Calculate the vapor pressure of water above a solution prepared by adding 24.0g of lactose to 200.0g of water

Calculate the vapor pressure of water above a solution prepared by adding 24.0g of lactose to 200.0g of water at 338 K. (Vapor-pressure of water at 338 K 187.5 torr.)

I've done this problem ten times, and I still can't seem to get the correct answer. I used Raoult's, so I'm not sure what to do. Thanks for any help!

nH2O = 200.0 g/18 g/mol = 100/9 mol
nlactose = nC12H22O11 = 24.0 g/342 g/mol= 4/57 mol
X(H2O) = 100/9 : (100/9 + 4/57) = 475/478
P(vap H2O) = X(H2O) x Po(H2O) = 475/478 x 187.5 torr = 186.3232 torr