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 a+b+c+d+e?
We have this system
a + c = 23
a + d = 20
b + e = 24
e + c = 21
b + d = 22 add these equations together
2 ( a + b + c + d + e) = 20 + 21 + 22 + 23 + 24
2 ( a + b + c + d + e) = 110
a + b + c + d + e = 110 / 2
a + b + c + d + e = 55