Word problem

[beater]

Aunt Marge is giving candy to each of her nephews and nieces. She has 20 candy pieces and she gives candy to children according to her wish. Thus, Robert gets 2 more candy pieces than Kate. Bill gets 6 less than Mary. Mary, in turn, gets 2 more candy pieces than Robert. Kate gets 2 more candy pieces than Bill. How many candy pieces does Kate get?

a) 2
b) 4
c) 6
d) 8
e) 10

[DanaJ]

You have the following equations:
R = K + 2
B = M - 6
M = R + 2
K = 2 + B so B = K -2.

Then you have M = B + 6 = K -2 +6 = K + 4.
R + B + M + K = 20, which means that K +2 + K - 2 + K +4 + K = 4K + 4 = 20, so K = 4.

Answer B.