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The public library has exactly 2 floors. It has 2/3 as many shelves on
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01 Apr 2022, 01:58
01 Apr 2022, 01:58
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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 5/6 as many books per shelf as the first floor, what fraction of the library's books are on the first floor?
A. 1/4
B. 5/14
C. 5/9
D. 9/14
E. 5/6
A. 1/4
B. 5/14
C. 5/9
D. 9/14
E. 5/6
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Re: The public library has exactly 2 floors. It has 2/3 as many shelves on
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01 Apr 2022, 05:41
01 Apr 2022, 05:41
2
Carcass wrote:
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 5/6 as many books per shelf as the first floor, what fraction of the library's books are on the first floor?
A. 1/4
B. 5/14
C. 5/9
D. 9/14
E. 5/6
A. 1/4
B. 5/14
C. 5/9
D. 9/14
E. 5/6
Let's choose values that satisfy the given information...
The library has 2/3 as many shelves on its 2nd floor as it does on its 1st.
So, let's say there are 3 shelves on the 1st floor, which means there are 2 shelves on the 2nd floor
The second floor has 5/6 as many books per shelf as the first floor
So, let's say there are 6 books per shelf on the first floor, which means there are 5 books per shelf on the second floor.
The total number of books on the first floor = (3)(6) = 18 books
The total number of books on the second floor = (2)(5) = 10 books
The TOTAL number of books in the library = 18 + 10 = 28
What fraction of the library's books are on the first floor?
Of the library's 28 books, 18 are on the first floor.
Answer: 18/28 = 9/14
Answer: D
General Discussion
Re: The public library has exactly 2 floors. It has 2/3 as many shelves on
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01 Apr 2022, 03:38
01 Apr 2022, 03:38
2
\(2 floors.\)
It has 2/3 as many shelves on its 2nd floor as it does on its 1st.
Let's say the no of shelves on 1st floor \(= 3x\) so the no of shelves on 2nd floor \(= 2x\)
The second floor has 5/6 as many books per shelf as the first floor,
Let's say books per shelf on the first floor \(= 6y\) so books per shelf on the second floor \(= 5y\)
Total books on first floor \(= 18xy\) & on second floor \(= 10xy\)
Total books \(= 28xy\)
Fraction of books on first floor \(= \frac{18xy}{28xy} = \frac{9}{14}\)
Answer D
It has 2/3 as many shelves on its 2nd floor as it does on its 1st.
Let's say the no of shelves on 1st floor \(= 3x\) so the no of shelves on 2nd floor \(= 2x\)
The second floor has 5/6 as many books per shelf as the first floor,
Let's say books per shelf on the first floor \(= 6y\) so books per shelf on the second floor \(= 5y\)
Total books on first floor \(= 18xy\) & on second floor \(= 10xy\)
Total books \(= 28xy\)
Fraction of books on first floor \(= \frac{18xy}{28xy} = \frac{9}{14}\)
Answer D
