Solvent Fraction After Repeated Replacement

A homogeneous mixture of water and solvent has $20%$ solvent. $20%$ of the mixture is removed and replaced with water, thus forming a new homogeneous mixture. Then $20%$ of the resulting homogeneous mixture is removed and replaced with solvent, thus forming a final homogeneous mixture. What fraction of the final mixture is solvent? The answer is in the form $\frac{\alpha}{\beta}$ where $\alpha$ and $\beta$ are coprime positive integers. Input the value of $\alpha + \beta$.