added to it. The equation states that the result is 43 less than three times the number. Our goal is to find the original number.

Step 1: Translate the Problem into an Equation

Let's denote the original number as x. According to the problem, when 73 is added to x, the result is 43 less than three times x. We can write this as an equation:

x + 73 = 3x - 43

Step 2: Simplify the Equation

To solve for x, we need to simplify the equation by getting all the terms involving x on one side and the constants on the other side.

x + 73 = 3x - 43

Subtract x from both sides:

73 = 2x - 43

Step 3: Isolate the Variable

Now, we need to isolate the variable x by getting rid of the constant term on the right-hand side.

73 = 2x - 43

Add 43 to both sides:

116 = 2x

Step 4: Solve for x

Finally, we can solve for x by dividing both sides by 2.

116 = 2x

Divide both sides by 2:

x = 58

Conclusion

We have found the original number to be 58.

Solution Explanation

The solution to this problem involves translating the given equation into a mathematical expression, simplifying the equation, isolating the variable, and solving for x. By following these steps, we were able to find the original number that satisfies the given condition.

Example Use Case

This problem can be used as an example of how to solve linear equations in algebra. It demonstrates the importance of following the order of operations and simplifying equations to isolate the variable.

Real-World Application

This type of problem can be applied to real-world scenarios where we need to find a value that satisfies a given condition. For example, in finance, we might need to find the initial investment that will result in a certain return after a certain period.

Tips and Tricks

When solving linear equations, it's essential to follow the order of operations and simplify the equation by getting all the terms involving the variable on one side and the constants on the other side. Additionally, make sure to isolate the variable by getting rid of any constant terms on the right-hand side.

Common Mistakes

One common mistake when solving linear equations is to forget to simplify the equation or to isolate the variable. Make sure to follow the steps outlined above to avoid these mistakes.

Further Reading

For more practice problems and examples, check out the following resources:

  • Khan Academy: Linear Equations
  • Mathway: Linear Equations
  • Wolfram Alpha: Linear Equations

References

  • [1] "Algebra" by Michael Artin
  • [2] "Linear Algebra" by Jim Hefferon
  • [3] "Mathematics for Computer Science" by Eric Lehman

Note: The references provided are for further reading and are not directly related to the solution of the problem.

Q: What is the problem asking for?

A: The problem is asking for a number that, when 73 is added to it, the result is 43 less than three times the number.

Q: How do I start solving this problem?

A: To start solving this problem, you need to translate the given condition into a mathematical equation. Let's denote the original number as x. According to the problem, when 73 is added to x, the result is 43 less than three times x. We can write this as an equation: x + 73 = 3x - 43.

Q: What is the next step in solving this problem?

A: The next step is to simplify the equation by getting all the terms involving x on one side and the constants on the other side. Subtract x from both sides: 73 = 2x - 43.

Q: How do I isolate the variable x?

A: To isolate the variable x, you need to get rid of the constant term on the right-hand side. Add 43 to both sides: 116 = 2x.

Q: What is the final step in solving this problem?

A: The final step is to solve for x by dividing both sides by 2. x = 58.

Q: What is the original number that satisfies the given condition?

A: The original number that satisfies the given condition is 58.

Q: Can you provide an example use case for this problem?

A: This problem can be used as an example of how to solve linear equations in algebra. It demonstrates the importance of following the order of operations and simplifying equations to isolate the variable.

Q: How does this problem relate to real-world applications?

A: This type of problem can be applied to real-world scenarios where we need to find a value that satisfies a given condition. For example, in finance, we might need to find the initial investment that will result in a certain return after a certain period.

Q: What are some common mistakes to avoid when solving this problem?

A: One common mistake when solving linear equations is to forget to simplify the equation or to isolate the variable. Make sure to follow the steps outlined above to avoid these mistakes.

Q: Where can I find more practice problems and examples?

A: For more practice problems and examples, check out the following resources:

  • Khan Academy: Linear Equations
  • Mathway: Linear Equations
  • Wolfram Alpha: Linear Equations

Q: Are there any additional resources that can help me understand this problem better?

A: Yes, there are several resources that can help you understand this problem better. Some recommended resources include:

  • "Algebra" by Michael Artin
  • "Linear Algebra" by Jim Hefferon
  • "Mathematics for Computer Science" by Eric Lehman

Q: Can you provide a summary of the solution?

A: The solution to this problem involves translating the given equation into a mathematical expression, simplifying the equation, isolating the variable, and solving for x. By following these steps, we were able to find the original number that satisfies the given condition.

Q: What is the final answer to this problem?

A: The final answer to this problem is 58.