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 .