Practice algebraic expressions

Oct 13, 2025 by magicalceylontours.com 100 views

Solving the Puzzle of Two Brothers: A Mathematical Exploration

In this article, we will delve into a mathematical puzzle involving two brothers and their share of a certain amount. The puzzle is presented in the form of a multiple-choice question, where we need to determine the capital of the two brothers when a specific value is given. We will also explore the possible individual share of the brothers based on the given options.

Let's break down the problem and understand what is being asked. We are given a multiple-choice question with two parts:

Q. 11: What is the capital of the two brothers when $m = 500$ ?
Q. 12: Which of the following can be the individual share of the brothers?

The first question asks us to find the capital of the two brothers when the value of $m$ is 500. The second question asks us to determine the possible individual share of the brothers based on the given options.

To solve the first question, we need to find the capital of the two brothers when $m = 500$ . The capital is given by the expression $m + 21$ . Substituting $m = 500$ , we get:

\text{Capital} = 500 + 21 = 521

However, none of the options match this value. Let's re-examine the options and see if we can find a connection between them.

Looking at the options, we notice that they are all in the form of $m + 21$ . This suggests that the capital of the two brothers is indeed $m + 21$ . However, we need to find the correct value of $m$ that satisfies the given options.

Let's analyze the options and see if we can find a value of $m$ that satisfies them. We can start by substituting the values of $m$ into the expression $m + 21$ and see if we get any of the options.

For option A, we have $(m + 3)(m + 7) = m^2 + 10m + 21$ . This expression is not equal to any of the options.

For option B, we have $(m - 3)(m + 7) = m^2 + 4m - 21$ . This expression is also not equal to any of the options.

For option C, we have $(m - 3)(m + 7) = m^2 + 4m - 21$ . This expression is also not equal to any of the options.

For option D, we have $(m - 3)(m + 7) = m^2 + 4m - 21$ . This expression is also not equal to any of the options.

However, we notice that option C is close to the correct value. If we substitute $m = 500$ , we get:

(500 - 3)(500 + 7) = 497 \times 507 = 252,399

This value is close to the correct value, but it is not equal to any of the options.

Let's re-examine the options and see if we can find a connection between them. We notice that options A, B, and C are all in the form of $(m - 3)(m + 7)$ . This suggests that the individual share of the brothers is indeed $(m - 3)(m + 7)$ .

To solve the second question, we need to determine the possible individual share of the brothers based on the given options. We have already analyzed the options and found that they are all in the form of $(m - 3)(m + 7)$ .

In conclusion, the capital of the two brothers when $m = 500$ is not equal to any of the options. However, the individual share of the brothers is indeed $(m - 3)(m + 7)$ . This suggests that the puzzle is designed to test our understanding of algebraic expressions and our ability to analyze and solve mathematical problems.

The final answer to Q. 11 is not provided in the options. However, the individual share of the brothers is $(m - 3)(m + 7)$ .

Based on our analysis, we recommend the following:

Practice algebraic expressions: The puzzle requires a good understanding of algebraic expressions and their manipulation. Practicing algebraic expressions will help you develop the skills needed to solve this puzzle.
Analyze and solve mathematical problems: The puzzle requires you to analyze and solve mathematical problems. Practicing problem-solving will help you develop the skills needed to tackle this puzzle.
Use algebraic techniques: The puzzle requires the use of algebraic techniques such as factoring and expanding expressions. Practicing these techniques will help you develop the skills needed to solve this puzzle.

By following these recommendations, you will be well-equipped to tackle this puzzle and other mathematical challenges.
Q&A: Solving the Puzzle of Two Brothers

A: The capital of the two brothers when $m = 500$ is not equal to any of the options. However, the individual share of the brothers is indeed $(m - 3)(m + 7)$ .

A: To determine the individual share of the brothers, you need to analyze the options and find a connection between them. In this case, the options are all in the form of $(m - 3)(m + 7)$ .

A: The expression $(m - 3)(m + 7)$ represents the individual share of the brothers. This expression is derived from the given options and is a key part of solving the puzzle.

A: To practice algebraic expressions and problem-solving skills, you can try the following:

Practice algebraic expressions: Try to manipulate and simplify algebraic expressions to develop your skills.
Solve mathematical problems: Practice solving mathematical problems to develop your problem-solving skills.
Use algebraic techniques: Practice using algebraic techniques such as factoring and expanding expressions to develop your skills.

A: Some common algebraic techniques used in problem-solving include:

Factoring: Factoring involves expressing an algebraic expression as a product of simpler expressions.
Expanding: Expanding involves expressing an algebraic expression as a sum of simpler expressions.
Simplifying: Simplifying involves reducing an algebraic expression to its simplest form.

A: To apply algebraic techniques to solve mathematical problems, you can try the following:

Read the problem carefully: Read the problem carefully and identify the key elements.
Identify the algebraic expression: Identify the algebraic expression involved in the problem.
Apply algebraic techniques: Apply algebraic techniques such as factoring, expanding, and simplifying to solve the problem.

A: Some tips for solving mathematical problems include:

Read the problem carefully: Read the problem carefully and identify the key elements.
Identify the algebraic expression: Identify the algebraic expression involved in the problem.
Apply algebraic techniques: Apply algebraic techniques such as factoring, expanding, and simplifying to solve the problem.
Check your work: Check your work to ensure that you have solved the problem correctly.

A: To check your work when solving mathematical problems, you can try the following:

Re-read the problem: Re-read the problem to ensure that you have understood it correctly.
Check your calculations: Check your calculations to ensure that you have performed the correct operations.
Verify your answer: Verify your answer to ensure that it is correct.

By following these tips and practicing algebraic expressions and problem-solving skills, you will be well-equipped to tackle mathematical challenges and solve problems with confidence.