Suppose Olivia has $$x$$ correct answers. $$5x-2(10-x)=29$$, $$x=7$$. 
In a mathematics contest with ten problems, a student gains $$5$$ points for a correct answer and loses $$2$$ points for an incorrect answer. If Olivia answered every problem and her score was $$29$$, how many correct answers did she have? 

[A] $$5$$ 
[B] $$6$$ 
[C] $$7$$ 
[D] $$8$$ 
[E] $$9$$ 