Number of Pencils in Each Box

Oct 13, 2025 by leolavanderia.com.br 85 views

Mr. Moretti is a teacher who wants to distribute pencils to his students. He has a total of 18 boxes of pencils, and each box contains a certain number of pencils. To find the total number of pencils he gives to his students, we need to consider the number of pencils in each box and the total number of boxes.

Breaking Down the Problem

Let's break down the problem step by step:

Number of Pencils in Each Box: Mr. Moretti has 18 boxes of pencils. Let's assume that each box contains m pencils.
Total Number of Boxes: Mr. Moretti has a total of 18 boxes.
Total Number of Pencils: To find the total number of pencils, we need to multiply the number of pencils in each box (m) by the total number of boxes (18).

Analyzing the Options

Now, let's analyze the options given:

A. ${$ m + 2m $}$

This option represents the total number of pencils in 2 boxes, not 18 boxes. Therefore, it is not the correct answer.

B. ${$ 18(m + 2m) $}$

This option represents the total number of pencils in 18 boxes, where each box contains m + 2m pencils. This is equivalent to 3m pencils per box. Therefore, this option is a possible answer.

C. ${$ 18 + m + 2m $}$

This option represents the total number of pencils in 18 boxes, where each box contains m pencils and 2 boxes contain 2m pencils. This is equivalent to 18 + 3m pencils. Therefore, this option is not the correct answer.

D. ${$ 18m + 18(2m) $}$

This option represents the total number of pencils in 18 boxes, where each box contains m pencils and 18 boxes contain 2m pencils. This is equivalent to 36m pencils. Therefore, this option is not the correct answer.

E. ${$ 54m $}$

This option represents the total number of pencils in 18 boxes, where each box contains 3m pencils. This is equivalent to 54m pencils. Therefore, this option is a possible answer.

Conclusion

Based on our analysis, the correct options are:

B. ${$ 18(m + 2m) $}$
E. ${$ 54m $}$

Both options represent the total number of pencils Mr. Moretti gives to his students.

Why These Options Are Correct

These options are correct because they represent the total number of pencils in 18 boxes, where each box contains m pencils and the total number of boxes is 18. The correct options are:

B. ${$ 18(m + 2m) $}$: This option represents the total number of pencils in 18 boxes, where each box contains m + 2m pencils. This is equivalent to 3m pencils per box.
E. ${$ 54m $}$: This option represents the total number of pencils in 18 boxes, where each box contains 3m pencils. This is equivalent to 54m pencils.

What We Learned

In this problem, we learned how to analyze a mathematical expression and determine which options represent the total number of pencils Mr. Moretti gives to his students. We also learned how to simplify mathematical expressions and identify equivalent expressions.

Key Takeaways

When analyzing a mathematical expression, we need to consider the context of the problem.
We need to identify the variables and constants in the expression.
We need to simplify the expression and identify equivalent expressions.
We need to consider the total number of boxes and the number of pencils in each box.

Real-World Applications

This problem has real-world applications in various fields, such as:

Business: When calculating the total cost of goods sold, we need to consider the number of items sold and the price of each item.
Science: When calculating the total amount of a substance, we need to consider the number of samples and the amount of substance in each sample.
Engineering: When designing a system, we need to consider the number of components and the cost of each component.

Conclusion

Q: What is the problem about?

A: The problem is about Mr. Moretti, a teacher who wants to distribute pencils to his students. He has a total of 18 boxes of pencils, and each box contains a certain number of pencils. We need to find the total number of pencils he gives to his students.

Q: What are the options for the total number of pencils?

A: The options are:

A. ${$ m + 2m $}$
B. ${$ 18(m + 2m) $}$
C. ${$ 18 + m + 2m $}$
D. ${$ 18m + 18(2m) $}$
E. ${$ 54m $}$

Q: Which options are correct?

A: The correct options are B and E. These options represent the total number of pencils Mr. Moretti gives to his students.

Q: Why are options B and E correct?

A: Options B and E are correct because they represent the total number of pencils in 18 boxes, where each box contains m pencils and the total number of boxes is 18. Option B represents the total number of pencils in 18 boxes, where each box contains m + 2m pencils. This is equivalent to 3m pencils per box. Option E represents the total number of pencils in 18 boxes, where each box contains 3m pencils. This is equivalent to 54m pencils.

Q: What is the key takeaway from this problem?

A: The key takeaway from this problem is that when analyzing a mathematical expression, we need to consider the context of the problem, identify the variables and constants, simplify the expression, and identify equivalent expressions.

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

A: This problem has real-world applications in various fields, such as business, science, and engineering. When calculating the total cost of goods sold, we need to consider the number of items sold and the price of each item. When calculating the total amount of a substance, we need to consider the number of samples and the amount of substance in each sample. When designing a system, we need to consider the number of components and the cost of each component.

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

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

Not considering the context of the problem
Not identifying the variables and constants
Not simplifying the expression
Not identifying equivalent expressions

Q: How can I practice solving this type of problem?

A: You can practice solving this type of problem by:

Working through example problems
Practicing simplifying mathematical expressions
Identifying equivalent expressions
Considering the context of the problem

Q: What are some additional resources for learning more about this topic?

A: Some additional resources for learning more about this topic include:

Online tutorials and videos
Math textbooks and workbooks
Online math communities and forums
Math apps and software

Conclusion

In conclusion, the correct options for the total number of pencils Mr. Moretti gives to his students are B and E. These options represent the total number of pencils in 18 boxes, where each box contains m pencils and the total number of boxes is 18. We learned how to analyze a mathematical expression and determine which options represent the total number of pencils. We also learned how to simplify mathematical expressions and identify equivalent expressions.