Answer:
N = 43.2
F = 129.6
Total books = F + N = 129.6 + 43.2 = 172.8
Please note that number of books cannot be in fraction, there is some mistake in formulating the question!
But nevertheless, the key concept here is to learn how to set up such algebraic equations.
Step-by-step explanation:
Let F denotes fiction book
Let N denotes non-fiction book
There are 3 times as many fiction books as non-fiction in a library.
Mathematically,
F = 3N eq. 1
120 fiction books are loaned out and 24 non-fiction books
Mathematically,
F - 120 = remaining fiction books
N - 24 = remaining non-fiction books
There are now twice as many fiction books as non-fiction.
Mathematically,
2(remaining fiction books) = (remaining non-fiction books)
2(F - 120) = (N - 24) eq. 2
Substitute eq. 1 into eq. 2
2(3N - 120) = (N - 24)
Simplify the equation,
6N - 240 = N - 24
6N - N = 240 - 24
5N = 216
N = 216/5
N = 43.2
Please note that number of books cannot be in fraction, there is some mistake in formulating the question!
But nevertheless, the key concept here is to learn how to set up such algebraic equations.
So back to the problem.
F = 3N
F = 3(43.2)
F = 129.6
So the total books in the library are
Total books = fiction + non-fiction
Total books = F + N = 129.6 + 43.2 = 172.8
