Simple -one

$x + y = 80$ $\frac{1}{x} + \frac{1}{y}= \frac{4}{75}$ $\frac{x + y}{xy} = \frac{4}{75}$ $\frac{80}{xy} = \frac{4}{75}$ $4xy = 6000$ $xy = 1500$ $y = 80 - x$ $x(80 - x)= 1500$ $-x^{2} + 80x = 1500$ $x^{2} - 80x + 1500 = 0$

Getting the value for x gives you 30 and 50. Therefore, the answer is 30.