In my own personal utopia, health and nature would be top priorities. which detail best supports this central idea?
a. thomas more’s utopia was written as a social critique.
b. “utopia” is a greek word that means “no place.”
c. an emphasis on nutrition would be important in this society.
d. everyone has a different idea about a perfect society.

c. An emphasis on nutrition would be important in this society.

A "utopia" is a perfect society. In this case, More explains that in his perfect society, health and nature would be priorities. This means that in his society, people would be concerned about their well-being and the benefits that nature can bring them. It is likely that they would also try to protect nature. Nutrition would probably be a priority in this society, as good nutrition is vital for humans, and is also one of the main ways in which humans and nature interact.

the sentence that avoid faulty coordination is:

culture, which is well represented in philadelphia, plays a major role including theatre, music, and the visual arts.  

faulty coordination occurs when the writer gives equal importance two different ideas (clauses) which in fact are not equivalent. in order to correct a misplaced clause or idea, the writer can place less important or emphatic ideas in a relative clause as in the previous sentence.