I prefer using a Karnaugh table:

Your task is to find the smallest possible value of x. You have the following equations:

x + a + b = 0.55 .... (1)

x + c = 0.6 .... (2)

c + d + e = 0.45 .... (3)

b + e = 0.16 .... (4)

a + d = 0.24 .... (5)

and you want the smallest value of x for which these equations will be consistent.

So I get x = 0.15 which is equivalent to 15% so yes you're correct.

(No doubt someone will give a simple two line confirmation of this).