Well, the first 35 hours she works is $10 per hour.

So that's 350 already.
Subtract 350 from 455.

Our goal is to get 105.
After 35 hours, each hour after that she gets paid $15.
How many times can 15 go into 105?

We're done!
Take the first 35 hours she worked and add the 7 we got from our last equation.

She worked 42 hours to get $455 in one week.