solve equations

Alyse earns $15.40 per hour, and she earns time and a half for working past 8:00pm. Last week she worked 35 hours and earned $600.60. How many hours did she work past 8:00pm?

My goodness me. If there is any word problem that did not make sense to me before, this one is the most confusing. I... don't know how to start, let alone what to do with my information. And what do I know about Alyse's hours?! *cries*

let t = overtime hours

then 35-t = regular hours

(23.10)t + (15.40)(35-t) = 600.60

solve for t

A is the number of hours worked before 8
B is the number of hours worked past 8
A+B=35
A=35-b

time and a half = 15.4(1.5)=23.1

15.4(A)+23.1(B)=600.60

substitute 35-b for A.....solve