Let a, b, c, d and e be positive integers. The sum of the four numbers on each of the five segments connecting "points" of the star is 28. What is the value of the sum of a+b+c+d+e?

Solving the system, you get a = 11, b = 13, c = 12, d = 9, e = 9. So the answer is 11 + 13 + 12 + 9 + 9 = 54.