How to do this ratios problem without algebra?

Question

Dinesh had some fiction and nonfiction books. The number of fiction was $4/9$ of the total number of books. After he had donated $80$ fiction books and $25$ nonfiction books, there were $20\\%$ as many fiction books as nonfiction books. Find the total number of books Dinesh had at first. This question is for sixth grade. I got the answer by using algebra. $$\\frac49x-80=\\frac15\\left(\\frac59x-25\\right)\\\\ x=225$$ How do i solve/explain this without using algebra?

Answer 1

a=total number of fiction books sold

b=total number of nonfiction books sold

80=4/9 x a 25=5/9 x b

80x(9/4)=a 25x(9/5) xb

180=a 45=b

Total number of books sold = a+b or 225