Too long for comment :
If you want to solve the question by Hardy Weinberg, there are certain assumptions involved :-
1.There is random mating. People do not choose their mates on the basis of whether they carry PKU gene or not & mating among close relatives is not there.
2.No new PKU mutations happen.
3.There is no difference in the reproductive capacity of people with or without PKU gene.
If your study population fulfills these criterias, you can apply Hardy-Weinberg to calculate frequencies of various genotypes.
Because this question is homework ,such assumptions are not mentioned. And, at undergrad level,there is no other concept by which you can solve this question except HWE.
PS: Try to think what would happen if these assumptions are not fulfilled.
PSS: Even if you are solving a small homework question, do think about the logic behind every step. Though it may seem like a lot of work initially , it has enormous potential to teach you subtle concepts !