33% Of The Books In A School Library Are Fiction. If There Are…
33% of the books in a school library are fiction. If there are 1675 non-fiction books, how many books are there in the school library? How much fiction books are there?
With block model and Percentage and Rate solutions.
And please make sure to tell HOW MUCH THE FICTION BOOKS ARE.
PLEASE GIVE A VERY REASONABLE EXPLANATION
Answer:
To solve this problem, we can use both the block model and the percentage and rate solutions.
Block Model Solution:
Let’s represent the total number of books in the school library with the variable “T”. We know that 33% of the books are fiction, so we can represent the number of fiction books as 0.33T. Additionally, we are given that there are 1675 non-fiction books.
According to the problem, the total number of books in the library is the sum of the fiction and non-fiction books:
T = 0.33T + 1675
To solve for T, we can subtract 0.33T from both sides of the equation:
T – 0.33T = 1675
0.67T = 1675
Dividing both sides of the equation by 0.67:
T = 1675 / 0.67
T ≈ 2500
Therefore, there are approximately 2500 books in the school library.
To find the number of fiction books, we can substitute the value of T into the equation for fiction books:
Fiction books = 0.33T ≈ 0.33 * 2500 ≈ 825
Therefore, there are approximately 825 fiction books in the school library.
Percentage and Rate Solution:
We are given that 33% of the books in the library are fiction. This means that the ratio of fiction books to the total number of books is 33:100.
Let’s represent the total number of books in the library with the variable “T”. We can set up the proportion:
33/100 = Fiction books/T
To find the number of fiction books, we can cross-multiply:
33T = 100 * Fiction books
We know that there are 1675 non-fiction books, so the total number of books is the sum of fiction and non-fiction books:
T = Fiction books + 1675
Substituting the value of T from the proportion equation:
33T = 100 * Fiction books
33(Fiction books + 1675) = 100 * Fiction books
33Fiction books + 55175 = 100Fiction books
Rearranging the equation:
100Fiction books – 33Fiction books = 55175
67Fiction books = 55175
Dividing both sides of the equation by 67:
Fiction books ≈ 825
Therefore, there are approximately 825 fiction books in the school library.
The total number of books in the library is the sum of fiction and non-fiction books:
T = Fiction books + 1675
T ≈ 825 + 1675
T ≈ 2500
Therefore, there are approximately 2500 books in the school library.
In conclusion, there are approximately 2500 books in the school library, with approximately 825 of them being fiction books.
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