https://www.liveauctioneers.com/item/2 ... -and-back-again-irvine-ca

This book is a 4th printing and according to tolkienbooks.us, the 4th Printing was in July, 1975 (https://www.tolkienbooks.us/hob/us/hc/the-hobbit-1973)

Tolkien can't have signed this book.