Question 163080
Let x = 30 minute (or part of) work period after the first 30 minutes.
Then the job will cost $27 + $18x, depending on how long the job lasts.
You need to keep the job under (or less than) $100, so your equation would be:
27 + 18x < 100.  Now solve for x:
Subtract 27 from both sides to get:
18x < 73.
Divide both sides by 18 to solve for x to get:
x < 73/18, or x < 4.0555, but x has to be a whole number, so the first whole number less that this is 4.
So, how long did the technician work?
The first half hour at $27 dollars UP TO 4 more half hour segments.  The problem did not ask for what is the most amount of time could be worked, it only says that the job cost less than $100.  So the answer could be:
1 hour,
1 ½ hours,
2 hours,
2 ½ hours, or
3 hours !

Good luck !

JoeC