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?