Will this computer run League decently?

I need to buy a new laptop tomorrow because mine has become old and brittle and will most likely snap the screen off if I open it a couple more times. Being a college student who pays out of pocket my price range is limited and would like some input on how this laptop would handle. Keep in mind I do not care about fancy graphics levels, just in general how it will run.

-Current Toaster -4gbs of ram -1.8ghz dual core processor -Intel HD family Graphics -AVG ~50fps on low settings, ~35 when a lot of stuff is going on

-Possible New Toaster -Asus X540LA -intel 5th gen i3 2.2ghz -4gbs of ram

• I believe Intel HD graphics 4400

It's priced around $300 and I know its not some fancy gamey pants laptop. The only game I really play is League and other than that I use it for online classes at college. Can someone with similar specs give me an opinion on how well this will run.