Building light gaming pc for girlfriend

[textyyy]

Hello,
I recently upgraded my gaming rig, and was left with a few components from the upgrade. I have an fx 6300, 16gb of ddr3 1600, a coolermaster seidon, and a ASUS M5A99FX PRO R2.0 board. My girlfriend plays league of legends (yes I know) on her macbook (even worse) and is averaging around 20-25 fps on medium. I am curious if I would use my previous parts to get her something to run at 1080p 60+fps on high-very high. I would not mind purchasing used components and would like to be spending roughly 200-300 dollars Canadian. Any help would be appreciated, just not sure what direction to take.
Thank you

 

[Zerk2012]

http://www.tomshardware.com/reviews/league-of-legends-performance-benchmark,3484-8.html

That game is not very demanding. What you have will work just fine just buy a video card to go with it. The video card benchmarks are in the same link.

 

[TadashiTG]

You just need a cheapo GPU and the game will run super great. A new GTX1030 or RX550 would be overkill. You could hunt for a used 750 Ti and still be overkill. LoL is super eqsy to run and that is by deaign so it works on as many computers as possible.