I did have a problem with this issue, so I began offering scholarships for my classes, both partial and full, depending on financial need. I’m sad to say that in the twenty years that I’ve offered these scholarships, only a handful of students have applied for them.
About ten years ago I was hired by Sac State University to teach SAT prep classes at three high schools in the Sacramento area. These classes would be free to students and I would get paid by Sac State. Unfortunately, very few students took advantage of this opportunity. Of those that did come, some did not stay for the whole class and some did not attend all the sessions. In my other classes, students almost never leave early and when they have to miss a class due to illness or a schedule conflict, they try very hard to make up the class at one of my other locations. I encountered the same problem when I offered my class at a very reduced rate to children of friends of mine. They did not attend all the sessions. It seemed that they did not value the classes the same as those students who paid the full amount.
So although I’m sure that in some areas students who would like to take a prep class are not able to take one, it has been my experience that everyone is able to take my class but not many students from low income families have taken advantage of the opportunity.