The Burkes pay their babysitter​ $5 per hour before 11 P.M. and​ $7.50 after 11 P.M. One evening they went out for 6 hr and paid the sitter ​$40.00. What time did they come​ home?

Answer 1

Let "x" represent the number of hours they were out BEFORE 11 pm and "y" represent the number of hours they were out after 11 pm.

Then 5x + 7.5y = 40

And x + y = 6

If x + y = 6, then x = 6 - y

Plugging "6 - y" into the first equation in place of "x", we get:

5(6 - y) + 7.5y = 40

30 - 5y + 7.5y = 40

2,5y = 10

y = 4

If the number of hours after 11 pm is 4, then the number of hours before 11 pm was 2. So they left at 9:00 pm and got home at 3:00 am