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There are three times as many fiction books as non-fiction books in a library. 122 fiction books and 24 non-fiction books are loaned out. There are now twice as many non-fiction books as fiction books. How many books were in the library? i need an awnser quick ill mark you brainliest if you get it right

Respuesta :

Answer:

176 books

Step-by-step explanation:

Let's call the number of fiction books 'F', and the number of non-fiction books 'N'. Then, we can write the following system of equations:

eq1:

[tex]F = 3N[/tex]

eq2:

[tex]2*(F - 122) = (N - 24)[/tex]

[tex]2F - 244 = N - 24[/tex]

[tex]2F = N + 220[/tex]

Using the 'F' value from the first equation, we have:

[tex]6N = N + 220[/tex]

[tex]5N = 220[/tex]

[tex]N = 44\ books[/tex]

[tex]F = 3N = 132\ books[/tex]

The total number of books is:

[tex]F + N = 132 + 44 = 176\ books[/tex]

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