Inner city schools get a lot of government support. As a result, the spending per student for inner city schools is comparable to other schools. For example, in my state, the inner city schools $/student is actually more than my school district.
The big difference is the environment, particularly the environment at home. For example, Vietnamese boat people lived in inner cities, and they were essentially illiterate. And yet their kids (who went to the same inner city schools) excelled in academics because of their family environment!