What did philosophers of the enlightenment have faith in, believing it could answer questions and solve problems?

The answer is reason.  Philosophers of the Enlightenment believed that answer can be found through reasoning.  There were two types of reasoning during that time.  You have rationalism that relies on deduction and Empiricism which deals with experience. It took root due to the liberal atmosphere at the time.

i told you before its c

a.that is my answer.

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