Solving for the Original Number

Oct 13, 2025 by recoveryshake.com 147 views

Understanding the Problem

To solve this problem, we need to find the original number that, when multiplied by 0.75, equals 45. This involves setting up an equation and solving for the unknown number.

Setting Up the Equation

Let's denote the original number as 'x'. We are given that 0.75 of this number is equal to 45. Mathematically, this can be represented as:

0.75x = 45

Solving for the Original Number

To find the original number, we need to isolate 'x' on one side of the equation. This can be done by dividing both sides of the equation by 0.75.

x = 45 / 0.75

Calculating the Value

Now, let's calculate the value of 'x' by performing the division.

x = 60

Conclusion

Therefore, the original number is 60.

Why is This Problem Important?

This problem is important because it demonstrates the application of basic algebraic concepts, such as setting up and solving equations. It also highlights the importance of understanding fractions and decimals in mathematics.

Real-World Applications

This problem has real-world applications in various fields, such as finance, science, and engineering. For instance, in finance, understanding how to calculate percentages and fractions is crucial for making informed investment decisions. In science, being able to solve equations like this one is essential for modeling and predicting complex phenomena.

Common Mistakes to Avoid

When solving this problem, some common mistakes to avoid include:

Not setting up the equation correctly
Not isolating the variable 'x' on one side of the equation
Not performing the division correctly

Tips for Solving Similar Problems

To solve similar problems, follow these tips:

Read the problem carefully and understand what is being asked
Set up the equation correctly
Isolate the variable on one side of the equation
Perform the necessary operations to solve for the variable

Practice Problems

Try solving the following problem:

If 0.25 of a number is 20, what is the original number?

A. 20 B. 80 C. 100 D. 120

Answer

The answer is B. 80.

Conclusion

In conclusion, solving this problem requires setting up an equation and solving for the unknown number. By following the steps outlined in this article, you can confidently solve similar problems and apply your skills to real-world applications.

Frequently Asked Questions

Q: What is the original number if 0.75 of it is 45?

A: The original number is 60.

Q: How do I set up the equation to solve this problem?

A: To set up the equation, let 'x' represent the original number. Then, multiply 0.75 by 'x' to get 45. Mathematically, this can be represented as:

0.75x = 45

Q: How do I solve for the original number?

A: To solve for the original number, divide both sides of the equation by 0.75.

x = 45 / 0.75

Q: What is the real-world application of this problem?

A: This problem has real-world applications in various fields, such as finance, science, and engineering. For instance, in finance, understanding how to calculate percentages and fractions is crucial for making informed investment decisions.

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

A: Some common mistakes to avoid include:

Not setting up the equation correctly
Not isolating the variable 'x' on one side of the equation
Not performing the division correctly

Q: How can I practice solving similar problems?

A: To practice solving similar problems, try the following:

Read the problem carefully and understand what is being asked
Set up the equation correctly
Isolate the variable on one side of the equation
Perform the necessary operations to solve for the variable

Q: What is the answer to the practice problem: If 0.25 of a number is 20, what is the original number?

A: The answer is 80.

Q: Can I use a calculator to solve this problem?

A: Yes, you can use a calculator to solve this problem. However, it's also important to understand the underlying math concepts and be able to solve the problem manually.

Q: How do I know if I'm solving the problem correctly?

A: To ensure you're solving the problem correctly, follow these steps:

Read the problem carefully and understand what is being asked
Set up the equation correctly
Isolate the variable on one side of the equation
Perform the necessary operations to solve for the variable
Check your answer to make sure it makes sense in the context of the problem

Q: What if I get stuck on a problem like this?

A: If you get stuck on a problem like this, try the following:

Read the problem carefully and understand what is being asked
Break down the problem into smaller, more manageable parts
Ask for help from a teacher, tutor, or classmate
Use online resources, such as video tutorials or practice problems, to help you understand the concept

Q: Can I use this problem as a teaching tool?

A: Yes, you can use this problem as a teaching tool to help students understand the concept of solving equations and working with fractions and decimals.