Katie babysits for her neighbor and charges a certain amount per hour. she also charges 1.5 times as much for any hours after 8pm. if she is hired from 4pm until 1am and makes a total of $92, how much does she charge per hour?

4 p.m to 8 p.m is 4 hrsso she worked 4 regular hrs
8 p.m. to 1 a.m is 5 hrs...she she worked 5 hrs for 1.5 times as much

4x + 5(1.5x) = 92
4x + 7.5x = 92
11.5x = 92
x = 92 / 11.5
x = 8 < so she charged $ 8 per hr from 4 pm. to 8 pm.  and (8 * 1.5) = $ 12 per hr for hrs after 8 p.m