Ratio and Proportions - Minimum Integer Value

Let initial girls = $G$, initial boys = $G + 30$. New girls = $G + X$. New ratio $\frac{G + 30}{G + X} = \frac{3}{5} \implies 5G + 150 = 3G + 3X \implies 3X = 2G + 150 \implies X = \frac{2G}{3} + 50$. For minimum integer $X$, $G$ must be smallest positive integer divisible by 3, so $G = 3$. Then $X = \frac{2(3)}{3} + 50 = 52$.