[tex] \frac{x}{y} = \frac{3}{2} = > x = \frac{3y}{2} \\ \\ \frac{x \: + \: y}{2} \: + \: 30 = 450 \\ \\ \frac{ \frac{3y}{2} \: + \: ^{2)} y }{2} + 30 = 450 \\ \\ \frac{ \frac{3y}{2} \: + \: \frac{2y}{2} }{2} \: + \: 30 = 450 \\ \\ \frac{ \frac{3y \: + \: 2y}{2} }{2} = 450 \: - \: 30 \\ \\ \frac{ \frac{5y}{2} }{2} = 420 \\ \\ \frac{5y}{2} \cdot \frac{1}{2} = 420 \\ \\ \frac{5y}{4} \: = \: ^{4)} 420 \\ \\ 5y = 1680 \\ \\ y = \frac{1680}{5} \\ \\ y = 336 \\ \\ x = \frac{3 \cdot 336}{2} \\ \\ x = 504[/tex]
