A man weighing 750 n and a woman weighing 500 n have the same momentum. what is the ratio of the man's kinetic energy km to that of the woman kw?

Because weight W = M g, the ratio of weights equals the ratio of masses.

(M_m g) / (M_w g) = [ (p^2 Man) / (2 K_man) ] / [ (p^2 Woman) / (2 K_woman)

but p's are equal, so

K_m/K_m = (M_w g) / (M_m g) = W_woman / W_man = 450/680 = 0.662