The public library has exactly 2 floors.
The public library has exactly 2 floors. It has 2/3 as many shelves on its 2nd floor as it does on its 1st. If the second floor has 1/6 as many books per shelf as the first floor, what fraction of the library's books are on the first floor?
Answer/Solution
9/10
Steps/Work
Let x be the no of shelves and y be the no of books per shelf on first floor.
Now no of shelves on 2nd floor = (2/3)*x
no of books per shelf on 2nd floor = (1/6) * y
So total no books on first floor = xy and total no of books on 2nd floor = (2/3)*x*(1/6)*y = (1/9)*xy
fraction of library books on first floor = (xy)/(xy + (1/9)*xy)
=1 / (1+(1/9))
=9/10
So B
Now no of shelves on 2nd floor = (2/3)*x
no of books per shelf on 2nd floor = (1/6) * y
So total no books on first floor = xy and total no of books on 2nd floor = (2/3)*x*(1/6)*y = (1/9)*xy
fraction of library books on first floor = (xy)/(xy + (1/9)*xy)
=1 / (1+(1/9))
=9/10
So B