bookshelf

[ASMAA997]

A bookshelf holds both paperback and hardcover books. The ratio of paperback books to hardcover books is 22 to 3. How many paperback books are on the shelf?

(1) The number of books on the shelf is between 202 and 247, inclusive.

(2) If 18 paperback books were removed from the shelf and replaced with 18 hardcover books, the resulting ratio of paperback books to hardcover books on the shelf would be 4 to 1

My questions are :
at # 2:
when I solve :
( x-18)/(y+18)= 4/1

then , x-18=4 then x= 22
y+18=1 then y= 17 .

1- Is this way of solving right ?

because in the book they used another approach and the results are different .

[RonPurewal]

i don't really understand what you're doing.

are you implying that if A/B = 4/1, then A has to be 4, and B has to be 1?
i don't think you would make a mistake like that, since that's very clearly not true (they could be 8 and 2, or 12 and 3, or 400 and 100, or ... any two numbers in a 4:1 ratio)—but, that's what seems to be happening in your work.

in any case, we can't discuss this problem any further until it's posted in accordance with the forum rules.

please post:
• the entire text of the problem, exactly as originally provided
• the title, edition, and page number of the book from which it's taken

also, you mentioned an answer key that "does something different", so, please post the relevant portion of the answer key as well. thanks.