The table shows the number of books by male and female authors on a bookshelf. How many of the fiction books were written by female authors?
| | Male | Female | Total |
| :---------- | :--- | :----- | :---- |
| Fiction | 48 | | |
| Non-fiction | | | 69 |
| Total | 79 | | 143 |
Answer (2)
Calculate the number of non-fiction books written by male authors: N m = T m − F m = 79 − 48 = 31 .
Calculate the total number of books written by female authors: T f = T − T m = 143 − 79 = 64 .
Calculate the total number of fiction books: T F = T − T N = 143 − 69 = 74 .
Calculate the number of fiction books written by female authors: F f = T F − F m = 74 − 48 = 26 .
The number of fiction books written by female authors is 26 .
Explanation
Understanding the Problem We are given a table showing the number of books by male and female authors, categorized by fiction and non-fiction genres. Our goal is to find the number of fiction books written by female authors. Let's denote the number of fiction books written by male authors as F m , the number of fiction books written by female authors as F f , the number of non-fiction books written by male authors as N m , and the number of non-fiction books written by female authors as N f . We are also given the total number of books written by male authors ( T m ), the total number of books written by female authors ( T f ), the total number of non-fiction books ( T N ), and the overall total number of books ( T ).
Identifying Known Values From the table, we know:
F m = 48
T m = 79
T N = 69
T = 143
We need to find F f .
Calculating Non-Fiction Books by Male Authors First, let's find the number of non-fiction books written by male authors ( N m ). We know that the total number of books written by male authors is the sum of fiction and non-fiction books written by male authors: T m = F m + N m . Therefore, N m = T m − F m = 79 − 48 = 31
Calculating Total Books by Female Authors Next, let's find the total number of books written by female authors ( T f ). We know that the overall total number of books is the sum of books written by male and female authors: T = T m + T f . Therefore, T f = T − T m = 143 − 79 = 64
Calculating Non-Fiction Books by Female Authors Now, let's find the number of non-fiction books written by female authors ( N f ). We know that the total number of non-fiction books is the sum of non-fiction books written by male and female authors: T N = N m + N f . Therefore, N f = T N − N m = 69 − 31 = 38
Calculating Total Fiction Books Let's find the total number of fiction books ( T F ). We know that the overall total number of books is the sum of fiction and non-fiction books: T = T F + T N . Therefore, T F = T − T N = 143 − 69 = 74
Calculating Fiction Books by Female Authors Finally, we can find the number of fiction books written by female authors ( F f ). We know that the total number of fiction books is the sum of fiction books written by male and female authors: T F = F m + F f . Therefore, F f = T F − F m = 74 − 48 = 26
Final Answer Therefore, the number of fiction books written by female authors is 26.
Examples
Understanding how to categorize and analyze data in tables is a valuable skill in many real-life situations. For example, imagine you are organizing a school library and need to keep track of the types of books available (fiction vs. non-fiction) and the authors' demographics (male vs. female). By using a table like the one in this problem, you can easily see the distribution of books and ensure that the library has a diverse collection. This type of data analysis can also be applied to other areas, such as tracking sales data in a business or analyzing survey results in a research project.
The number of fiction books written by female authors is 26. This was calculated by analyzing the total numbers of books written by male and female authors in both genres. After finding all relevant totals, we deduced that 26 fiction books were authored by females.
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