Weighing scale error and the minimum number of same weights

Question

Problem: Philip’s weighing scale has an error of ±10 grams. What is the smallest number of identical copies of a book that Philip should weigh together so that the error of one book will be ±0.5 grams?

Attempted method: It's a contest math problem and there is no solution available on the internet. I started off with assuming that it's a manual weighing scale. I add a weight on one side and a book on the other side, the error is 10gm per book. If I add one more book to each side of the scale, the error is 20gm per 3 books. I tried this method but can't get to the right answer.

Answer 1

Suppose the true weight is $W$, and you weigh $n$ copies of the same book. The weight you will see will be in the range $$ nW\pm 10 $$ Dividing by $n$, the weight of a single book is now known to be $$ W\pm \frac{10}n $$ How should you choose $n$ so this is $W\pm 0.5$?