For this problem, you kind of have to work backwards. The first step is figuring out what percentage of 900 is 225--this way we can find out what percentage we need to take from the sample of 48. In order to find the percentage:
225 / 900 = 0.25 or 25% < this is the percentage of students the administrator predicts will be in favor of the dress code. Now we can assume that this means 25% of the original 48 asked were in favor.
So now, we need to find 25% of 48:
48 x 0.25 = 12 < this is the number of students out of the original 48 who were in favor of the new dress code.
Answer: 12 students