Select The Correct Answer.Your Personal Library Contains Books Written By 165 Authors. 60 % 60\% 60% Of The Authors Are Men. 40 % 40\% 40% Of The Authors Write Only Nonfiction Works. Additionally, 40 Of The Male Authors Write Only Nonfiction Works.

Introduction

In this article, we will delve into a mathematical problem involving percentages, proportions, and authorship. We will analyze the given information and use logical reasoning to arrive at the correct answer. Our goal is to provide a step-by-step solution to the problem, making it easy to understand and follow.

Problem Statement

Your personal library contains books written by 165 authors. $60\%$ of the authors are men, and $40\%$ of the authors write only nonfiction works. Additionally, 40 of the male authors write only nonfiction works. We need to determine the number of female authors who write only nonfiction works.

Step 1: Calculate the Number of Male Authors

First, let's calculate the number of male authors in the library. We know that $60\%$ of the authors are men, and there are 165 authors in total.

# Define variables
total_authors = 165
male_percentage = 0.6
male_authors = total_authors * male_percentage
print("Number of male authors:", male_authors)

Step 2: Calculate the Number of Female Authors

Next, we need to calculate the number of female authors in the library. Since $60\%$ of the authors are men, the remaining $40\%$ must be female.

# Calculate the number of female authors
female_authors = total_authors - male_authors
print("Number of female authors:", female_authors)

Step 3: Calculate the Number of Authors Who Write Only Nonfiction Works

We know that $40\%$ of the authors write only nonfiction works. Let's calculate the number of authors who write only nonfiction works.

# Calculate the number of authors who write only nonfiction works
nonfiction_authors = total_authors * 0.4
print("Number of authors who write only nonfiction works:", nonfiction_authors)

Step 4: Calculate the Number of Male Authors Who Write Only Nonfiction Works

We are given that 40 of the male authors write only nonfiction works. Let's calculate the number of male authors who write only nonfiction works.

# Calculate the number of male authors who write only nonfiction works
male_nonfiction_authors = 40
print("Number of male authors who write only nonfiction works:", male_nonfiction_authors)

Step 5: Calculate the Number of Female Authors Who Write Only Nonfiction Works

Now, let's calculate the number of female authors who write only nonfiction works. We know that $40\%$ of the authors write only nonfiction works, and 40 of the male authors write only nonfiction works. We can use this information to calculate the number of female authors who write only nonfiction works.

# Calculate the number of female authors who write only nonfiction works
female_nonfiction_authors = nonfiction_authors - male_nonfiction_authors
print("Number of female authors who write only nonfiction works:", female_nonfiction_authors)

Conclusion

In this article, we analyzed a mathematical problem involving percentages, proportions, and authorship. We used logical reasoning and step-by-step calculations to arrive at the correct answer. The number of female authors who write only nonfiction works is 32.

Final Answer

Q: What is the main goal of the problem?

A: The main goal of the problem is to determine the number of female authors who write only nonfiction works in a personal library containing books written by 165 authors.

Q: What is the percentage of male authors in the library?

A: The percentage of male authors in the library is $60\%$.

Q: What is the percentage of authors who write only nonfiction works?

A: The percentage of authors who write only nonfiction works is $40\%$.

Q: How many male authors write only nonfiction works?

A: 40 of the male authors write only nonfiction works.

Q: How can we calculate the number of female authors who write only nonfiction works?

A: To calculate the number of female authors who write only nonfiction works, we need to subtract the number of male authors who write only nonfiction works from the total number of authors who write only nonfiction works.

Q: What is the formula to calculate the number of female authors who write only nonfiction works?

A: The formula to calculate the number of female authors who write only nonfiction works is:

Female nonfiction authors = Total nonfiction authors - Male nonfiction authors

Q: What is the final answer to the problem?

A: The final answer to the problem is $\boxed{32}$.

Q: What is the significance of this problem?

A: This problem is significant because it requires the application of mathematical concepts such as percentages, proportions, and logical reasoning to arrive at the correct answer.

Q: How can this problem be applied in real-life scenarios?

A: This problem can be applied in real-life scenarios such as:

• Calculating the number of students who meet certain criteria in a school or university.
• Determining the number of employees who meet certain qualifications in a company.
• Analyzing data to make informed decisions in business or other fields.

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

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

• Not reading the problem carefully and understanding the given information.
• Not using the correct formula to calculate the number of female authors who write only nonfiction works.
• Not checking the units and making sure that the answer is in the correct format.

Q: How can this problem be modified to make it more challenging?

A: This problem can be modified to make it more challenging by:

• Increasing the number of authors in the library.
• Changing the percentage of male authors or authors who write only nonfiction works.
• Adding additional constraints or conditions to the problem.