Part A:
To model the minimum and maximum amounts that Kelsey could pay Wyatt, we can use an absolute value equation. Let's denote the number of hours Wyatt works beyond or before the scheduled time as 'x'. Since Kelsey might send him home up to 2 hours early or keep him up to 2 hours later, the absolute value equation can be written as:
|9 + x - 4| = 2
Here, 'x' represents the number of hours Wyatt works beyond or before the scheduled time, and the expression inside the absolute value represents the actual time Wyatt finishes work (9 AM + x hours) minus the desired end time (4 PM).
Part B:
To find the minimum and maximum amounts that Kelsey could pay Wyatt, we need to solve the absolute value equation.
|9 + x - 4| = 2
Let's consider two cases: when 9 + x - 4 is positive and when it is negative.
Case 1: 9 + x - 4 = 2
Solving this equation, we get:
x = 2 - 5
x = -3
In this case, Wyatt would finish 3 hours earlier than the desired end time.
Case 2: -(9 + x - 4) = 2
Solving this equation, we get:
-9 - x + 4 = 2
-x - 5 = 2
-x = 2 + 5
-x = 7
In this case, Wyatt would work 7 hours later than the desired end time.
Therefore, the minimum and maximum amounts that Kelsey could pay Wyatt are determined by the number of hours he works beyond or before the scheduled time.
Minimum amount: $12 per hour * 3 hours (he finishes 3 hours earlier) = $36
Maximum amount: $12 per hour * 7 hours (he works 7 hours later) = $84
So, the minimum amount Kelsey could pay Wyatt is $36, and the maximum amount is $84.
I hope this helps! :)