let

l = the money that Lisa has

r = the money that Rachel has

Lisa spends 1/2 of her money that is: l/2

Rachel spends 1/4 of her money that is: r/4

Is it possible for Rachel to have spent more money than Lisa?

Or in other words is the following inequality possible:

r/4 > l/2 multiply both sides by 4

r > 2l

this is possible only if Rachel has more then twice the money that Lisa has.