Answer
$23.66\ mmHg$
Work Step by Step
Number of moles of ethanol: $50.0\ mL\times 0.789\ g/mol\div 46.07\ g/mol=0.856\ mol$
Number of moles of water: $50.0\ mL\times 0.998\ g/mL\div 18.015\ g/mol=2.77\ mol$
Mole fraction of ethanol: $0.856/(0.856+2.77)=0.236$, of water: $1-0.236=0.764$
Total vapor pressure: $P=P_A^0x_A+P_B^0x_B=17.5\times 0.764+43.6\times 0.236=23.66\ mmHg$