Writing solution manual to a text book independently?

I want to write a solution manual to a book independently from the publisher, I had the class so I already did :). It is a tutorial book where you are supposed to enter your calculations as part of HW. The unfilled book is available from the publisher.

I anticipate low interest probably 50 per year, so I would like to use the publisher

HW unfilled book and write by hand the answers would using their book be considered copy right infringement. I see it go through the amazon ebook system as scanned pdf.

These were my original solutions, but I wonder legally if it need to go as a separate book, not using any of their graphs and text.

To me it looks like writing a comment on a book as a different book.