Katie and jennifer are playing a game. katie and jennifer bote started with 100 points. at the end of each turn katie points doubled. at the end of each turn jennifer points increased by 200. at the start of which turn will katie first have more points than jennifer?

It would take three turns 
The easiest way would probably just writing down each of the scores for the turns:
(Also, the reason why 100 isn't included is because they only have 100 points before the end of the first turn)

Katie- 200, 400, 800
Jenn- 300, 500, 700

Doing an equation is most of the time the easiest way for problems like this, but in this situation it would be pretty much pointless. Since they have an equal amount of points before the end of the first turn, hence you'll get zero. 

*also you misspelled "both"