I solved the question with a different perspective. "Connie gave away $150" > gives me the idea of sister doesnt receive any amount from Connie since it doesnt mention Connie giving $150 away to her sister. May or may not be correct. :)

Connie has twice as much money as Sister at first.
Split each unit into 3 parts, so that when Connie gives away 5 parts, Sister will have 3 times as much money as Connie.

We can then conclude that the five parts given away are $150. And each part is $30.
Connie initially has 6 parts, which is equals to $180