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Each shelf of a bookcase contains 24 books. If the librarian took out 42 books and rearranged the remaining books so that all shelves but one contained 16 books and the last shelf contained 22 books, how many shelves does the bookcase have?

The question says that initially each shelf has 24 books

Then after 42 are removed, one shelf is left with 22 and all the others with 16 So if there are x shelves, x-1 are left with 16 and the xth one with 22

Each shelf of a bookcase contains 24 books. If the librarian took out 42 books and rearranged the remaining books so that all shelves but one contained 16 books and the last shelf contained 22 books, how many shelves does the bookcase have?

Is there another way to solve this question ? like plug in or back solving etc. Thanks

Each shelf of a bookcase contains 24 books. If the librarian took out 42 books and rearranged the remaining books so that all shelves but the last one contained 16 books and the last shelf contained 22 books, how many shelves does the bookcase have?

A. 4 B. 5 C. 6 D. 8 E. 9

Denoting \(x\) the number of the shelves, we can build an equation: \(24x=16(x-1)+22+42\). Solving the equation, we get \(x=6\).

Obviously I am wrong. Solving mentally and using the mobile sceen is obviously not the right way to solve such problems. So the new equation is 24*n-42=16*(n-1)+ 22 n=6 hence c

the best way to solve this is by creating an equation. Even for plugging numbers you need to get the equation right.

before taking the 42 books out , we have total no. of books = 24x where x can be taken as no. of selves/... now after taking 42 books, there there are 16 books present in (x-1) selves and 22 books present in last self.. so we have no. of books = 42+16(x-1)+22

Equating we get

24x = 42+16(x-1)+22 24x = 42+16x-16+22 8x = 48 x=6 therefore total no. of selves = 6

Obviously I am wrong. Solving mentally and using the mobile sceen is obviously not the right way to solve such problems. So the new equation is 24*n-42=16*(n-1)+ 22 n=6 hence c

the best way to solve this is by creating an equation. Even for plugging numbers you need to get the equation right.

Posted from my mobile device

I made the same mistake the first time.

+1 made the same mistake but not sure if C is the right answer......

1) using the equation which I suggest because it is the quickest.

24x - 42= 16x +6 48= 8x x= 6

2) if you're not good with forming equations plug in the answers and always start with the median of the choices. C happened to be the right choice so it would be quick. But if it wasn't C the number you got would indicate whether you choice needed to be higher or lower.

the wording of this question was confusing.... When it said all shelves but one had 16 books and the last one had 22... It sounded as if one shelf was left with no books then others had 16 books then the last one had 22 books.

16(x-2) + 22. Confusing... However i understand the X-1 as well. _________________

24 books in each shelf post taking out 42 books -16 in each shelf and 22 in last all shelf will have 8 booksless ((24-16) and one shelf will have 2 books less(24-22) so, 8books *5shelves + 2book * 1 shelf = 42, which is the exact no of books taken out from the shelf of 24 hence the answer is 5+1=6 shelves

a better way to solve such problems would be to create an equation with 1 variable as the process above can get complicated if the no. of shelves are more or books are more or both

There is some logic that I'm missing. If 42 books are removed and yet replaced, it should have a net zero effect, in theory.. Why must (+/-) 42 books be in the equation?

There is some logic that I'm missing. If 42 books are removed and yet replaced, it should have a net zero effect, in theory.. Why must (+/-) 42 books be in the equation?

Thanks for your help with this

Hi mejia 401,

The quiz says that the librarian took 42 books and then rearranged the remaining books. It means that she/he rearranged the (x-42) books. (x: total book). The quiz does not says that she/he replace the missed books.