Subtracting 120 from Both Sides

Oct 13, 2025 by miodeya.com 18 views

Introduction

Mathematics is a subject that deals with numbers and their relationships. It is a fundamental subject that is used in various aspects of life, including science, engineering, economics, and finance. In this article, we will discuss a mathematical problem that involves an increased number in 8 and a decreased number in 3. We will use algebraic equations to solve the problem and find the value of the number.

Problem Statement

The problem statement is as follows:

"Three quarters of an increased number in 8 is equal to a fifth of the same decreased number in 3. What is the number?"

Algebraic Equation

Let's assume that the number is x. We can write the problem statement as an algebraic equation:

(3/4)(8 + x) = (1/5)(3 - x)

Simplifying the Equation

To simplify the equation, we can start by multiplying both sides by 20, which is the least common multiple of 4 and 5:

15(8 + x) = 4(3 - x)

Expanding the Equation

Next, we can expand the equation by multiplying the terms inside the parentheses:

120 + 15x = 12 - 4x

Combining Like Terms

Now, we can combine like terms by adding or subtracting the coefficients of the x terms:

120 + 15x + 4x = 12

Simplifying the Equation

We can simplify the equation by combining the x terms:

120 + 19x = 12

Subtracting 120 from Both Sides

To isolate the x term, we can subtract 120 from both sides of the equation:

19x = -108

Dividing Both Sides by 19

Finally, we can divide both sides of the equation by 19 to solve for x:

x = -108/19

Calculating the Value of x

To calculate the value of x, we can use a calculator or perform the division manually:

x = -5.684

Conclusion

In this article, we discussed a mathematical problem that involved an increased number in 8 and a decreased number in 3. We used algebraic equations to solve the problem and found the value of the number. The value of the number is -5.684.

Real-World Applications

This problem has real-world applications in various fields, including science, engineering, economics, and finance. For example, in finance, the problem can be used to calculate the value of a stock or a bond that has increased or decreased in value. In engineering, the problem can be used to calculate the stress or strain on a material that has been subjected to an increase or decrease in temperature.

Tips and Tricks

Here are some tips and tricks that can be used to solve this problem:

Use algebraic equations to represent the problem statement.
Simplify the equation by combining like terms.
Isolate the x term by subtracting or adding the coefficients of the x terms.
Divide both sides of the equation by the coefficient of the x term to solve for x.

Frequently Asked Questions

Here are some frequently asked questions that can be used to clarify the problem:

What is the problem statement?
How can we represent the problem statement as an algebraic equation?
How can we simplify the equation by combining like terms?
How can we isolate the x term by subtracting or adding the coefficients of the x terms?
How can we divide both sides of the equation by the coefficient of the x term to solve for x?

References

Here are some references that can be used to learn more about the problem:

[1] Algebraic Equations, Wikipedia.
[2] Simplifying Algebraic Equations, Math Is Fun.
[3] Isolating Variables, Khan Academy.

Conclusion

In conclusion, this article discussed a mathematical problem that involved an increased number in 8 and a decreased number in 3. We used algebraic equations to solve the problem and found the value of the number. The value of the number is -5.684. This problem has real-world applications in various fields, including science, engineering, economics, and finance. We also provided tips and tricks that can be used to solve this problem, as well as frequently asked questions and references that can be used to learn more about the problem.

Introduction

In our previous article, we discussed a mathematical problem that involved an increased number in 8 and a decreased number in 3. We used algebraic equations to solve the problem and found the value of the number. In this article, we will provide a Q&A section to clarify any doubts or questions that readers may have.

Q&A

Q: What is the problem statement?

A: The problem statement is as follows: "Three quarters of an increased number in 8 is equal to a fifth of the same decreased number in 3. What is the number?"

Q: How can we represent the problem statement as an algebraic equation?

A: We can represent the problem statement as an algebraic equation by letting x be the number. The equation is:

(3/4)(8 + x) = (1/5)(3 - x)

Q: How can we simplify the equation by combining like terms?

A: We can simplify the equation by combining like terms by multiplying both sides of the equation by 20, which is the least common multiple of 4 and 5:

15(8 + x) = 4(3 - x)

Q: How can we isolate the x term by subtracting or adding the coefficients of the x terms?

A: We can isolate the x term by subtracting 120 from both sides of the equation:

19x = -108

Q: How can we divide both sides of the equation by the coefficient of the x term to solve for x?

A: We can divide both sides of the equation by 19 to solve for x:

x = -108/19

Q: What is the value of the number?

A: The value of the number is -5.684.

Q: What are some real-world applications of this problem?

A: This problem has real-world applications in various fields, including science, engineering, economics, and finance. For example, in finance, the problem can be used to calculate the value of a stock or a bond that has increased or decreased in value. In engineering, the problem can be used to calculate the stress or strain on a material that has been subjected to an increase or decrease in temperature.

Q: What are some tips and tricks that can be used to solve this problem?

A: Here are some tips and tricks that can be used to solve this problem:

Use algebraic equations to represent the problem statement.
Simplify the equation by combining like terms.
Isolate the x term by subtracting or adding the coefficients of the x terms.
Divide both sides of the equation by the coefficient of the x term to solve for x.

Q: What are some frequently asked questions that can be used to clarify the problem?

A: Here are some frequently asked questions that can be used to clarify the problem:

What is the problem statement?
How can we represent the problem statement as an algebraic equation?
How can we simplify the equation by combining like terms?
How can we isolate the x term by subtracting or adding the coefficients of the x terms?
How can we divide both sides of the equation by the coefficient of the x term to solve for x?

Conclusion

In conclusion, this article provided a Q&A section to clarify any doubts or questions that readers may have about the problem. We hope that this article has been helpful in understanding the problem and its solution.

References

Here are some references that can be used to learn more about the problem:

[1] Algebraic Equations, Wikipedia.
[2] Simplifying Algebraic Equations, Math Is Fun.
[3] Isolating Variables, Khan Academy.

Additional Resources

Here are some additional resources that can be used to learn more about the problem:

[1] Algebraic Equations, Mathway.
[2] Simplifying Algebraic Equations, IXL.
[3] Isolating Variables, Purplemath.

Contact Us

If you have any questions or need further clarification on the problem, please do not hesitate to contact us. We are here to help and want to ensure that you have a clear understanding of the problem and its solution.