Aminah had an equal number of sunflowers and roses. She gave away $\frac{3}{5}$ of the sunflowers and some roses. In the end, she was left with $\frac{1}{4}$ of the total number of flowers. What fraction of the roses did she give away? Ans: ___

1. Establish a common base for the number of sunflowers and roses.

Let the initial number of sunflowers be $5$ units and the initial number of roses be $5$ units (since they are equal and we need to take $\frac{3}{5}$ of sunflowers).
Total initial flowers = $5 + 5 = 10$ units.

2. Determine the number of flowers left in the end.

In the end, she was left with $\frac{1}{4}$ of the total number of flowers.
Total flowers left = $\frac{1}{4} \times 10$ units = $2.5$ units.

3. Determine the number of sunflowers left.

She gave away $\frac{3}{5}$ of the sunflowers, so she had $1 - \frac{3}{5} = \frac{2}{5}$ of the sunflowers left.
Sunflowers left = $\frac{2}{5} \times 5$ units = $2$ units.

4. Calculate the number of roses left and the fraction given away.

Roses left = Total left - Sunflowers left = $2.5 - 2 = 0.5$ units.
Roses given away = Initial roses - Roses left = $5 - 0.5 = 4.5$ units.
Fraction of roses given away = $\frac{4.5}{5} = \frac{9}{10}$.