Breaking Down the Relationships

Oct 13, 2025 by talynt.org 85 views

The Positive Number A is 230% of the Number B and A is 60% of Number C if C is P% of B Which of the Following is the Closest to Value of P

Understanding the Problem

In this problem, we are given three numbers: A, B, and C. We are also given two relationships between these numbers: A is 230% of B, and A is 60% of C. Additionally, we are told that C is P% of B. Our goal is to find the value of P.

Breaking Down the Relationships

Let's start by breaking down the first relationship: A is 230% of B. This means that A is equal to 2.3 times B. Mathematically, we can write this as:

A = 2.3B

Next, let's look at the second relationship: A is 60% of C. This means that A is equal to 0.6 times C. Mathematically, we can write this as:

A = 0.6C

Finding the Relationship Between B and C

Now that we have two equations involving A, we can set them equal to each other to find the relationship between B and C. We can do this by substituting the expression for A from the first equation into the second equation:

2.3B = 0.6C

To solve for C in terms of B, we can divide both sides of the equation by 0.6:

C = (2.3B) / 0.6

C = 3.83B

Finding the Value of P

Now that we have the relationship between B and C, we can find the value of P. We are told that C is P% of B, so we can write this as:

C = (P/100)B

Substituting the expression for C in terms of B that we found earlier, we get:

3.83B = (P/100)B

To solve for P, we can divide both sides of the equation by B and multiply both sides by 100:

P = (3.83/1) * 100

P = 383

Conclusion

Based on the relationships given in the problem, we have found that the value of P is approximately 383. This means that C is approximately 383% of B.

Key Takeaways

A is 230% of B and A is 60% of C.
C is P% of B.
The value of P is approximately 383.

Real-World Applications

This problem can be applied to a variety of real-world scenarios, such as:

Finance: If a company's revenue is 230% of its expenses, and its expenses are 60% of its profits, then what percentage of its revenue is its profits?
Business: If a company's sales are 230% of its costs, and its costs are 60% of its revenue, then what percentage of its sales is its revenue?
Economics: If a country's GDP is 230% of its imports, and its imports are 60% of its exports, then what percentage of its GDP is its exports?

Final Thoughts

In conclusion, this problem requires us to use algebraic manipulation to find the value of P. By breaking down the relationships between A, B, and C, we were able to find the value of P, which is approximately 383. This problem can be applied to a variety of real-world scenarios, and it requires us to think critically and use algebraic manipulation to solve.
The Positive Number A is 230% of the Number B and A is 60% of Number C if C is P% of B Which of the Following is the Closest to Value of P

Q&A: Understanding the Problem and Its Solutions

Q: What is the problem asking for?

A: The problem is asking us to find the value of P, where C is P% of B, given that A is 230% of B and A is 60% of C.

Q: How do we start solving the problem?

A: We start by breaking down the relationships between A, B, and C. We are given two equations: A = 2.3B and A = 0.6C. We can set these equations equal to each other to find the relationship between B and C.

Q: How do we find the relationship between B and C?

A: We can substitute the expression for A from the first equation into the second equation: 2.3B = 0.6C. To solve for C in terms of B, we can divide both sides of the equation by 0.6: C = (2.3B) / 0.6.

Q: What is the relationship between B and C?

A: The relationship between B and C is C = 3.83B.

Q: How do we find the value of P?

A: We are told that C is P% of B, so we can write this as: C = (P/100)B. Substituting the expression for C in terms of B that we found earlier, we get: 3.83B = (P/100)B. To solve for P, we can divide both sides of the equation by B and multiply both sides by 100: P = (3.83/1) * 100.

Q: What is the value of P?

A: The value of P is approximately 383.

Q: What does this problem have to do with real-world scenarios?

A: This problem can be applied to a variety of real-world scenarios, such as finance, business, and economics. For example, if a company's revenue is 230% of its expenses, and its expenses are 60% of its profits, then what percentage of its revenue is its profits?

Q: What are some key takeaways from this problem?

A: Some key takeaways from this problem are:

A is 230% of B and A is 60% of C.
C is P% of B.
The value of P is approximately 383.

Q: How can we use algebraic manipulation to solve this problem?

A: We can use algebraic manipulation to solve this problem by breaking down the relationships between A, B, and C, and then using substitution and division to find the value of P.

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

A: Some common mistakes to avoid when solving this problem include:

Not breaking down the relationships between A, B, and C.
Not using substitution and division to find the value of P.
Not checking the units of the variables.

Q: How can we check our work and make sure we have the correct solution?

A: We can check our work by plugging in the value of P back into the original equations and making sure that they are true. We can also use a calculator to check our work and make sure that we have the correct solution.

Conclusion