Answer
(a) $W_E = 539~N$
(b) $W_M = 89.1~N$
Work Step by Step
(a) Let $W_E$ be the person's weight on the earth:
$W_E = m~g_E$
$W_E = (55.0~kg)(9.80~m/s^2)$
$W_E = 539~N$
(b) Let $W_M$ be the person's weight on the moon;
$W_M = m~g_M$
$W_M = (55.0~kg)(1.62~m/s^2)$
$W_M = 89.1~N$