Need Help with Equation Word Problem

Hello all. Well, I received such wonderful help the first time I used this forum so I am returning with yet another equation word problem that has me stumped. When I check my work, the answer I keep coming up with is not making any sense and does not fit. Here is the problem followed by the answer I keep getting, hopefully someone will see what I am doing wrong and steer me in the right direction(Happy)

*Use an equation to solve*: Patricia’s bill for one year of college is $24,500. The tuition

charge costs $4,000 more than the room and board costs. This bill also includes $500

for fees and other charges. How much is the yearly tuition charge?

24,500 - 4,000

=20,500/2

=10,250 + 500

=10,750 (my answer)

As you can see, this makes no sense because if you take my answer, add the room and board, the other charges and the 4,000 which gives you 1,000 too much

10,750 + 10,250 + 500 + 4000 = 25,500

RE: Need Help with Equation Word Problem

Thank you so much. If I am correctly solving for "r" the answer would be 10,000 is that correct? Thank you again for your help, I really appreciate it.