Respuesta :
Answer:
Step-by-step explanation:
There are 100 books in the library, divided into four categories. The books' ratio is as follows: 3 science fiction books to every two history books and four history books to every three comic books. The remaining books are art books. How many art books are there in the library, if we know that it holds nine comic books?
SF/HIS= 3/2
HIST/COM = 4/3
COM=9
HIS= 4/3 x9 =12
SF=3/2 X 12=18
9+12+18 =39
100-39=61 ART
The number of arts books in the library is 61
The ratio of science to history books = 3:2
The ratio of history to comic books = 4:3
Multiply the ratio of science to history books by 2/2
The ratio of science to history books = 6:4
Therefore, the ratio of science to history to comic books = 6:4:3
Total ratio = 6+4+3
Total ratio = 13
Let the number of art books be n
Total number of books = 100
Total number of science, history, and art books = 100-n
Number of comic books = 9
Number of comic books = [3/13] x (100-n)
9 = [3/13] x (100-n)
9(13) = 300 - 3n
117 = 300 - 3n
3n = 183
n = 183/3
n = 61
There are 61 art books in the library
Learn more on ratio here: https://brainly.com/question/2328454
