2011 AMC 10A Problem 17

From the condition about the sequence, we get that $$A + B + C = 30$$$$B = 25 - A.$$ Similarly, we get $$B + C + D = 30$$$$D = A.$$ Propagating these values through the sequence and repeating the condition for every consecutive triple, we get that $$E = 25 - A, F = 5, G = A,$$ and finally, $H = 25 - A.$ The desired sum is then $$A + 25 - A = 25.$$ Thus, C is the correct answer.