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Each shelf of a bookcase contained 12 books. If the librarian took out 21 books and rearranged the remaining books so that all shelves but the last one contained 8 books and that last shelf contained 11 books, how many shelves does the bookcase have?

Each shelf of a bookcase contained 12 books. If the librarian took out 21 books and rearranged the remaining books so that all shelves but the last one contained 8 books and that last shelf contained 11 books, how many shelves does the bookcase have?

A. 5 B. 6 C. 7 D. 8 E. 9

Say there are total of \(x\) shelves, then: \(12*x=21+8*(x-1)+11\), which gives \(x=6\).

Each shelf of a bookcase contained 12 books. If the librarian took out 21 books and rearranged the remaining books so that all shelves but the last one contained 8 books and that last shelf contained 11 books, how many shelves does the bookcase have?

A. 5 B. 6 C. 7 D. 8 E. 9

Say there are total of \(x\) shelves, then: \(12*x=21+8*(x-1)+11\), which gives \(x=6\).

Answer: B

Hi Bunuel,

Thanks for the explanation. However, why do you subtract "1" from 8*(x-1)? Can you please verify?

Each shelf of a bookcase contained 12 books. If the librarian took out 21 books and rearranged the remaining books so that all shelves but the last one contained 8 books and that last shelf contained 11 books, how many shelves does the bookcase have?

A. 5 B. 6 C. 7 D. 8 E. 9

Say there are total of \(x\) shelves, then: \(12*x=21+8*(x-1)+11\), which gives \(x=6\).

Answer: B

Hi Bunuel,

Thanks for the explanation. However, why do you subtract "1" from 8*(x-1)? Can you please verify?

Thank you so much. Aram

We are told that all shelves but the last one contained 8 books, so the number of shelves with 8 books is x - 1.
_________________

What if we plug in values? For example we have 6 shelves, thus 6*12=72 books - remove 21 books=51-11 books=40/8=5 shelves left+1 with 11 books=6 justify and 8 shelves, 8*12=96-21=75-11=64/8=8 shelves with 8 books + 1 shelf with 11 books=9 thus 8 doesn't equal 9. So we have only 6 is the correct choice.

Could someone please help explain to me why the following equation would not work for this problem? I got 8, which is the wrong answer, but am trying to figure out where my thought process crapped out on me. Thanks for your help.

12 books per shelf minus 21 books = 8 books per shelf + 11 on the last shelf 12x - 21 = 8x + 11 x = 8

Are the 21 books removed from equation all together?

Could someone please help explain to me why the following equation would not work for this problem? I got 8, which is the wrong answer, but am trying to figure out where my thought process crapped out on me. Thanks for your help.

12 books per shelf minus 21 books = 8 books per shelf + 11 on the last shelf 12x - 21 = 8x + 11 x = 8

Are the 21 books removed from equation all together?

Could someone please help explain to me why the following equation would not work for this problem? I got 8, which is the wrong answer, but am trying to figure out where my thought process crapped out on me. Thanks for your help.

12 books per shelf minus 21 books = 8 books per shelf + 11 on the last shelf 12x - 21 = 8x + 11 x = 8

Are the 21 books removed from equation all together?

The problem in highlighted part. You missed that All but one. So it should be 8(x -1). What you did is that you multiplied by 8x and add another self with 11.