Ashraf had some money at first. He spent $15\%$ of it on food and $\char36{}810$ on a new laptop. He then gave $20\%$ of the remainder to his brother. In the end, he had $\char36{}304$ left.

1. Determine the percentage of the remainder that is left after giving 20% to the brother

Ashraf gave $20\%$ of the remainder to his brother, which means the amount he has left represents $100\% - 20\% = 80\%$ of the remainder.

Let the remainder be $R$.
$80\% \text{ of } R = \$304$

2. Calculate the amount of money given to the brother

Since $80\%$ of the remainder is $\char36{}304$, we can find the $20\%$ given to his brother by dividing by 4:
$\text{Amount given to brother} = 20\% \text{ of } R = \frac{\$304}{4} = \$76$