Let's say we have 10 moles of water vapour. So by Raoult's law, P(A)=38.76/58.76*1.5=0.989atm and P(water vapour)=0.011atm. So by Avogadro's principle we would have 89.9 moles of A. Would this be correct?Excellent. Now you're starting to understand.
So the total number of moles of liquid you have is 58.76. Now, to do the calculation we wish to carry out, you are going to need to specify the number of moles of vapor present in the cylinder at 1 atm total pressure. This is because, when we compress the system, the total number of moles of liquid plus vapor present in the system doesn't change. So please specify the number of moles of vapor present at 1 atm. Then, please determine (from Raoult's law) the number of moles of water and of species A present in the vapor at 1 atm. Then determine the total number of moles of water and the total number of moles of species A present in the cylinder (vapor plus liquid).