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------------------------------------------------ The Burkes pay their babysitter $5 per hour before 11 P.M. and $7.50 per hour after 11 P.M. One evening they went out for 4 hours and paid the sitter $27.50. What time did they come home?

The Burkes came home at 2 A.M. after being out for 1 hour before 11 P.M. and 3 hours after 11 P.M. They paid the babysitter $27.50 for the 4-hour duration.

Explanation:

To determine the time that the Burkes came home, we need to use the information given in the question:

The babysitter is paid $5 per hour before 11 P.M. and $7.50 after 11 P.M.
The Burkes went out for 4 hours and paid the sitter $27.50.

Before 11 P.M., the sitter earns $5 per hour. So if the Burkes were out for x hours before 11 P.M., the sitter earned $5 * x.

After 11 P.M., the sitter earns $7.50 per hour. So if the Burkes were out for y hours after 11 P.M., the sitter earned $7.50 * y.

We know that the Burkes were out for a total of 4 hours and paid the sitter $27.50. So,

$5 * x + $7.50 * y = $27.50

Since the Burkes were out for a total of 4 hours, we have x + y = 4.

We can solve these two equations simultaneously to find the values of x and y:

First, solve x + y = 4 to get x = 4 - y.

Substitute x = 4 - y into the first equation:

$5 * (4 - y) + $7.50 * y = $27.50

$20 - $5y + $7.50y = $27.50

$2.50y = $7.50

y = 3

Substitute y = 3 into x = 4 - y:

x = 4 - 3

x = 1

So, the Burkes were out for 1 hour before 11 P.M. and 3 hours after 11 P.M., which means they came home at 2 A.M.