L.H.
I agree about not finding someone for that price. I am a certified teacher and I used to tutor before I had two kiddos running around the house. I felt so bad for young families, so I only charged $45 and only did families from church. Many of my friends charged much more than that.
I don't know what they charge, but you might call http://www.risingscholars.com/ they are tutors that come to the home.
That is the price range for getting a good Jr. or Sr. in high school (maybe a college kid too). They can be really responsible but you might have to provide a bit more direction to the teen.
Best wishes.