Curious: how hard is it for people to get access to free university education there?

My home country - Brazil - offers free university education, and actually our federal universities are the best in the country. While there are quotas for certain socially disadvantaged groups of people (e.g. racial quotas), the sad reality is that regular seats are taken mostly by rich kids whose parents can afford to pay them prep courses - because the admissions process is incredibly difficult. So our free higher education system ends up doing a poor job in helping upward social mobility, and people who are not well-off end up going to private colleges whose schedules allow them to work and pay for their tuition.